Prioritizing Digital Economy Drivers of Inflation Using an Intelligent-Based Fuzzy Decision Framework: Implications for Financial Risk Management

Abstract

This study aims to identify and prioritize digital economy factors affecting inflation and to determine effective policy strategies for managing digitally driven inflationary pressures in the context of financial systems and risk dynamics. The analysis considers twelve key digital economy indicators, including e-commerce penetration, digital payment systems, internet infrastructure, price transparency, digital advertising, Industry 4.0 technologies, data-driven inventory and demand systems, fintech adoption, cryptocurrency usage, and digital financial access. In parallel, eight policy strategies are evaluated, covering digital price transparency, expansion of digital payments, digital logistics optimization, digital public services, smart manufacturing, intelligent-based demand forecasting, fintech integration, and digital workforce development. The study employs a novel intelligent-supported decision-making framework integrating an attention-based expert weighting approach, generalized fractal fuzzy sets, the MEREC method, and the ARLON technique. The empirical design is based on expert evaluations obtained from ten specialists with at least 12 years of experience in digital economy, finance, and policymaking. Rather than relying on country-specific or time-series inflation datasets, the study examines the structural relationship between digitalization and inflation through a multi-criteria expert-based approach, with data collected in 2025. The findings indicate that e-commerce penetration and the prevalence of digital payment systems are the most influential factors affecting inflation. In addition, digital price transparency and the expansion of digital payment systems emerge as the most effective strategies for mitigating inflationary pressures. These results provide important insights into how digital transformation reshapes inflation dynamics, monetary transmission mechanisms, and inflation-related financial risks. The proposed model offers a robust and systematic framework for analyzing inflation in digitalized economies and supports policymakers and financial decision-makers in managing emerging risks in intelligent-driven economic environments.

1. Introduction

Inflation is a fundamental macroeconomic phenomenon that refers to the decrease in the purchasing power of money because of a sustained and widespread increase in the general price level over time. This process negatively impacts the well-being of those with fixed and low incomes by allowing individuals to purchase fewer goods and services with the same income. Inflation can deepen economic inequalities by distorting income distribution and weaken long-term investment decisions by eroding the real value of savings. It also hinders the healthy functioning of price signals, making rational decision-making difficult for producers and consumers. A high and unpredictable inflationary environment increases economic uncertainty, causes instability in financial markets, and threatens the sustainability of economic growth (Nikiforidis et al., 2025). Therefore, controlling inflation is a necessary policy objective for maintaining economic stability and social welfare. The effective and reliable implementation of monetary policy in combating inflation should be supported by an independent central banking approach that prioritizes price stability. Furthermore, ensuring fiscal discipline, efficient use of public spending, and keeping budget deficits under control also play a critical role in reducing inflationary pressures. Structural reforms aimed at increasing production capacity can alleviate supply-side bottlenecks and limit cost-driven inflation (Kadolkar et al., 2025). Market regulations that strengthen competition discipline pricing behavior, while digitalization and productivity increases stand out as factors supporting price stability in the long term. This holistic approach shows that inflation should be addressed not only through short-term interventions but also through permanent and balanced policies.

Digital economy factors can have direct and indirect effects on inflation by transforming market structure and price formation processes. E-commerce penetration increases competition by facilitating price comparisons between different sellers and can limit the pricing behavior of firms (Liu et al., 2025). The widespread use of digital payment systems can create demand-side pressures in the short term by increasing the speed and volume of transactions, but it also strengthens the effectiveness of monetary policy by reducing the informal economy. Increased internet access and speed facilitate access to information and play a role in limiting excessive price increases by increasing price transparency. The intensity of digital advertising can trigger price increases in certain periods due to its power to drive consumer demand, but it can also have cost-reducing effects in the long term by increasing marketing efficiency (Oyadeyi, 2025). The widespread adoption of Industry 4.0 technologies reduces costs and alleviates supply-side inflationary pressures by enabling automation and increased efficiency in production processes. The widespread adoption of fintech can stimulate economic activity by expanding access to financial services, which can affect prices through increased demand. The increase in cryptocurrency adoption has the potential to weaken traditional monetary policy channels by altering money circulation and payment habits (Guo et al., 2025). In this context, holistic strategies are needed to address inflationary problems stemming from the digital economy. A digital price transparency strategy strengthens the competitive market structure by limiting arbitrary pricing behavior by firms (Octaviani et al., 2025). The widespread adoption of digital payment systems reduces informal transactions, increasing economic traceability and contributing to price stability. Digital logistics and supply chain optimization reduces transportation and inventory costs, limiting cost inflation. Developing digital public services enables more efficient use of public resources, reducing indirect inflationary pressures. Supporting Industry 4.0 and smart manufacturing technologies increases production capacity, contributing to long-term price stability.

Identifying which digital economy factors have a stronger impact on inflation has become a fundamental requirement for accurately understanding inflation dynamics today. Since the digitalization process simultaneously transforms price formation mechanisms, consumer behavior, and money circulation, not all digital factors have the same impact on inflation. Therefore, the inability to determine which digital elements trigger or limit inflation more significantly weakens the effectiveness of policies implemented to combat inflation (Kumar & Kumar Chauhan, 2026). Accurately identifying the most effective factors in combating inflation allows for more rational use of limited resources and the rapid development of targeted strategies. Otherwise, simultaneous and scattered interventions across all digital areas increase policy costs and make it difficult to achieve the desired results. This kind of uncertainty prolongs the fight against inflation, leads to policy delays, and negatively affects the expectations of economic actors (Kyriazis, 2026). Furthermore, a lack of prioritization can lead to misjudgments of inflationary pressures originating from the digital economy and policy errors. However, a review of the existing literature reveals that studies systematically identifying which digital economy factors are more decisive in determining inflation are quite limited (Ali, 2026). This constitutes a significant gap in the inflation literature. This gap leads to both theoretical uncertainties and a lack of direction in policy implementation. In an economy where digitalization is rapidly deepening, the persistence of such uncertainty leads to a decrease in the effectiveness of the fight against inflation. Therefore, the need for a new prioritization analysis that prioritizes digital economy factors, reveals their relative effects, and guides decision-makers is clear.

This study aims to identify which digital economy factors have a stronger and more decisive impact on inflation. The main motivation for the study is the increasing complexity of inflation dynamics in rapidly digitalizing economic structures, and the limited number of studies in the existing literature that systematically analyze the relative importance of these factors. In this context, the goal is to provide an analytical and decision-supporting framework that reveals which digital elements should be prioritized in the fight against inflation. The study proposes a new model integrating intelligent-based approaches with fuzzy multi-criteria decision-making models. The research process begins with a comprehensive literature review, resulting in the identification of 12 criteria representing the relationship between the digital economy and inflation, and 8 strategies addressing these issues. To strengthen the model’s decision-making infrastructure, opinions are sought from 10 different experts in the field, and the relative influence of the experts in the evaluation processes is calculated using the attention-based expert weighting approach.

This study adopts an expert-based evaluation framework rather than relying on country-specific or time-series datasets. Therefore, the analysis does not focus on a single economy but instead examines the structural relationship between digital economy factors and inflation in a generalized context applicable to digitally transforming economies. The empirical basis of the study consists of evaluations provided by ten experts with at least 12 years of professional experience in areas such as digital economy, financial systems, monetary policy, and economic analysis. The experts were selected using purposive sampling to ensure domain expertise and diversity of perspectives. This approach is consistent with decision-making studies where expert knowledge is used to evaluate complex and multidimensional phenomena that cannot be directly captured through conventional datasets. The data collection process was conducted in 2025.

Subsequently, the MEREC method is applied to objectively weight the criteria, and the prioritization of strategies is carried out using the ARLON approach. In addition, generalized fractal fuzzy sets developed by the authors are integrated into the decision-making process to more realistically model uncertainty and complexity. Thanks to this holistic structure, the proposed model offers a strong contribution in terms of both methodological innovation and application. The study primarily seeks to answer two main research questions: (1) Which criteria among the digital economy factors have the strongest impact on inflation, and how are the relative importance levels of these criteria ranked? (2) Which strategies developed to reduce or manage the effects of the identified digital economy factors on inflation are more prioritized and effective? In this respect, the study aims to offer important theoretical and policy-oriented implications for inflation analysis in digitalized economic structures.

Although this study adopts an expert-based multi-criteria decision-making framework, its contribution is directly aligned with core themes in financial economics and risk management. Digital economy factors significantly influence inflation dynamics, which in turn play a central role in shaping monetary policy effectiveness, financial market stability, and risk management strategies. Inflation is a key determinant of interest rates, asset valuation, portfolio allocation, and financial risk exposure. In this context, the increasing digitalization of economic and financial systems introduces new channels affecting monetary transmission mechanisms, liquidity conditions, and systemic risk. By identifying and prioritizing digital economy factors that drive inflation, this study contributes to a better understanding of emerging inflation risks in digitalized financial environments. Therefore, the proposed framework provides valuable insights for policymakers, central banks, and financial market participants concerned with inflation forecasting, financial stability, and risk management in the digital era.

This study fills a significant gap in the inflation literature by revealing the relative effects of digital economy factors on inflation through a systematic priority analysis. Furthermore, thanks to its unique model integrating intelligent-powered and fuzzy multi-criteria decision-making approaches, it offers a methodologically innovative and applicable framework for analyzing inflation in digitalized economies. The decision-making model proposed in this study offers significant advantages in several aspects compared to existing multi-criteria decision-making approaches widely used in the literature. (1) One of the most fundamental innovations of the model is the calculation of the importance weights of experts using the attention-based expert weighting approach technique. The failure to consider expert weights is one of the main criticisms frequently voiced in the literature regarding multi-criteria decision-making models. However, there is no common approach in the literature regarding how to determine the relative importance levels of experts. In some studies, expert weights are determined based on demographic characteristics such as age, education level, and professional experience, but such approaches are criticized for not adequately reflecting the true contribution of expert opinions. The attention-based approach used in the proposed model excludes the demographic characteristics of the experts and directly focuses on the structural consistency of their evaluations, the level of consensus between opinions, and outlier behavior, thus offering a more objective and data-driven expert weighting process. The artificial intelligence component of the proposed framework is derived from the attention mechanism, which represents one of the fundamental concepts widely used in contemporary machine learning and deep learning architectures. Rather than employing predictive machine learning models or neural network training procedures, the study adapts the core logic of attention-based weighting to evaluate the relative importance of expert judgments. Accordingly, the intelligent-related contribution of the framework should be understood as the incorporation of an attention-inspired intelligent weighting mechanism into the decision-making process rather than the application of a full-scale artificial intelligence prediction model. This adaptation enables a data-driven and dynamic assessment of expert contributions while preserving the interpretability and transparency required in multi-criteria decision-making environments. (2) The proposed framework does not introduce generalized fractal fuzzy sets as a new theoretical development. Generalized fractal fuzzy sets were originally introduced by Kou et al. (2025) as an advanced uncertainty modeling structure capable of representing different fuzzy environments through a flexible parameterization mechanism. The novelty of the present study lies in integrating the existing GFFS framework with the attention based expert weighting approach, MEREC, and ARLON techniques within a unified decision-making architecture for analyzing digital economy driven inflation dynamics. Therefore, the contribution of this study is methodological integration and application to a new problem domain rather than the development of a new fuzzy set theory. (3) Another important advantage of the model is that the criterion weights are determined using the MEREC technique. While numerous criterion weighting methods such as AHP, Entropy, CRITIC, and SWARA exist in the literature, some of these techniques rely on subjective evaluations, and others fail to adequately reflect the interaction between criteria. In a complex and multidimensional problem area such as the digital economy and inflation, the ability to objectively measure the relative effects of criteria on the system makes the MEREC method more suitable. MEREC determines weights by analyzing the effects of criteria in the decision matrix using a decay-based approach, and in this respect, it more accurately reflects the true contribution levels of the criteria. When these three fundamental advantages are considered together, it is seen that the proposed model is both methodologically innovative and offers a more reliable and applicable decision support tool in the analysis of complex economic problems.

