Search Results (52)

The assessment of sustainable ecological carrying capacity (SECC) serves as a crucial scientific foundation for supporting high-quality urbanization, advancing ecological civilization, and achieving the strategic goals of the “Dual Carbon” initiative. However, existing assessment methods largely rely on subjective expert scoring, making them difficult to apply at the large-scale urban level; simultaneously, traditional fuzzy assessment frameworks lack effective mechanisms for representing uncertainty when dealing with objective panel data. This paper proposes a temporal-uncertainty-driven interval-valued Fermatean fuzzy set (TU-IVFFS) theoretical framework and integrates it with an improved decision-making trial and evaluation laboratory (DEMATEL), the method based on the removal effects of criteria (MEREC), and the measurement of alternatives and ranking according to compromise solution (MARCOS) approach to construct an integrated urban ecological carrying capacity assessment framework: TU-IVFF-DEMATEL-MEREC-MARCOS. Using panel data from 2021 to 2024 for 690 major Chinese cities (at the county-level-city level and above) as the sample, the analysis found that Beijing, Guangzhou, Shenzhen, Nanjing, and Chongqing ranked in the top five for SECC, while some small cities in the northeast and northwest ranked lower. Sensitivity analysis showed that the city rankings remained stable across the entire range of weight combination coefficients λ ∈ [0, 1], verifying the robustness of the proposed framework. This study provides a methodological breakthrough for the reproducible and generalizable assessment of urban ecological carrying capacity in large-scale samples. Full article

Selecting the right energy storage system (ESS) for grid integration is a high-stakes decision involving conflicting technical, economic, environmental, and risk criteria under deep uncertainty. The existing fuzzy multi-criteria decision-making (MCDM) methods either fail to capture neutral or abstaining expert judgments or treat evaluation criteria as independent, which is an unrealistic assumption in complex engineering decisions. To address both limitations simultaneously, this study develops four new aggregation operators by extending the Bonferroni mean (BM) into the q-rung picture fuzzy sets (q-RPFSs) framework: the q-RPFBM-based, q-RPFWBM-based, q-RPFGBM-based, and q-RPFWGBM-based operators. Unlike the existing q-RPFS operator families (Dombi, Frank, Fermatean, Yager, Maclaurin), which aggregate criteria independently, BM-based operators explicitly model pairwise interactions among criteria with a structurally distinct aggregation logic that is especially critical when criteria such as cost, risk, reliability, and environmental impact are mutually correlated. The theoretical validity of the operators is confirmed through proofs of idempotency, monotonicity, and boundedness. Applied to a comprehensive ESS selection problem for Türkiye (covering nine alternatives across nineteen sub-criteria and five main criteria, including an explicit risk dimension), the framework consistently identifies pumped hydro storage as the optimal choice. Sensitivity analyses under varying q, s, and t parameters, as well as perturbed criterion weights, confirm the robustness of this ranking. The proposed framework offers energy planners and decision-makers a principled and transparent tool for evaluating ESS under high uncertainty and criterion interdependence. Full article

This study presents an integrated Multi-Criteria Decision-Making (MCDM) approach to select the most suitable sustainable packaging for logistics operations under uncertainty. The aim of this study is to identify the most suitable eco-friendly packaging options for reducing packaging waste, by considering several criteria. The methodology combines the SWARA and TOPSIS methods within a Fermatean Fuzzy Set (FFS) framework to address the ambiguity in expert evaluations and the qualitative nature of decision-making criteria. The research considers various sustainable packaging alternatives, including recycled cardboard, recycled plastic, biodegradable plastic, and compostable plastic, while incorporating criteria such as production cost, environmental impact, reusability, and material specifications. The approach offers a robust and comprehensive decision-making tool for companies aiming to improve sustainability in their logistics operations while mitigating the environmental impact of packaging waste. The results demonstrate that the direct incorporation of fuzzy numbers notably influences the ranking outcomes compared to traditional methods, and comparing the considered approach with different MCDM methods yields various recommendations for sustainable packaging selection. Full article