Despite the apparent methodological complexity of the proposed framework, each component is incorporated to address a specific limitation observed in the existing literature. Traditional multi-criteria decision-making approaches often rely on either subjective expert weighting, simplified uncertainty modeling, or static prioritization structures, which may lead to biased or incomplete results when analyzing complex economic phenomena such as digital inflation. The attention-based expert weighting mechanism is introduced to overcome the limitations of demographic-based or equal-weight assumptions by capturing consensus structure and behavioral consistency among experts. In addition, generalized fractal fuzzy sets are employed to model nonlinear and irregular uncertainty patterns that cannot be adequately represented by classical or even advanced fuzzy extensions. Finally, the integration of MEREC and ARLON enables both objective criterion weighting and robust alternative prioritization under varying normalization structures. Therefore, the integrated framework is not a matter of methodological expansion, but a necessity to ensure analytical accuracy, robustness, and realism in capturing the multidimensional nature of digital economy–inflation interactions. It should be noted that this study does not focus on a specific country or a single economic system. Instead, it adopts a generalized and conceptual perspective to analyze the relationship between digital economy factors and inflation. The proposed framework is designed to capture structural interactions that are applicable across different economic contexts, particularly in economies undergoing digital transformation. Therefore, rather than being limited to country-specific macroeconomic conditions, the study aims to provide a broadly applicable decision-support model that can be adapted to various national settings.

This study is structured as follows. Section 2 presents a comprehensive review of the relevant literature, focusing on the relationship between digital economy factors and inflation, as well as existing methodological approaches used to analyze this relationship. Section 3 introduces the proposed methodology in detail and explains the integrated artificial intelligence and fuzzy multi-criteria decision-making framework developed in this study. Section 4 reports the empirical analysis results, including the prioritization of digital economy factors and the ranking of inflation mitigation strategies. Section 5 discusses the findings by interpreting their economic and policy implications and comparing them with insights from the existing literature. Finally, Section 6 concludes the study by summarizing the main contributions, highlighting policy recommendations, and outlining potential directions for future research.

2. Literature Review

2.1. Theoretical Background of Digitalization and Inflation

The relationship between digitalization and inflation can be theoretically grounded in several established economic frameworks. From a microeconomic perspective, digitalization intensifies price competition and reduces information asymmetry, consistent with search theory and market efficiency arguments, thereby exerting downward pressure on prices. At the same time, the increased use of digital platforms and algorithms in pricing aligns with theories of imperfect competition, where firms may adjust prices dynamically based on real-time data, potentially amplifying price volatility. From a macroeconomic standpoint, digital payment systems and fintech innovations influence money velocity and the transmission mechanism of monetary policy, which are central components of quantity theory and New Keynesian models. Furthermore, digitalization affects production efficiency and cost structures through technological progress, consistent with endogenous growth theory, contributing to long-term disinflationary effects. However, demand-side expansions driven by financial inclusion and digital consumption channels may generate short-term inflationary pressures. Therefore, the interaction between digitalization and inflation reflects a complex balance between cost-reducing technological effects and demand-enhancing financial and consumption dynamics, which justifies the need for a multidimensional analytical framework.

2.2. Digitalization and Technological Infrastructure

Digitalization and technological infrastructure are key criteria in examining the relative effects of digital economy factors on inflation. The concept of digitalization in the economy is defined as the continuation of economic activities using digital technologies (Xia et al., 2024). In this context, digitalization plays a major role in the advancement of digital globalization. There is a strong relationship between inflation and financial technologies, as digital financial tools contribute to accelerating economic development (Oyadeyi, 2025). Furthermore, digital stores operate with more transparent pricing policies compared to traditional stores, contributing to lower prices by intensifying competition (Aparicio et al., 2024). Pundir et al. (2024) highlighted that digital infrastructure, and data analytics significantly influence e-commerce penetration, while Emara and Zecheru (2024) emphasized that increased use of digital technologies has a deflationary effect and contributes to slowing inflation dynamics.

2.3. Digital Competition, Transparency, and Market Dynamics

Digital competition, transparency, and market dynamics constitute another important dimension in understanding the inflationary effects of the digital economy. As digitalization advances, artificial intelligence algorithms are increasingly used in pricing decisions, reshaping competition and market structures (Sanchez-Cartas & Katsamakas, 2024). The digital economy enables prices to become more flexible and rapidly adjustable (Aparicio et al., 2024). Online platforms and price comparison tools enhance transparency, reducing price dispersion and strengthening competition (Zamani et al., 2024). Martin (2024) noted that digital platforms influence both consumer behavior and price competition, while Bernhardt et al. (2025) showed that transparency effects vary across markets. Similarly, Lee et al. (2024) argued that digital advertising expenditures have heterogeneous effects depending on political and cultural integration levels.

2.4. Digital Production and Logistics

Digital production and logistics represent another key channel through which digitalization affects inflation. Explainable artificial intelligence (XAI) technologies enhance trust and transparency in production systems, facilitating the adoption of intelligent-based solutions (Nikiforidis et al., 2025). These technologies support smart manufacturing systems that reduce costs and improve efficiency (Jaskó & Ruppert, 2025). Artificial intelligence contributes to economic development by increasing productivity and reducing average costs (Kalai et al., 2024). Tan et al. (2024) emphasized that machine learning improves inventory efficiency, while Sukolkit et al. (2024) highlighted cost optimization through data-driven inventory management. Octaviani et al. (2025) also underlined the importance of integrating AI into supply chain processes for more effective decision-making and operational efficiency.

2.5. Digital Labor and Demand Dynamics

Digital labor markets and demand dynamics are also critical in analyzing the inflationary impact of digitalization. The flexible nature of digital labor platforms allows them to adapt to demand fluctuations (Jiang et al., 2024). Regulatory frameworks play a key role in shaping these markets, where excessive regulation may limit job creation, while insufficient regulation may lead to instability (Jeyaraj et al., 2025). The increasing use of digital labor platforms and automation technologies contributes to balancing labor market dynamics (Kadolkar et al., 2025). Moreover, intelligent-based forecasting systems enhance demand prediction capabilities (Jamarani et al., 2024). R Azmi et al. (2024) demonstrated that machine learning improves forecasting accuracy, while Jahin et al. (2025) highlighted the importance of demand forecasting for supply chain efficiency and resilience.

2.6. Digital Finance and Payment Systems

Digital finance and payment systems constitute a major dimension of the relationship between digitalization and inflation. There is a long-term positive relationship between digital payments and economic activity (Kahveci & Gurgur, 2025). The integration of digital finance increases transaction efficiency and financial inclusion. Demirel and Topcu (2024) showed that intelligent-based banking services facilitate financial transactions. Becker (2026) emphasized that central bank digital currencies reduce the cost of holding cash during inflationary periods, while Zhou (2024) argued that CBDCs enhance monetary policy effectiveness. Ozili (2024) also highlighted the role of digital currencies in inflation control. However, Kebede et al. (2024) noted that increased financial inclusion may generate short-term demand-side inflationary pressures.

2.7. Summary of Digital Economy Factors

Based on the literature review, digital economy factors affecting inflation can be grouped into several key dimensions: technological infrastructure, market competition and transparency, production and logistics efficiency, labor market transformation, and financial digitalization. These dimensions represent different transmission channels through which digitalization influences inflation, including cost reduction, demand stimulation, and monetary transmission mechanisms. Accordingly, the twelve criteria selected in this study are designed to capture these multidimensional interactions in a comprehensive and structured manner, providing a strong basis for the subsequent priority analysis.

3. Methodology

The methodological framework of the study consists of several integrated steps designed to systematically evaluate and prioritize digital economy factors and policy strategies. First, digital economy criteria and policy strategies are identified through a comprehensive literature review. Second, expert evaluations are collected and structured into decision matrices. Third, an attention-based expert weighting approach is applied to determine the relative importance of each expert based on consensus structure and evaluation consistency. Fourth, generalized fractal fuzzy sets are used to model uncertainty and transform linguistic evaluations into numerical forms. Fifth, the MEREC method is employed to calculate objective weights of the criteria. Finally, the ARLON technique is applied to rank the policy strategies based on the weighted decision matrix. This structured approach ensures analytical consistency and robustness in evaluating the complex relationship between digitalization and inflation. This part presents the definitions of generalized fractal fuzzy sets (GFFFSs), attention-based expert weighting approach, MEREC and ARLON, respectively. These methods allow for word-based processing, expert weighting, criterion prioritization, and ranking of alternatives, respectively.

3.1. Attention-Based Expert Weighting Approach

Step 1: Definition and stacking of expert matrices.

Each expert evaluation is represented in matrix form. In this way, the numerical evaluations given by the experts are compiled under a single matrix structure with Equation (1) so that the values can be processed.

An evaluation matrix is generated for each specialist e:

$$X^{\left(e\right)}=\left[x_{ak}^{\left(e\right)}\right]\in R^{A\times K},e=1,2,\dots ,E$$

(1)

• $E$: number of experts
• $A$: number of rows (row size in the matrix)
• $K$: number of columns (column size in the matrix)
• $x_{ak}^{\left(e\right)}$: The score given by the expert to cell ath row–kth column

The evaluation matrices $X^{\left(e\right)}$, obtained from multiple experts, are stacked on top of each other to obtain a single three-dimensional matrix structure for ease of analysis. In this structure, called a tensor, the first dimension is the expert index, the second dimension is the row index, and the third dimension is the column index. Each matrix obtained from the experts is stacked in a tensor with three-dimensional Equation (2).

$$\mathcal{X}\in R^{E\times A\times K},{\mathcal{X}}_{\mathcal{e}\mathcal{a}\mathcal{k}}=x_{ak}^{\left(e\right)}$$

(2)

Step 2: Calculation of the consensus (average) matrix.

The consensus matrix contains only the arithmetic means of valid expert evaluations for each cell and expresses the common tendency of the experts. This serves as a reference in later stages to measure how well the experts agree with other expert evaluations. At the same time, the difference between each expert’s evaluation matrix and the consensus matrix is used in calculating the signals that measure expert credibility and behavioral characteristics. Here, Equation (3) is used to calculate the consensus matrix representing the common tendency of the experts.

$$\overline{X}=\left[{\overline{x}}_{ak}\right], {\overline{x}}_{ak}={\displaystyle \frac{1}{\left|{\mathsf{\Omega }}_{ak}\right|}}{\sum }_{e\in {\mathsf{\Omega }}_{ak}}{x}_{ak}^{\left(e\right)}$$

(3)

• $\overline{X}$: Consensus (average) matrix
• ${\mathsf{\Omega }}_{ak}$: incomplete set of experts for cell ($a$, $k$)
• $\left|{\mathsf{\Omega }}_{ak}\right|$: Number of experts who gave a valid answer in the relevant cell

Step 3: Summation of rows and columns in the consensus matrix.

This was used to analyze the dominant patterns of expert decision-making and the structural consistency of expert evaluations. The calculated consensus row and column sums will be used in subsequent stages to calculate the structural consistency measures of the experts’ responses. Equation (4) is used to obtain the sum of the rows of the consensus matrix, and Equation (5) is used to obtain the sum of the columns of the consensus matrix:

$$\overline{r}=\left[{\overline{r}}_a\right], {\overline{r}}_a={\displaystyle {\sum }_{k=1}^K}{\overline{x}}_{ak}$$

(4)

$$\overline{c}=\left[{\overline{c}}_k\right], {\overline{c}}_k={\displaystyle {\sum }_{a=1}^A}{\overline{x}}_{ak}$$

(5)

• $\overline{r}$: Consensus row profile
• $\overline{c}$: Consensus column profile

Step 4: Calculation of Expert Signals

Five signals were generated for each expert’s response to calculate expert weightings: completeness, discriminability, outlier rate, distance to consensus, and structural consistency. Additionally, consensus similarity was derived from the inverse of consensus distance.

Step 4.1. Calculating the Completeness Signal

In decision-making processes, it may not always be possible for experts to answer every question due to reasons such as lack of information and uncertainty. At this point, the completeness signal is a quantitative measure that expresses the extent to which each expert participates completely in the evaluation process. The lower the percentage of missing cells an expert has, the higher the completeness score. The completeness score is a normalized value between 0 and 1. First, the number of missing cells in the expert’s matrix, expressed as $\mathrm{NaN}\left(X^{\left(e\right)}\right)$ e, is determined using Equation (6). The resulting number of missing cells is divided by the total number of cells A.K. Finally, the completeness score is calculated by taking the inverse of the resulting missing cell percentage, which is between 0 and 1.

$${\mathrm{comp}}_{\mathrm{e}}=1-{\displaystyle \frac{\mathrm{NaN}\left(X^{\left(e\right)}\right)}{A\cdot K}}$$

(6)

• $\mathrm{NaN}\left(X^{\left(e\right)}\right)$: number of missing cells in the eth expert’s matrix
• ${\mathrm{comp}}_{\mathrm{e}}\in \left[0,1\right]$: The closer the value got to 1, the more complete the expert’s answer.
• $A\cdot K$: Total number of cells

The results obtained from Equation (6) are interpreted as follows:

• ${\mathrm{comp}}_{\mathrm{e}}=1$: The expert answered all the cells.
• ${\mathrm{comp}}_{\mathrm{e}}\to 0$: The expert’s contribution to the evaluation process was limited.

Step 4.2: Calculation of the Discrimination Signal

Equation (7) represents the discrimination signal calculated with the standard deviation and calculates whether the answers given by the experts have similar scores between rows and columns. ${\mathrm{disc}}_{\mathrm{e}}$ indicates that experts who receive high values put more significant differences between the criteria. Accordingly, this signal is included in the model as it shows the discriminative power of the experts.

$${\mathrm{disc}}_{\mathrm{e}}=\mathrm{std}\left(X^{\left(e\right)}\right)$$

(7)

Step 4.3. Calculation of Extreme Ratio

Equation (8) is a measure that shows how often extreme scores are used in expert evaluations. This signal aims to reveal the tendency to lean towards extremes, which may indicate that expert decisions may be less stable or based on extreme judgments, and is a penalty element.

$${\mathrm{ext}}_{\mathrm{e}}={\displaystyle \frac{1}{N_e}}{\sum }_{\left(a,k\right)\in {\mathcal{I}}_{\mathcal{e}}}\mathbb{I}\left\{x_{ak}^{\left(e\right)}\le {\tau }_L \vee x_{ak}^{\left(e\right)}\ge {\tau }_H\right\}$$

(8)

• ${\tau }_L$: low end threshold
• ${\tau }_H$: high end threshold
• ${\mathcal{I}}_{\mathcal{e}}$: e expert’s complete cell indexes
• $N_e={|\mathcal{I}}_{\mathcal{e}}|$:
• $\mathbb{I}\left( \right)$: indicator function (1 if condition is true, 0 otherwise)

Step 4.4. Calculation of Consensus Distance

This measurement shows the difference between each expert’s evaluation matrix and the consensus matrix, which shows the common tendency of all experts. Equation (9) represents the Frobenius norm. Using the Frobenius norm, the matrix is converted into a single distance value. Here, Equation (10) represents the expert’s distance from the consensus. Thus, the difficulty of making individual comparisons at the cell level is overcome.

$${\parallel A\parallel }_F=\sqrt{{\displaystyle {\sum }_{a=1}^A}{\displaystyle {\sum }_{k=1}^K}{a}_{ak}^2}$$

(9)

$$d_e=|X^{\left(e\right)}-\overline{X}{|}_F$$

(10)

• $d_e$: A greater distance indicates that the expert has deviated more from the consensus.

The difference between expert assessments and the consensus value, which indicates the common trend, quantitatively shows how close or far the expert is from the group decision. A high difference value means that the expert has deviated from the group trend and that their assessments are less consistent with the assessments of other experts.

Step 4.5. Calculation of the Structural Consistency Signal

The row sums (Equation (11)) and column sums (Equation (12)) of each expert’s evaluation matrix were calculated, and the direction and extent to which the expert highlighted the criteria were summarized. The row and column profiles of the expert were extracted:

$$r^{\left(e\right)}=\left(r_a^{\left(e\right)}\right), r_a^{\left(e\right)}={\sum }_{k=1}^K{x}_{ak}^{\left(e\right)}$$

(11)

$$c^{\left(e\right)}=\left(c_k^{\left(e\right)}\right), c_k^{\left(e\right)}={\sum }_{k=1}^A{x}_{ak}^{\left(e\right)}$$

(12)

In the step of comparing the row and column structure of the expert with the consensus, the correlation between the row profile of the expert and the row profile of the consensus was first calculated, and then the correlation between the column profile of the expert and the column profile of the consensus was calculated. Equation (13) represents Pearson correlation.

$$\rho \left(u,v\right)=\left\{\begin{array}{cc}\hfill 0,& std\left(u\right)<\epsilon veya std\left(v\right) < \epsilon \hfill \\ \hfill corr(u,v),& aksi halde\hfill \end{array}\right.$$

(13)

• $\epsilon$: numerical stability constant

Equation (14) shows the process of calculating row and column correlations:

$${\rho }_{\mathrm{row}}^{\left(e\right)}=\rho \left(r^{\left(e\right)},\overline{r}\right),\hspace{1em} {\rho }_{\mathrm{col}}^{\left(e\right)}=\rho \left(c^{\left(e\right)},\overline{c}\right)$$

(14)

Row and column correlations obtained with Equation (14) are averaged with Equation (15) and converted from the range [−1, 1] to the range [0, 1] to obtain a single structural consistency score.

$${\mathrm{consist}}_{\mathrm{e}}={\displaystyle \frac{\left(\frac{{\mathsf{\rho }}_{\mathrm{row}}^{\left(e\right)}+{\mathsf{\rho }}_{\mathrm{col}}^{\left(e\right)}}{2}\right)+1}{2}}$$

(15)

Here, the closer the value of ${\mathrm{consist}}_{\mathrm{e}}$ ∈ [0, 1] is to 1, the more the expert’s structural profile is in line with the consensus.

Step 5. Min–Max normalization

Since the signals were measured with different scales, they were normalized based on the smallest and largest values to make them comparable to each other. In this step, the values were converted to the [0, 1] range. This process also prevented the numerical magnitude of the signals from dominating the model.

Equation (16) meets the step of normalizing the signals with min–max:

$$\mathrm{minmax}\left(v_i\right)={\displaystyle \frac{v_i-\min \left(v\right)}{\max \left(v\right)-\min \left(v\right)+\mathsf{\epsilon }}}$$

(16)

Min–max normalization was applied to the discrimination signal, which expresses the distribution of expert responses, in Equation (17).

$${\mathrm{disc}}_{\mathrm{e}}^{\left(\mathrm{n}\right)}=\mathrm{minmax}\left({\mathrm{disc}}_{\mathrm{e}}\right)$$

(17)

Min–max normalization was also applied to the distance signal, which shows how much the expert evaluations deviate from the consensus matrix, in Equation (18).

$$d_e^{\left(n\right)}=\mathrm{minmax}\left(d_e\right)$$

(18)

• Superscript $\left(n\right)$: normalized value

The similarity measure representing the proximity of consensus is obtained by taking the inverse of the normalized consensus distance value. Equation (19) defines the inverse of the distance as “consensus similarity”:

$${\mathrm{cons}}_{\mathrm{e}}=1-d_e^{\left(n\right)}$$

(19)

Equation (20) is the extreme value signal representing the expert’s tendency to give extreme values, it was normalized by the min–max method and used as the penalty term for the model.

$${\mathrm{ext}}_{\mathrm{e}}^{\left(\mathrm{n}\right)}=\mathrm{minmax}\left({\mathrm{ext}}_{\mathrm{e}}\right)$$

(20)

Step 6: Calculating the Attention score ($z_e$).

Equation (21) shows that the signals calculated for each expert in the study are linearly combined into a single score. Here, ${\mathrm{e}\mathrm{x}\mathrm{t}}_e^{\left(n\right)}$ takes a negative value as it is modeled as punishment since the extreme response behavior. A linear composite score for each expert:

$$z_e={\mathsf{\beta }}_{\mathrm{comp}}{\mathrm{comp}}_{\mathrm{e}}+{\mathsf{\beta }}_{\mathrm{disc}}{\mathrm{disc}}_{\mathrm{e}}^{\left(\mathrm{n}\right)}+{\mathsf{\beta }}_{\mathrm{cons}}{\mathrm{cons}}_{\mathrm{e}}+{\mathsf{\beta }}_{\mathrm{consist}}{\mathrm{consist}}_{\mathrm{e}}-{\mathsf{\beta }}_{\mathrm{ext}}{\mathrm{ext}}_{\mathrm{e}}^{\left(\mathrm{n}\right)}$$

(21)

• $z_e$: raw attention score
• $\beta$: signal significance coefficients

Step 7: Calculation of the final expert weights (${\mathsf{\alpha }}_e$)

The largest value among the calculated scores of all experts is subtracted from each score. Thanks to Equation (22), the exponential function is prevented from growing excessively and the calculations remain numerically stable.

$$\widetilde{z_e}=z_e-\underset{j}{\max }\left(z_j\right)$$

(22)

The corrected scores are passed through the softmax function as in step 1, thus obtaining the final weighted scores for the experts. The weights obtained as a result of Equation (23), which add up to 1, are a probabilistic distribution reflecting the relative importance of the expert contributions.

$${\mathsf{\alpha }}_e={\displaystyle \frac{\exp \left(\widetilde{z_e}\right)}{{\sum }_{j=1}^E\exp \left(\widetilde{z_e}\right)}}$$

(23)

3.2. GFFSs

Generalized fractal fuzzy sets are a type of fuzzy set defined by degrees of membership $\left(s\right)$ and non-membership $\left(t\right)$. The characteristic of this set is that it allows comparison of results by differentiating the power of the degrees. In other words, if the power is equal to two, this set exhibits the properties of a Pythagorean fuzzy set. Similarly, if the power is equal to three, this set corresponds to a Fermatean fuzzy set. Furthermore, if the power is log(4)/log(3), log(3)/log(2), or log(2)/log(3), the fuzzy set satisfies the properties of KSFSs, STFSs, or CDFSs (Kou et al., 2025).

A GFFS $\left(\tilde{G}\right)$ in finite universe of discourse is described in Equation (24).

$$\tilde{G}=\left\{u,\left(s_{\tilde{G}}\left(u\right),t_{\tilde{G}}\left(u\right)\right)\left|u\in \mathcal{S}\right.\right\}$$

(24)

These degrees met the conditions in Equation (25).

$$0\le s_{\tilde{G}}^p\left(u\right)+t_{\tilde{G}}^p\left(u\right)\le 1$$

(25)

wherein p is the power for fuzzy set as 2, 3, log(4)/log(3), log(3)/log(2), or log(2)/log(3). Let ${\tilde{G}}_1$ and ${\tilde{G}}_2$ be any two GFFNs, and $\lambda , a$ are positive numbers, then some operations are identified with Equations (26)–(29).

$${\tilde{G}}_1+{\tilde{G}}_2=\left(\begin{array}{c}\sqrt[p]{{\displaystyle \frac{s_{{\tilde{G}}_1}^p+s_{{\tilde{G}}_2}^p-s_{{\tilde{G}}_1}^p{s}_{{\tilde{G}}_2}^p-(1-a)s_{{\tilde{G}}_1}^p{s}_{{\tilde{G}}_2}^p}{1-(1-a)s_{{\tilde{G}}_1}^p{s}_{{\tilde{G}}_2}^p}}}\\ {\displaystyle \frac{t_{{\tilde{G}}_1}{t}_{{\tilde{G}}_2}}{\sqrt[p]{a+\left(1-a\right)\left(t_{{\tilde{G}}_1}+t_{{\tilde{G}}_2}-t_{{\tilde{G}}_1}{t}_{{\tilde{G}}_2}\right)}}}\end{array}\right)$$

(26)

$${\tilde{G}}_1\times {\tilde{G}}_2=\left(\begin{array}{c}{\displaystyle \frac{s_{{\tilde{G}}_1}{s}_{{\tilde{G}}_2}}{\sqrt[p]{a+\left(1-a\right)\left(s_{{\tilde{G}}_1}+s_{{\tilde{G}}_2}-s_{{\tilde{G}}_1}{s}_{{\tilde{G}}_2}\right)}}}\\ \sqrt[p]{{\displaystyle \frac{t_{{\tilde{G}}_1}^p+t_{{\tilde{G}}_2}^p-t_{{\tilde{G}}_1}^p{t}_{{\tilde{G}}_2}^p-(1-a)t_{{\tilde{G}}_1}^p{t}_{{\tilde{G}}_2}^p}{1-(1-a)t_{{\tilde{G}}_1}^p{t}_{{\tilde{G}}_2}^p}}}\end{array}\right)$$

(27)

$$\lambda {\tilde{G}}_1=\left(\begin{array}{c}\sqrt[p]{{\displaystyle \frac{{\left(1+(a-1)s_{{\tilde{G}}_1}^p\right)}^{\lambda }-{\left(1-s_{{\tilde{G}}_1}^p\right)}^{\lambda }}{{\left(1+\left(a-1\right)s_{{\tilde{G}}_1}^p\right)}^{\lambda }-\left(a-1\right){\left(1-s_{{\tilde{G}}_1}^p\right)}^{\lambda }}}}\\ {\displaystyle \frac{\sqrt[p]{a}{t}_{{\tilde{G}}_1}^{\lambda }}{\sqrt[p]{{\left(1+\left(a-1\right)\left(1-t_{{\tilde{G}}_1}^p\right)\right)}^{\lambda }+(a-1)t_{{\tilde{G}}_1}^{p\lambda }}}}\end{array}\right)$$

(28)

$${\left({\tilde{G}}_1\right)}^{\lambda }=\left(\begin{array}{c}{\displaystyle \frac{\sqrt[p]{a}{s}_{{\tilde{G}}_1}^{\lambda }}{\sqrt[p]{{\left(1+\left(a-1\right)\left(1-s_{{\tilde{G}}_1}^p\right)\right)}^{\lambda }+\left(a-1\right)s_{{\tilde{G}}_1}^{p\lambda }}}}\\ \sqrt[p]{{\displaystyle \frac{{\left(1+\left(a-1\right)t_{{\tilde{G}}_1}^p\right)}^{\lambda }-{\left(1-t_{{\tilde{G}}_1}^p\right)}^{\lambda }}{{\left(1+\left(a-1\right)t_{{\tilde{G}}_1}^p\right)}^{\lambda }-\left(a-1\right){\left(1-t_{{\tilde{G}}_1}^p\right)}^{\lambda }}}}\end{array}\right)$$

(29)

Assume that $\tilde{G}$ is any GFFSs, then score and accuracy functions are defined with the help of Equations (30) and (31).

$$\mathbb{S}\left(\tilde{G}\right)={\displaystyle \frac{1}{2}}\left(1+s_{\tilde{G}}^p-t_{\tilde{G}}^p\right)$$

(30)

$$\hslash \left(\tilde{G}\right)=s_{\tilde{G}}^p+t_{\tilde{G}}^p$$

(31)

3.3. GFF-MEREC Based ARLON

This approach, created by integrating a combination of MEREC and ARLON methods with GFFSs, provides more realistic results by incorporating objective weighting and two various logarithmic normalizations. GFFSs enable comparative results to be obtained, while sensitivity can be ensured with the parameter of the ARLON method. The calculation procedure for this approach is described below.

Firstly, linguistic evaluations in e expert matrices are transformed into GFFNs in Table 1 according to linguistic variables.

Table 1. Linguistic Variables.

	s	t
EH	0.9	0.1
VH	0.8	0.2
H	0.7	0.3
MH	0.6	0.4
M	0.5	0.5
ML	0.4	0.6
L	0.3	0.7
VL	0.2	0.8
EL	0.1	0.9

Next, these GFFNs of rth expert $\left({\tilde{h}}^r\right)$ are multiplied by expert weight and then expert-weighted GFFNs are summed. Equation (32) is used for this. Thus, GFF-decision matrix illustrated in Equation (33) is obtained (Seikh & Chatterjee, 2025).

$${\tilde{d}}_{ij}={\displaystyle \sum _{r=1}^e}\left({ew}_r{\tilde{h}}_{ij}^r\right)$$

(32)

$$\tilde{D}={\left[{\tilde{d}}_{ij}\right]}_{m\times n}$$

(33)

Afterwards, GFF-decision matrix $\left(D=\left[d_{ij}\right]\right)$ is defuzzified by Equation (34).

$$d_{ij}=\mathbb{S}\left({\tilde{d}}_{ij}\right)+1$$

(34)

Next, elements of normalized matrix are calculated with the help of Equations (35) and (36).

$${\mathfrak{y}}_{ij}={\displaystyle \frac{\underset{i}{\min }{d}_{ij}}{d_{ij}}}; for benefit$$

(35)

$${\mathfrak{y}}_{ij}={\displaystyle \frac{d_{ij}}{\underset{i}{\max } d_{ij}}}; for cost$$

(36)

After that, the overall performances of alternatives are estimated using Equation (37).

$$P_{ij}^{\prime }=\ln \left(1+\left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n}\left|\ln {\mathfrak{y}}_{ij}\right|\right)\right)$$

(37)

Similarly, the performances of alternatives by removing each criterion are established with Equation (38).

$$P_{ij}^{\prime }=\ln \left(1+\left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1, k\ne j}^n}\left|\ln {\mathfrak{y}}_{ik}\right|\right)\right)$$

(38)

Absolute deviations between overall performances and performances of alternatives are summed by Equation (39).

$${∆}_j={\displaystyle \sum _{i=1}^m}\left|P_{ij}^{\prime }-P_{ij}^{\prime }\right|$$

(39)

In last step of MEREC, the priorities of criteria are obtained using Equation (40).

$$w_j={\displaystyle \frac{{∆}_j}{{\sum }_{j=1}^n{∆}_j}}$$

(40)

After obtaining the priorities of the criteria, two different logarithmic normalization operations are applied to the defuzzified matrix. The first logarithmic normalization is defined in Equations (41) and (42) (Yalçın et al., 2025).

$${FN}_{ij}^{+}={\displaystyle \frac{\ln d_{ij}}{\ln \left({\prod }_{i=1}^m{d}_{ij}\right)}}; for benefit$$

(41)

$${FN}_{ij}^{-}={\displaystyle \frac{1-\frac{\ln d_{ij}}{\ln \left({\prod }_{i=1}^m{d}_{ij}\right)}}{m-1}}; for cost$$

(42)

The second logarithmic normalization is described in Equations (43) and (44).

$${SN}_{ij}^{+}={\displaystyle \frac{{\log }_2{d}_{ij}}{{\sum }_{i=1}^m{\log }_2{d}_{ij}}}$$

(43)

$${SN}_{ij}^{-}=1-{\displaystyle \frac{{\log }_2{d}_{ij}}{{\sum }_{i=1}^m{\log }_2{d}_{ij}}}$$

(44)

Afterwards, Heron matrix $\left(\mathfrak{H}=\left[{\mathcal{h}}_{ij}\right]\right)$ is created by Equation (45).

$${\mathcal{h}}_{ij}=\left(1-\theta \right)\sqrt{{FN}_{ij}{SN}_{ij}}+\theta {\displaystyle \frac{{FN}_{ij}+{SN}_{ij}}{2}}$$

(45)

wherein $\theta$ refers to the parameter of impact between two logarithmic normalizations. $\theta \in \left[0, 1\right]; FN:{FN}^{+},{FN}^{-}; SN:{SN}^{+},{SN}^{-}$. Next, weighted heron matrix is computed with Equation (46).

$${w\mathcal{h}}_{ij}={\mathcal{h}}_{ij}{w}_j$$

(46)

The totals of weighted heron values by benefit of cost criteria for each alternative are calculated using Equations (47) and (48).

$$C_i=\sum _{j\in cost}{w\mathcal{h}}_{ij}$$

(47)

$$B_i=\sum _{j\in benefit}{w\mathcal{h}}_{ij}$$

(48)

Finally, the scores of alternatives are obtained by Equation (49).

$$R_i=B_i^{\gamma }+C_i^{\left(1-\gamma \right)}$$

(49)

wherein $\gamma$ is the ratio of the number of benefit criteria to number or total criteria.

4. Analysis

Although the empirical structure of this study is based on expert evaluations, several measures are implemented to ensure the robustness and reliability of the results. First, the use of ten domain experts with substantial professional experience provides a balanced and informed evaluation base consistent with similar studies in the literature. Second, the proposed attention-based expert weighting approach reduces the potential bias associated with small sample sizes by assigning data-driven importance levels based on consensus structure and behavioral consistency rather than treating all experts equally. Third, a comprehensive sensitivity analysis is conducted by testing different parameter values and comparing alternative decision-making methods, including ARLON, RAM, and TOPSIS. The consistency of the results across these different scenarios confirms the stability and robustness of the findings, mitigating concerns related to sample size limitations.

This part presents the results of methodology for used to examine the relative effects of digital economy factors on inflation. For this purpose, factors measuring the impact of the digital economy on inflation are identified. A list of these factors, their types, and the abbreviations used in the analysis are summarized in Table 2.

Table 2. Factor, Type and Abbreviation.

Factor	Abb.	Description
E-commerce Penetration	ECOMM	Reflects the extent of online retail activity, influencing price competition and reducing firms’ pricing power through increased transparency and lower transaction costs.
Prevalence of Digital Payment Systems	DPAYS	Represents the adoption of digital payment methods, affecting transaction efficiency, consumption velocity, and monetary policy transmission.
Internet Prevalence and Speed Index	INTSP	Indicates the level of digital connectivity, enhancing information flow and reducing search costs in markets.
Online Price Tracking and Price Transparency	PRTRN	Measures the availability of real-time price information, limiting opportunistic pricing and increasing competition.
Digital Advertising Intensity	DGADV	Captures demand stimulation effects through targeted marketing, potentially increasing short-term inflationary pressures.
Prevalence of Industry 4.0 Technologies	IND40	Reflects automation and smart production systems that improve efficiency and reduce production costs.
Data-Driven Inventory Management	DDINV	Indicates optimization of inventory management, reducing inefficiencies and supply-side inflation.
Prevalence of Digital Workforce	DGWRK	Represents labor flexibility and productivity gains from digital work structures.
Use of Data-Driven Demand Forecasting Systems	DDFOR	Captures predictive analytics improving supply-demand matching and price stability.
Fintech Prevalence	FINTE	Reflects financial innovation and inclusion affecting credit access and consumption patterns.
Crypto/CBDC Usage Rate	CRCBD	Max Represents digital currency usage impacting monetary policy and financial stability.
Digital Financial Access Index	DFACC	Measures inclusion in formal financial systems, influencing both demand and stability.

E-commerce penetration affects inflation primarily through its impact on market competition and price formation mechanisms. Increased online retail activity reduces search costs and enhances price transparency, thereby limiting firms’ ability to sustain high markups, which is consistent with search theory and competitive market frameworks (Aparicio et al., 2024; Zamani et al., 2024). However, the growing dominance of large digital platforms and the use of algorithmic pricing may introduce elements of imperfect competition, potentially enabling coordinated pricing behavior (Sanchez-Cartas & Katsamakas, 2024). Similarly, the prevalence of digital payment systems influences inflation through both demand-side and monetary transmission channels. Increased transaction efficiency and accessibility of digital payments may stimulate short-term consumption, contributing to demand-driven inflation (Kebede et al., 2024). At the same time, digital payment systems improve the effectiveness of monetary policy by enhancing traceability and reducing informality, which supports long-term price stability (Kahveci & Gurgur, 2025). These findings suggest that digital economy factors influence inflation through multiple interconnected channels, including competition, information asymmetry, demand dynamics, and monetary transmission mechanisms. This multidimensional impact highlights the importance of evaluating digitalization within a comprehensive analytical framework grounded in established economic theories.

Digital advertising intensity influences inflation by shaping consumer demand and accelerating consumption cycles through targeted and personalized marketing. While this can increase short-term demand-driven inflation, improved matching between products and consumers may reduce inefficiencies and stabilize prices over time. The prevalence of Industry 4.0 technologies affects inflation by enhancing productivity through automation, smart manufacturing, and real-time process optimization. These efficiency gains lower marginal production costs, generating structural deflationary pressures in the medium to long run. Data-driven inventory management impacts inflation by reducing excess inventories and minimizing supply-demand mismatches. Improved inventory optimization lowers storage and wastage costs, contributing to more stable prices and reduced supply-side inflation. The prevalence of a digital workforce influences inflation by increasing labor productivity and enabling flexible work arrangements that reduce operational costs. However, rising demand for high-skilled digital labor may create wage pressures in specific sectors, partially offsetting productivity gains.

The use of data-driven demand forecasting systems affects inflation by improving firms’ ability to anticipate consumption patterns and adjust supply accordingly. This reduces demand volatility and price fluctuations, supporting smoother inflation trajectories. Fintech prevalence influences inflation by expanding access to financial services and improving credit allocation efficiency. While enhanced financial inclusion may stimulate consumption and short-term inflation, improved financial intermediation contributes to long-term price stability. Crypto and CBDC usage rates affect inflation through their impact on monetary sovereignty, payment efficiency, and money supply control. While decentralized crypto usage may weaken traditional monetary transmission, CBDCs can strengthen policy effectiveness and enhance inflation management. The digital financial access index influences inflation by broadening participation in formal financial systems and increasing transaction efficiency. Greater financial inclusion can stimulate aggregate demand, but improved savings, payments, and credit mechanisms support more balanced and controllable inflation dynamics. At the same time, strategies for relative effects of digital economy factors on inflation are determined. These strategies and abbreviations are shared in Table 3.

Table 3. Strategy and Abbreviation.

Strategy	Abb.
Digital Price Transparency Strategy	DRTRN
Expansion of Digital Payment Systems	EPAYS
Digital Logistics and Supply Chain Optimization	DGLOG
Development of Digital Public Services	DGOPS
Industry 4.0 and Smart Manufacturing Technologies	IND4T
Intelligent-based Demand Forecasting Systems	AIDFS
Digital Finance–Fintech Integration	DFINT
Digital Workforce and Remote Work Ecosystem	DGWRE

Digital price transparency strategies contribute to combating inflation by limiting firms’ ability to apply excessive markups and by strengthening competitive pressure through real-time price monitoring. Enhanced transparency improves consumer price awareness and anchors inflation expectations, supporting more stable price formation. The expansion of digital payment systems supports inflation control by improving transaction efficiency and strengthening monetary policy transmission mechanisms. By reducing informality and enhancing payment traceability, digital payments enable more effective liquidity management and price stabilization. Digital logistics and supply chain optimization mitigate inflationary pressures by reducing transportation costs, delivery delays, and inventory inefficiencies. Advanced digital coordination across supply chains enhances resilience to shocks and limits cost-push inflation.

The development of digital public services contributes to inflation management by increasing efficiency in public administration and reducing operational costs. Digitalization of public services also improves resource allocation and limits fiscal inefficiencies that may otherwise translate into inflationary pressures. Industry 4.0 and smart manufacturing technologies help combat inflation by increasing productivity through automation, real-time monitoring, and process optimization. These technologies reduce marginal production costs and enhance supply-side capacity, generating structural disinflationary effects. Intelligent-based demand forecasting systems support inflation control by enabling firms and policymakers to anticipate demand fluctuations more accurately. Improved forecasting reduces supply-demand mismatches and price volatility, contributing to smoother inflation dynamics.

Digital finance and fintech integration enhance inflation management by improving access to financial services and optimizing credit allocation. More efficient financial intermediation supports productive investment while reducing speculative excesses that can amplify inflation. A digital workforce and remote work ecosystem contribute to inflation control by lowering operational and labor-related costs through flexible work arrangements. Increased labor productivity and reduced geographic constraints help moderate wage pressures and support overall price stability.

The expert panel used in this study consists of ten specialists with extensive professional experience in fields directly related to digital economy, finance, and economic policy. All experts have a minimum of 12 years of experience and have been actively involved in areas such as financial systems, monetary policy analysis, digital transformation, and applied economic research. The experts were selected using purposive sampling to ensure both domain expertise and diversity of perspectives across academia and industry. To preserve confidentiality, individual identities and institutional affiliations are not disclosed; however, all participants meet the predefined qualification criteria. In addition, all experts participated voluntarily, and no conflicts of interest were identified that could affect the objectivity of their evaluations. This structured and transparent selection process enhances the credibility and reproducibility of the expert-based analysis.

Experts were recruited through purposive sampling based on their demonstrated expertise in digital economy, financial systems, monetary policy, digital transformation, and applied economic analysis. In addition to the minimum requirement of 12 years of professional experience, participants were required to possess either substantial academic publication records, senior professional responsibilities, policy advisory experience, or practical involvement in digital economy initiatives. The selection process aimed to ensure diversity in professional backgrounds while maintaining a high level of subject matter expertise. To preserve the independence of judgments, experts completed the evaluation process individually and were not informed about the identities or responses of other participants. No group discussions, consensus meetings, or interactive evaluation sessions were conducted during the data collection process. These procedures were implemented to minimize potential peer influence and to ensure that all assessments reflected independent expert opinions.

Although the identities of the experts were kept confidential to preserve anonymity, the expert panel included participants from different geographical and institutional contexts to increase the diversity and representativeness of perspectives. The experts were affiliated with institutions and professional environments located in Türkiye, Azerbaijan, and broader Eurasian and emerging digital economy contexts. This geographical diversity was intentionally considered because digital economy dynamics, financial infrastructures, regulatory environments, and inflation transmission mechanisms may vary across regions. Therefore, incorporating experts with different regional experiences strengthened the contextual robustness and transferability of the evaluations while reducing the risk of geographically concentrated bias in the decision-making process.

The linguistic evaluations are presented in Appendix A. All participants gave their informed consent for inclusion before they participated in the research.

4.1. Application and Findings of Attention-Based Expert Weighting Method

This study, which aims to determine the relative effects of digital economy factors on inflation, included opinions from 10 different experts. In line with the research objective, the interaction levels between 12 defined criteria and 8 strategies were analyzed. Expert evaluations were collected through a structured questionnaire consisting of 96 questions in total, with each interaction rated on a scale of 1–9.

Since the experts had different areas of expertise and experience levels, expert weighting was applied. Accordingly, the experts’ individual evaluations and their adherence to within-group evaluation patterns were analyzed using five different signals: completeness, discriminability, outlier rate, distance from consensus, and structural consistency. This study proposes an attention-based expert weighting model calculated using a softmax function that combines these signals under a holistic structure and utilizes the weighting principles of the attention mechanism in deep learning (Soydaner, 2022; Vaswani et al., 2017).

First, the definition and stacking of expert matrices are performed. The expert evaluation matrix, consisting of 8 rows and 12 columns, is expressed by Equation (1) and is defined separately for each expert. In the study, the evaluations obtained from 10 experts are combined within the scope of Equation (2), which represents a three-dimensional tensor structure with dimensions of 10 × 8 × 12. Then, the consensus (mean) matrix is calculated. In this process, the individual expert evaluations regarding the interaction between each strategy and criterion are combined by taking the arithmetic mean within the scope of the consensus matrix expressed by Equation (3). Accordingly, the mean matrix shown in Table 4 shows the general trend between criteria and strategies by combining the evaluations obtained from 10 different experts under a single representative structure.

Table 4. Consensus matrix of expert evaluations.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	8.3	7.7	7.7	8.1	1.6	7.9	7.8	8.3	7.7	7.9	7.7	7.9
EPAYS	6.5	7.0	7.0	7.1	2.3	6.4	7.4	7.3	7.2	6.7	7.1	7.0
DGLOG	6.4	6.9	6.4	6.0	3.2	6.3	6.5	6.5	6.8	6.5	7.2	5.9
DGOPS	6.7	5.9	5.3	6.0	2.6	5.6	6.5	6.0	5.9	5.8	5.9	5.5
IND4T	5.6	6.0	6.0	5.5	3.0	5.9	5.3	5.3	5.4	5.1	5.1	5.4
AIDFS	5.9	5.3	5.4	5.8	3.0	5.5	5.8	5.7	5.1	6.0	5.6	5.1
DFINT	5.0	4.8	6.3	5.1	2.8	6.0	5.6	5.5	5.7	5.9	5.4	5.3
DGWRE	4.5	5.1	5.5	5.5	3.2	5.5	5.3	5.1	6.1	5.3	6.6	5.5

In the next step, the rows and columns of the consensus matrix are summed. The rows of the consensus matrix obtained as a result of Equation (3) are summed to calculate the row profile expressed by Equation (4) and the column profile represented by Equation (5). The details of this matrix are denoted in Table 5.

Table 5. Consensus Matrix Row Totals.

Strategies	Row Profile
DRTRN	88.6
EPAYS	79.0
DGLOG	74.6
DGOPS	67.7
IND4T	63.6
AIDFS	64.2
DFINT	63.4
DGWRE	63.2

On the other side, the column totals values are also given in Table 6.

Table 6. Consensus Matrix Column Totals.

Strategies	Column Profile
ECOMM	48.9
EPAYS	48.7
INTSP	49.6
DRTRN	49.1
DGADV	21.7
IND4T	49.1
DDINV	50.2
DGWRK	49.7
DDFOR	49.9
FINTE	49.2
CRCBD	50.6
DFACC	47.6

The row and column values in Table 6 and Table 7 were calculated for use in a signal analysis to measure expert consistency. These results in the tables simply indicate which strategies and criteria were most prominent among the experts.

Table 7. Signal Measurements of Expert Assessments.

	Completeness	Discriminativeness	Consensus Distance	Structural Consistency	Extreme Value
Expert 1	1	1.67	10.48	0.97	0.16
Expert 2	1	1.65	10.33	0.98	0.19
Expert 3	1	1.63	9.90	0.97	0.18
Expert 4	1	1.65	9.58	0.98	0.19
Expert 5	1	1.58	9.15	0.97	0.17
Expert 6	1	1.67	9.88	0.97	0.16
Expert 7	1	1.62	10.65	0.98	0.21
Expert 8	1	1.77	9.67	0.98	0.26
Expert 9	1	1.54	9.31	0.97	0.16
Expert 10	1	1.61	9.55	0.95	0.15

Following this, the process of calculating expert signals takes place. The weights of the 10 experts who gave opinions within the scope of the study were calculated by considering the individual evaluations of the experts and the intragroup structure of these evaluations. In line with this calculation, expert evaluations were measured through 5 different signals: completeness defined by Equation (6), discriminability expressed by Equation (7), outlier rate calculated using Equation (8), distance to consensus measured by Equations (9) and (10), and structural consistency obtained as a result of Equations (11)–(15). Signal measurements of expert assessments are demonstrated in Table 7.

Table 7 shows the five characteristics of the expert evaluations, representing the results obtained before the normalization process. A completeness level of 1 for all experts indicates that all experts answered all questions in the question set. Limited differences were observed between the discriminative power and consensus distance results. The structural consistency results being close to 1 for all 10 experts shows that the evaluation patterns are consistent with the overall structure. These results serve as fundamental input for the normalization and subsequent attention-based weighting steps.

It should be noted that all experts completed the questionnaire without any missing responses because the data collection process was conducted under a controlled survey design that required all evaluation items to be answered before submission. As a result, the completeness signal reached its maximum value of 1.00 for all experts. Although completeness did not contribute to differentiation among experts in the present application, it was intentionally retained within the proposed weighting framework to ensure methodological generalizability. In applications where missing evaluations occur, the completeness signal can play an important role in distinguishing expert participation levels and influencing the final weighting results. Therefore, in this study, expert differentiation was primarily driven by the remaining signals, namely discriminability, consensus distance, structural consistency, and extreme value behavior.

The next step is related to min–max normalization. With the normalization step expressed by Equation (16), the signal values calculated for the opinions of 10 experts are converted to the range [0, 1] using the min–max method so that they can be compared and processed. In this context, the consensus similarity values calculated for the discriminant, consensus distance and inverse consensus distance signal calculated with Equations (17)–(20) and finally the extreme value ratio is normalized.

Furthermore, the attention score ($z_e$) is calculated. The normalized signal values calculated for each expert are combined under a single score using a linear equation, Equation (21), which is an intermediate measure. In addition, the final expert weights (${\mathsf{\alpha }}_e$) are calculated. The calculated expert weights are re-scaled using Equation (22) with the largest score as a reference to avoid the risk of the exponential function becoming oversized. The final attention weights are passed through the softmax function using Equation (23), creating a distribution whose sum is equal to 1. Signal values after normalization and the final weights of the experts are indicated in Table 8.

Table 8. Signal values after normalization and the final weights of the experts.

	Completeness	Discriminativeness	Consensus Distance	Structural Consistency	Extreme Value	z Score	Weights
Expert 1	1	0.55	0.11	0.97	0.09	2.54	0.09
Expert 2	1	0.51	0.22	0.98	0.36	2.34	0.07
Expert 3	1	0.41	0.50	0.97	0.27	2.60	0.09
Expert 4	1	0.49	0.71	0.98	0.36	2.81	0.11
Expert 5	1	0.20	1.00	0.97	0.18	2.99	0.13
Expert 6	1	0.59	0.51	0.97	0.09	2.98	0.13
Expert 7	1	0.37	0.00	0.98	0.55	1.80	0.04
Expert 8	1	1.00	0.65	0.98	1.00	2.64	0.09
Expert 9	1	0.00	0.89	0.97	0.09	2.77	0.11
Expert 10	1	0.31	0.73	0.95	0.00	2.99	0.13

Table 9 shows the final signal values and sexpert weights obtained from normalization and attention-based weighting. This table shows that experts with low consensus distances, in other words, those exhibiting within-group evaluation patterns and low levels of deviation, also have proportionally higher weights if a high structural consistency ratio is observed. Accordingly, it was concluded that the experts with the highest weights are Expert 5, Expert 6, and Expert 10, and the experts with the lowest weights are Expert 7 and Expert 2. These results demonstrate that the proposed attention-based approach can data-drivenly differentiate expert weights.

Table 9. GFF-decision Matrix.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40
DRTRN	(0.861, 0.138)	(0.782, 0.217)	(0.789, 0.21)	(0.824, 0.175)	(0.162, 0.834)	(0.804, 0.195)
EPAYS	(0.655, 0.345)	(0.698, 0.301)	(0.7, 0.299)	(0.722, 0.277)	(0.235, 0.759)	(0.634, 0.365)
DGLOG	(0.642, 0.357)	(0.716, 0.283)	(0.633, 0.366)	(0.601, 0.397)	(0.314, 0.684)	(0.637, 0.361)
DGOPS	(0.683, 0.315)	(0.61, 0.388)	(0.539, 0.459)	(0.631, 0.366)	(0.271, 0.727)	(0.559, 0.438)
IND4T	(0.582, 0.415)	(0.597, 0.402)	(0.627, 0.371)	(0.573, 0.424)	(0.284, 0.714)	(0.612, 0.386)
AIDFS	(0.602, 0.396)	(0.531, 0.466)	(0.55, 0.447)	(0.587, 0.411)	(0.308, 0.688)	(0.566, 0.432)
DFINT	(0.488, 0.509)	(0.482, 0.516)	(0.644, 0.354)	(0.515, 0.483)	(0.263, 0.733)	(0.612, 0.386)
DGWRE	(0.452, 0.547)	(0.513, 0.484)	(0.569, 0.429)	(0.555, 0.443)	(0.328, 0.67)	(0.568, 0.43)
	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	(0.799, 0.2)	(0.85, 0.149)	(0.774, 0.225)	(0.79, 0.209)	(0.78, 0.219)	(0.813, 0.186)
EPAYS	(0.75, 0.249)	(0.738, 0.261)	(0.724, 0.275)	(0.676, 0.323)	(0.718, 0.281)	(0.701, 0.298)
DGLOG	(0.651, 0.347)	(0.673, 0.324)	(0.702, 0.296)	(0.668, 0.329)	(0.743, 0.256)	(0.599, 0.399)
DGOPS	(0.648, 0.35)	(0.628, 0.369)	(0.631, 0.366)	(0.592, 0.405)	(0.589, 0.409)	(0.575, 0.423)
IND4T	(0.515, 0.483)	(0.556, 0.441)	(0.525, 0.472)	(0.51, 0.489)	(0.522, 0.476)	(0.57, 0.427)
AIDFS	(0.594, 0.403)	(0.577, 0.42)	(0.516, 0.482)	(0.613, 0.385)	(0.57, 0.429)	(0.509, 0.487)
DFINT	(0.581, 0.418)	(0.585, 0.412)	(0.572, 0.426)	(0.628, 0.37)	(0.527, 0.471)	(0.542, 0.457)
DGWRE	(0.536, 0.462)	(0.507, 0.49)	(0.624, 0.375)	(0.546, 0.45)	(0.668, 0.331)	(0.573, 0.425)

4.2. Evaluation of Strategies for Relative Effects of Digital Economy Factors on Information

The linguistic evaluations in Table 4 are transformed into GFFNs according to Table 1. This section presents intermediate tables for p = 3. Comparisons of results for other values of p are summarized in this manuscript. GFFNs are multiplied by expert weights and summed. Thus, GFF-decision matrix is obtained. This matrix is illustrated in Table 9.

Afterwards, defuzzified decision matrix is estimated. The defuzzified matrix is displayed in Table 10.

Table 10. Defuzzified Decision Matrix.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	1.812	1.738	1.744	1.776	1.213	1.757	1.753	1.801	1.731	1.745	1.736	1.766
EPAYS	1.627	1.664	1.666	1.684	1.280	1.610	1.709	1.698	1.686	1.645	1.681	1.667
DGLOG	1.617	1.680	1.610	1.583	1.347	1.613	1.625	1.644	1.668	1.640	1.703	1.582
DGOPS	1.652	1.591	1.533	1.609	1.311	1.550	1.622	1.606	1.608	1.577	1.574	1.562
IND4T	1.568	1.580	1.605	1.561	1.322	1.592	1.513	1.547	1.522	1.509	1.519	1.558
AIDFS	1.584	1.527	1.542	1.572	1.343	1.555	1.578	1.564	1.514	1.594	1.557	1.509
DFINT	1.492	1.486	1.619	1.513	1.304	1.592	1.567	1.570	1.560	1.606	1.523	1.535
DGWRE	1.461	1.512	1.557	1.546	1.359	1.557	1.530	1.507	1.602	1.539	1.639	1.560

Next, elements of normalized matrix are calculated. The types of factors are shown in Table 2. The results of the normalization process according to these factor types are given in Table 11.

Table 11. Normalized Decision Matrix.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.807	0.855	0.879	0.852	0.892	0.882	0.863	0.837	0.875	0.865	0.875	0.854
EPAYS	0.898	0.893	0.920	0.898	0.942	0.962	0.885	0.887	0.898	0.917	0.904	0.905
DGLOG	0.904	0.885	0.952	0.956	0.991	0.961	0.931	0.917	0.908	0.920	0.892	0.954
DGOPS	0.885	0.934	1000	0.941	0.964	1000	0.933	0.938	0.941	0.957	0.965	0.966
IND4T	0.932	0.941	0.955	0.969	0.972	0.973	1000	0.974	0.995	1000	1000	0.968
AIDFS	0.922	0.973	0.994	0.963	0.988	0.997	0.959	0.963	1000	0.947	0.975	1000
DFINT	0.980	1000	0.947	1000	0.960	0.973	0.966	0.959	0.971	0.939	0.998	0.983
DGWRE	1000	0.983	0.984	0.979	1000	0.996	0.989	1000	0.945	0.980	0.927	0.967

After that, the overall performances of strategies for relative effects of digital economy factors on inflation are estimated. The overall performances of these strategies are exhibited in Table 12.

Table 12. Overall Performances.

	p
DRTRN	0.139
EPAYS	0.091
DGLOG	0.070
DGOPS	0.049
IND4T	0.027
AIDFS	0.027
DFINT	0.027
DGWRE	0.021

At the same time, the performances of strategies for relative effects of digital economy factors on inflation by removing each factor are established. These performances by removing are expressed in Table 13.

Table 13. Performances by Removing.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.124	0.128	0.130	0.128	0.131	0.130	0.129	0.126	0.130	0.129	0.130	0.128
EPAYS	0.083	0.083	0.085	0.083	0.087	0.088	0.082	0.082	0.083	0.085	0.084	0.084
DGLOG	0.062	0.060	0.066	0.066	0.069	0.067	0.064	0.063	0.062	0.063	0.061	0.066
DGOPS	0.039	0.043	0.049	0.044	0.046	0.049	0.043	0.043	0.044	0.045	0.046	0.046
IND4T	0.021	0.022	0.023	0.024	0.025	0.025	0.027	0.025	0.027	0.027	0.027	0.024
AIDFS	0.020	0.025	0.026	0.024	0.026	0.027	0.023	0.024	0.027	0.022	0.025	0.027
DFINT	0.026	0.027	0.023	0.027	0.024	0.025	0.024	0.024	0.025	0.022	0.027	0.026
DGWRE	0.021	0.020	0.020	0.019	0.021	0.021	0.020	0.021	0.017	0.019	0.015	0.018

Absolute deviations between overall performances and performances of strategies are summed. In last step of MEREC, the priorities of factors are obtained. The results are demonstrated in Table 14.

Table 14. Total Absolute Deviations and Weights of Factors.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
$∆$	0.056	0.044	0.030	0.036	0.023	0.020	0.038	0.043	0.038	0.038	0.038	0.032
w	0.128	0.100	0.068	0.082	0.053	0.047	0.088	0.098	0.087	0.088	0.087	0.074

When Table 14 is examined, e-commerce penetration and the prevalence of digital payment systems emerge as the most important factors measuring the impact of the digital economy on inflation, with relative weights of 0.128 and 0.100, respectively, for p = 3. This result indicates that digital inflation dynamics are primarily shaped by the transformation of consumption channels and payment infrastructures rather than by purely technological or production-oriented digital factors. E-commerce penetration affects inflation through intensified price competition, reduced search costs, and increased price transparency, which generally exert downward pressure on prices by limiting firms’ market power; however, platform concentration and algorithmic pricing may partially offset these effects by enabling coordinated price adjustments. Similarly, the prevalence of digital payment systems influences inflation by increasing transaction efficiency and consumption velocity, potentially stimulating short-term demand while simultaneously enhancing the effectiveness of monetary policy transmission through improved traceability and liquidity monitoring. The joint prominence of these two factors suggests that digital inflation is closely linked to how prices are formed and how money circulates within digital markets, rather than to digitalization in production alone. From a policy perspective, this finding implies that inflation management in digital economies should prioritize regulatory oversight of e-commerce platforms, promote fair competition and transparent pricing mechanisms, and support the expansion of secure, interoperable digital payment systems. Strategically, integrating real-time price monitoring tools, encouraging cashless transactions, and aligning fintech regulations with macroeconomic stabilization objectives can help mitigate inflationary risks arising from the digitalization of consumption and payments. The prioritizations of factors are summarized for the other values of p in Table 15.

Table 15. Prioritizations of Factors by Various p Values.

p	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
2	0.130	0.101	0.067	0.082	0.052	0.044	0.088	0.098	0.088	0.091	0.086	0.072
3	0.128	0.099	0.067	0.083	0.056	0.043	0.088	0.099	0.088	0.092	0.086	0.070
1.262	0.129	0.101	0.068	0.082	0.052	0.045	0.088	0.097	0.087	0.090	0.086	0.073
1.585	0.130	0.101	0.067	0.082	0.052	0.045	0.088	0.098	0.088	0.091	0.086	0.073
0.631	0.128	0.100	0.068	0.082	0.053	0.047	0.088	0.098	0.087	0.088	0.087	0.074

As can be seen from the prioritization values in Table 15, the most important factor remains the same across all values of p, indicating a high level of consistency in the results. This stability suggests that the relative importance of the identified factor is robust to changes in the model’s parameterization and is not driven by a specific weighting assumption or sensitivity setting. In methodological terms, the invariance of rankings across different p values strengthens the reliability and internal validity of the analysis, implying that the prioritization outcome reflects a structural relationship rather than a parameter-dependent artifact. Consequently, this consistency enhances the credibility of the findings and supports their use as a solid basis for policy formulation and strategic decision-making in the context of digital inflation analysis. After obtaining the priorities of the factors, two different logarithmic normalization operations are applied to the defuzzified decision matrix. The first logarithmic normalization is computed as in Table 16.

Table 16. First Logarithmic Normalization.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.158	0.148	0.146	0.152	0.130	0.150	0.147	0.153	0.144	0.147	0.144	0.153
EPAYS	0.130	0.136	0.134	0.138	0.126	0.126	0.141	0.138	0.137	0.132	0.136	0.138
DGLOG	0.128	0.139	0.125	0.122	0.123	0.127	0.127	0.130	0.134	0.131	0.139	0.124
DGOPS	0.134	0.124	0.112	0.126	0.125	0.116	0.127	0.124	0.125	0.120	0.118	0.120
IND4T	0.120	0.122	0.125	0.118	0.124	0.123	0.109	0.114	0.110	0.109	0.109	0.120
AIDFS	0.123	0.113	0.114	0.120	0.123	0.117	0.120	0.117	0.109	0.123	0.116	0.111
DFINT	0.107	0.106	0.127	0.110	0.125	0.123	0.118	0.118	0.117	0.125	0.110	0.115
DGWRE	0.101	0.111	0.117	0.115	0.123	0.117	0.112	0.107	0.124	0.114	0.129	0.120

The second logarithmic normalization is calculated in Table 17.

Table 17. Second Logarithmic Normalization.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.158	0.148	0.146	0.152	0.910	0.150	0.147	0.153	0.144	0.147	0.144	0.153
EPAYS	0.130	0.136	0.134	0.138	0.885	0.126	0.141	0.138	0.137	0.132	0.136	0.138
DGLOG	0.128	0.139	0.125	0.122	0.862	0.127	0.127	0.130	0.134	0.131	0.139	0.124
DGOPS	0.134	0.124	0.112	0.126	0.874	0.116	0.127	0.124	0.125	0.120	0.118	0.120
IND4T	0.120	0.122	0.125	0.118	0.871	0.123	0.109	0.114	0.110	0.109	0.109	0.120
AIDFS	0.123	0.113	0.114	0.120	0.863	0.117	0.120	0.117	0.109	0.123	0.116	0.111
DFINT	0.107	0.106	0.127	0.110	0.877	0.123	0.118	0.118	0.117	0.125	0.110	0.115
DGWRE	0.101	0.111	0.117	0.115	0.858	0.117	0.112	0.107	0.124	0.114	0.129	0.120

Afterwards, Heron matrix is created. This matrix for $\theta$ with 0.5 are illustrated in Table 18.

Table 18. Heron Matrix $(\theta =0.5).$

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.158	0.148	0.146	0.152	0.432	0.150	0.147	0.153	0.144	0.147	0.144	0.153
EPAYS	0.130	0.136	0.134	0.138	0.420	0.126	0.141	0.138	0.137	0.132	0.136	0.138
DGLOG	0.128	0.139	0.125	0.122	0.409	0.127	0.127	0.130	0.134	0.131	0.139	0.124
DGOPS	0.134	0.124	0.112	0.126	0.415	0.116	0.127	0.124	0.125	0.120	0.118	0.120
IND4T	0.120	0.122	0.125	0.118	0.413	0.123	0.109	0.114	0.110	0.109	0.109	0.120
AIDFS	0.123	0.113	0.114	0.120	0.410	0.117	0.120	0.117	0.109	0.123	0.116	0.111
DFINT	0.107	0.106	0.127	0.110	0.416	0.123	0.118	0.118	0.117	0.125	0.110	0.115
DGWRE	0.101	0.111	0.117	0.115	0.407	0.117	0.112	0.107	0.124	0.114	0.129	0.120

Next, Heron matrix is multiplied by the weights of factors. The weighted heron matrix is displayed in Table 19.

Table 19. Weighted Heron Matrix.

	ECOMM	DPAYS	INTSP	PRTRN	DGADV	IND40	DDINV	DGWRK	DDFOR	FINTE	CRCBD	DFACC
DRTRN	0.020	0.015	0.010	0.012	0.023	0.007	0.013	0.015	0.013	0.013	0.012	0.011
EPAYS	0.017	0.014	0.009	0.011	0.022	0.006	0.012	0.014	0.012	0.012	0.012	0.010
DGLOG	0.016	0.014	0.009	0.010	0.022	0.006	0.011	0.013	0.012	0.012	0.012	0.009
DGOPS	0.017	0.012	0.008	0.010	0.022	0.005	0.011	0.012	0.011	0.011	0.010	0.009
IND4T	0.015	0.012	0.008	0.010	0.022	0.006	0.010	0.011	0.010	0.010	0.009	0.009
AIDFS	0.016	0.011	0.008	0.010	0.022	0.005	0.011	0.011	0.009	0.011	0.010	0.008
DFINT	0.014	0.011	0.009	0.009	0.022	0.006	0.010	0.012	0.010	0.011	0.009	0.009
DGWRE	0.013	0.011	0.008	0.009	0.022	0.005	0.010	0.010	0.011	0.010	0.011	0.009

Afterwards, the totals of weighted heron values by benefit of cost factors for each strategy are calculated. The totals of strategies for relative effects of digital economy factors on inflation are exhibited in Table 20.

Table 20. Totals of Strategies.

	B	C
DRTRN	0.142	0.023
EPAYS	0.128	0.022
DGLOG	0.123	0.022
DGOPS	0.117	0.022
IND4T	0.110	0.022
AIDFS	0.111	0.022
DFINT	0.109	0.022
DGWRE	0.108	0.022

Finally, the scores of strategies for relative effects of digital economy factors on inflation are obtained. The results by p are summarized in Table 21.

Table 21. Scores by Various p Values.

	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
DRTRN	0.883	0.886	0.889	0.892	0.894	0.897	0.899	0.902	0.904	0.906	0.908
EPAYS	0.867	0.870	0.872	0.875	0.878	0.880	0.883	0.885	0.887	0.890	0.892
DGLOG	0.860	0.863	0.865	0.868	0.871	0.873	0.876	0.878	0.880	0.882	0.885
DGOPS	0.854	0.857	0.860	0.862	0.865	0.867	0.870	0.872	0.874	0.877	0.879
IND4T	0.846	0.849	0.851	0.854	0.857	0.859	0.862	0.864	0.866	0.868	0.871
AIDFS	0.846	0.849	0.852	0.855	0.857	0.860	0.862	0.865	0.867	0.869	0.871
DFINT	0.845	0.848	0.851	0.854	0.856	0.859	0.861	0.863	0.866	0.868	0.870
DGWRE	0.843	0.846	0.849	0.851	0.854	0.857	0.859	0.861	0.864	0.866	0.868

As can be inferred from the scores reported in Table 21, digital price transparency strategy and the expansion of digital payment systems emerge as the most appropriate policy responses to the relative effects of digital economy factors on inflation. This finding indicates that inflationary pressures in increasingly digitalized economies are not solely driven by traditional demand- or cost-based mechanisms, but are significantly shaped by information asymmetries, pricing behavior, and transaction infrastructures inherent in digital markets. Digital price transparency directly addresses inflation by constraining firms’ ability to engage in opportunistic pricing, reducing hidden markups, and intensifying competitive discipline through real-time price visibility, thereby anchoring inflation expectations. Similarly, the expansion of digital payment systems enhances the effectiveness of monetary policy transmission by improving transaction traceability, reducing informal economic activity, and allowing policymakers to monitor liquidity flows more accurately. Together, these mechanisms suggest that digital inflation is closely linked to how efficiently prices are formed and how smoothly money circulates within digital ecosystems. From a policy perspective, this result implies that inflation management strategies should prioritize regulatory frameworks that promote transparent digital pricing platforms, strengthen consumer access to price information, and encourage the widespread adoption of interoperable and secure digital payment infrastructures. Strategically, integrating digital price monitoring tools with central bank analytics, incentivizing cashless transactions, and harmonizing fintech regulations can enhance price stability and mitigate digitally driven inflationary risks in the medium and long term.

4.3. Sensitivity Analysis

Sensitivity analysis is applied to demonstrate the reliability of the results and to assess the robustness of the proposed model. In this context, calculations are conducted by comparing outcomes derived from alternative methodological approaches as well as from different values of the parameter p, allowing the evaluation of how sensitive the results are to changes in modeling assumptions. This approach enables the identification of potential instabilities or parameter-driven distortions in the rankings and weight distributions. The consistency of results across different methods and p values indicates that the model produces stable and dependable outcomes, thereby strengthening its methodological validity and supporting the credibility of the empirical findings.

To further validate the proposed attention-based expert weighting mechanism, additional robustness and comparative analyses are incorporated into the study. Specifically, the results are evaluated across different parameter values and alternative decision-making frameworks, including ARLON, RAM, and TOPSIS methods. The consistency of the obtained rankings across these different approaches demonstrates that the findings are not sensitive to the choice of method and confirms the stability of the results. Moreover, the attention-based weighting approach provides an additional advantage by incorporating consensus structure, behavioral consistency, and outlier sensitivity, which are not simultaneously captured in conventional equal-weight or simple aggregation techniques. Therefore, rather than replacing existing methods, the proposed approach enhances expert aggregation by providing a more data-driven and structurally informed weighting mechanism. The comparative results are presented in Table 22.

Table 22. Comparative Results.

p	2			3			1.262
Model	ARLON	RAM	TOPSIS	ARLON	RAM	TOPSIS	ARLON	RAM	TOPSIS
DRTRN	0.899	1.458	1.000	0.900	1.458	1.000	0.900	1.458	1.000
EPAYS	0.881	1.456	0.569	0.882	1.455	0.570	0.881	1.456	0.569
DGLOG	0.873	1.455	0.474	0.875	1.454	0.473	0.873	1.455	0.474
DGOPS	0.867	1.453	0.395	0.870	1.453	0.395	0.867	1.453	0.395
IND4T	0.857	1.452	0.219	0.862	1.452	0.217	0.856	1.452	0.219
AIDFS	0.858	1.452	0.243	0.863	1.452	0.243	0.857	1.452	0.242
DFINT	0.856	1.452	0.176	0.862	1.452	0.178	0.856	1.452	0.175
DGWRE	0.853	1.452	0.156	0.859	1.452	0.157	0.853	1.452	0.157
p	1.585			0.631
Model	ARLON	RAM	TOPSIS	ARLON	RAM	TOPSIS
DRTRN	0.899	1.458	1.000	0.897	1.458	1.000
EPAYS	0.881	1.456	0.569	0.880	1.455	0.569
DGLOG	0.873	1.455	0.474	0.873	1.454	0.473
DGOPS	0.866	1.454	0.395	0.867	1.453	0.393
IND4T	0.856	1.452	0.219	0.859	1.452	0.218
AIDFS	0.857	1.452	0.243	0.860	1.452	0.241
DFINT	0.855	1.452	0.175	0.859	1.452	0.175
DGWRE	0.852	1.452	0.156	0.857	1.452	0.157

According to Table 22, the rankings of strategies for the relative effects of digital economy factors on inflation remain identical across all values of p. This result clearly demonstrates that the proposed model exhibits strong robustness under varying parameter settings and that the prioritization of strategies is not influenced by changes in the model’s sensitivity structure. Such stability implies that the decision-making framework captures the intrinsic relationships between digital economy factors and inflation rather than reflecting parameter-dependent or method-specific biases. From a validation perspective, the invariance of rankings across different p values confirms that the model produces consistent and reliable outputs even under alternative scenarios and assumptions. This robustness enhances the internal validity of the analysis and strengthens confidence in the empirical findings. Moreover, the consistency of strategic rankings suggests that the identified policy and strategic recommendations are resilient to model variation, increasing their applicability and usefulness for policymakers and practitioners seeking to address inflationary challenges in digitalized economic environments.

5. Discussion

One of the most effective criteria in examining the relative effects of digital economy factors on inflation is e-commerce penetration. E-commerce sites allow consumers to track prices instantly and compare prices. This increases competition between prices, thereby limiting price increases. Indeed, Mućk et al. (2025) examined the effect of e-commerce penetration on inflation in their study. The study, conducted on twenty-five economies, stated that the increasing popularity of e-commerce is effective in curbing inflation. In another similar study, Liu et al. (2025) analyzed the impact of digital inclusive finance on e-commerce. The study stated that digitalization is occurring more rapidly in developed countries and that the use of these systems suppresses inflation. In another study, Popescu et al. (2025) indicated that the development of e-commerce applications is a revolution in terms of supply and demand. The study provided a sector-based analysis and examines supply dynamics. Finally, Sak et al. (2025) pointed out that digital economy applications can be implemented at a lower cost compared to traditional economic applications. This situation will also have a downward effect on inflation.

Digital price transparency is one of the most effective strategies for examining the relative effects of digital factors on inflation. Price transparency allows consumers to compare the prices of the same goods or services across different sellers (Berends & Gerpott, 2025). The fact that prices set for the same product are tracked instantly by consumers brings prices closer together. This reduces price differences for the same product and strengthens price stability. Indeed, Asmyatullin and Glavina (2025) stated in their study that digitalization is important in terms of sustainable development. The study indicates that digitalization brings prices closer together, thereby aligning economic indicators and providing stabilization. In another similar study, Sun (2025) argued that digital finance supports economic growth in Latin American countries. The study noted that digital payment tools and digital performance are important in ensuring economic stability. Finally, Kabashkin et al. (2025) highlighted that token-based payment systems standardize heterogeneous services in the aviation sector. These payment systems were described as a fair token across various service types.

The findings of this study provide several concrete policy implications for managing inflation in increasingly digitalized economies. First, policymakers should prioritize regulatory frameworks that enhance price transparency across digital platforms, as this mechanism directly constrains opportunistic pricing behavior and strengthens competitive discipline. Second, the expansion of secure and interoperable digital payment systems should be supported, as these systems improve monetary policy transmission and enable more effective monitoring of liquidity flows. Third, regulatory oversight of large e-commerce platforms is essential to prevent market concentration and algorithm-driven pricing practices that may offset the deflationary benefits of digital competition. In addition, integrating real-time digital price monitoring tools into central bank policy frameworks can enhance early detection of inflationary pressures. Finally, coordinated policies that simultaneously address digital consumption dynamics and financial inclusion are necessary to balance short-term demand-side inflationary effects with long-term efficiency gains. These implications highlight that effective inflation management in the digital era requires not only traditional macroeconomic tools but also targeted digital economy policies.

It should be explicitly noted that the findings of this study are derived from expert-based evaluations rather than direct empirical analysis of inflation time series or macroeconomic datasets. Therefore, the results reflect the perceived relative importance of digital economy factors rather than statistically verified causal effects. However, this does not reduce the relevance of the findings; instead, it provides a structured interpretation of expert knowledge in a complex and evolving domain where comprehensive empirical data may be limited or lagging. Moreover, the identified priority factors, such as e-commerce penetration and digital payment systems, are consistent with existing empirical studies highlighting their influence on price formation, consumption dynamics, and monetary transmission mechanisms. In this respect, the results can be interpreted as forward-looking indicators that complement empirical findings and provide valuable insights for understanding emerging inflation dynamics in digitalized economies.

Although the proposed framework is based on expert evaluations rather than direct macroeconomic observations, the prioritization results can serve as a complementary analytical layer for future empirical research. In particular, the identified priority factors, such as e commerce penetration and digital payment systems, may be empirically examined through panel data models, structural equation approaches, or time series analyses using inflation indicators, digital economy indices, and monetary variables across countries. Therefore, the current study should not be interpreted as a substitute for empirical inflation analysis, but rather as a structured decision support framework that helps identify and prioritize the most relevant digital economy dimensions requiring empirical verification. Future studies may integrate the proposed fuzzy decision-making framework with real macroeconomic datasets to test the consistency of expert-based prioritizations under different economic environments and regulatory contexts.

Although some of the identified key factors, such as e-commerce penetration and digital payment systems, may appear intuitive at a general level, the contribution of the proposed methodological framework lies in its ability to quantify, validate, and structurally prioritize these factors within a complex and multidimensional decision environment. Unlike simpler analytical approaches, the integrated model captures nonlinear uncertainty through generalized fractal fuzzy sets, accounts for heterogeneity and behavioral consistency in expert evaluations via the attention-based weighting mechanism, and systematically evaluates the relative influence of each factor using objective weighting techniques. This enables the identification of not only which factors are important, but also the degree of their importance, their robustness across different parameter settings, and their interaction within a broader system of digital economy dynamics. Therefore, the methodological complexity provides deeper analytical insights by transforming intuitive assumptions into empirically structured, validated, and policy-relevant findings that could not be reliably obtained through conventional or simplified methods.

6. Conclusions

This study aimed to identify which digital economy factors exert stronger influences on inflation and to determine effective strategies for managing digitally driven inflationary pressures. To achieve this objective, a novel decision-making framework integrating artificial intelligence techniques with fuzzy multi-criteria decision-making methods was developed. Based on expert evaluations, twelve digital economy criteria and eight policy strategies were analyzed using an attention-based expert weighting approach, MEREC for criterion weighting, and ARLON for strategy prioritization, while uncertainty was modelled through generalized fractal fuzzy sets. The analysis results indicate that e-commerce penetration and the prevalence of digital payment systems are the most influential digital economy factors affecting inflation, whereas digital price transparency and the expansion of digital payment systems emerge as the most effective strategies for inflation control. By systematically prioritizing digital economy factors and mitigation strategies, this study fills an important gap in the inflation literature and provides a robust, policy-oriented framework that enhances both methodological rigor and practical relevance.

Despite relying on an expert based analytical structure, the study contributes to the financial economics and risk management literature by providing a systematic framework for identifying emerging inflation-related risks associated with digital transformation. The proposed methodology is specifically designed to address the multidimensional and uncertain nature of digital economy inflation dynamics that cannot be adequately captured through simplified linear approaches alone. Rather than increasing methodological complexity for its own sake, the integrated framework combines expert weighting, uncertainty modeling, and objective prioritization techniques to improve analytical consistency and decision support capability in complex economic environments. In this respect, the study offers both a conceptual contribution by clarifying the transmission channels between digitalization and inflation and a methodological contribution by proposing a robust decision-making framework that can support future empirical and policy-oriented research.

Despite its contributions, this study has several theoretical and methodological limitations that should be acknowledged. First, the analysis relies on expert judgments, which, although systematically weighted through an attention-based approach, may still reflect subjective perspectives and contextual biases. Second, the proposed model focuses on a predefined set of digital economy factors and strategies, which may not fully capture all emerging dimensions of digitalization and their evolving impact on inflation. In addition, the generalized fractal fuzzy sets, while offering greater flexibility in modeling uncertainty, increase computational complexity and may limit the model’s accessibility for broader applications. Future research could address these limitations by incorporating larger and more diverse expert panels, integrating empirical macroeconomic data with expert-based decision models, and extending the proposed framework to dynamic or longitudinal settings. Furthermore, adapting the model to different country contexts or combining it with alternative weighting and ranking techniques may enhance its generalizability and contribute to a deeper understanding of digital inflation dynamics.

Another limitation of the study is related to the relatively limited size of the expert panel, which may affect the generalizability of the findings across different economic and institutional contexts. Although the participating experts were selected through purposive sampling to ensure substantial professional experience and diversity of perspectives, expert based evaluations may still involve subjective judgments, cognitive biases, and region-specific interpretations of digital economy dynamics. Experts may place greater emphasis on factors that are more visible within their professional or regional environments. Therefore, the prioritization results should be interpreted as structured expert perceptions rather than universally generalizable conclusions. Future studies may improve robustness by employing larger and more geographically diversified expert panels, Delphi based iterative consensus methods, stratified sampling approaches, or hybrid frameworks combining expert evaluations with empirical macroeconomic datasets. The findings of this study should be interpreted within the scope of an expert based decision-making framework. The reported rankings and priority levels do not constitute direct empirical verification of causal inflation drivers based on country level, panel, or time series data. Instead, they reflect structured expert assessments regarding the relative importance of digital economy factors and the effectiveness of related policy strategies. Therefore, the results provide a decision support perspective on digital inflation dynamics rather than definitive empirical evidence of causal relationships. Future studies may extend this framework by integrating country specific datasets and econometric analyses to empirically validate the relationships identified through expert evaluations.