Multi-criteria decision-making (MCDM) involves evaluating alternatives under uncertain, vague, and conflicting criteria. While fuzzy set theories, such as intuitionistic, pythagorean, fermatean, and q-rung orthopair fuzzy sets have advanced uncertainty modeling, they remain limited to capturing extreme judgments where membership reaches a value of one alongside significant non-membership. The recently introduced q-fractional fuzzy set (q-FrFS) addresses these shortcomings via a flexible constraint, making it suitable for extreme contexts. However, existing q-FrFS methodologies lack robust aggregation mechanisms capable of balancing trade-offs and modulating compensation during information fusion. To overcome this, this study proposes a novel class of Frank-based aggregation operators tailored specifically to q-FrFS environments. Leveraging the parameterized structure of Frank t-norms and t-conorms, we develop two operators: q-FrFFWA (Frank weighted averaging) and q-FrFFWG (Frank weighted geometric) alongside their essential algebraic properties. These operators enhance the representation and fusion of complex and uncertain data. Furthermore, we present a comprehensive MCDM framework utilizing the proposed operators and demonstrate its applicability by selecting optimal vehicle routing software for last-mile delivery. Sensitivity and comparative analyses affirm the stability and credibility of the proposed methodology. This research contributes to the evolving landscape of fuzzy decision-making by integrating the expressive power of q-FrFS with the adaptive flexibility of Frank aggregation, offering a potent tool for modeling and analyzing multidimensional uncertainties in complex decision environments. Full article

Scientific planning and optimal development of multi-type power sources are critical prerequisites for supporting the robust evolution of emerging power systems. However, existing techno-economic evaluation methods often face challenges such as higher-order uncertainty and weight conflicts, making it difficult to provide reliable support for comparing and selecting power source schemes. To address this, this paper proposes an improved Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on Fermatean Fuzzy Sets (FFS) for techno-economic evaluation of multi-type power sources. First, building on the traditional TOPSIS framework, we introduce Fermatean Fuzzy Sets to construct a FF Hybrid Weighted Distance (FFHWD) measure. This measure simultaneously captures the subjective importance of evaluation indicators and decision-makers’ risk preferences. Second, we design a subjective-objective coupled weighting strategy integrating Fuzzy Analytic Hierarchy Process (FAHP) and Entropy Weight Method (EWM) to achieve dynamic weight balancing, effectively mitigating biases caused by single weighting approaches. Finally, the FFHWD is integrated into the improved TOPSIS framework by defining FF positive and negative ideal solutions. The comprehensive closeness coefficients of each power source scheme are calculated to enable robust ranking and optimal selection of multi-type power source alternatives. Empirical analysis of five representative power generation technologies—thermal power, hydropower, wind power, photovoltaics (PV), and energy storage—demonstrates the following comprehensive techno-economic ranking: hydropower > photovoltaics > thermal power > wind power > energy storage. Hydropower achieves the highest closeness coefficient (−0.4198), whereas energy storage yields the lowest value (−2.8704), effectively illustrating their respective advantages and limitations within the evaluation framework. This research provides scientific decision-making support and methodological references for optimizing multi-type power source configurations and planning new power systems. Full article

Medicine and vaccine supply chains in Nigeria are socio-technical systems exposed to persistent uncertainty and disruption. Existing studies rarely integrate systems thinking with uncertainty-aware decision tools to jointly prioritize challenges and policy responses. This study asks which policy mix most effectively strengthens these supply chains while balancing multiple, conflicting criteria and stakeholder judgments. We develop a two-stage Fermatean fuzzy framework that first weights 35 challenges using Fermatean Fuzzy Stepwise Weight Assessment Ratio Analysis (FF-SWARA) and then ranks four policy alternatives via Fermatean Fuzzy VIšeKriterijumska Optimizacija I Kompromisno Resenje (FF-VIKOR), based on expert elicitation and linguistic assessments. Results identify interruption of drug supplies, limited vaccine funding, cold-chain potency loss, human resource shortages, and product damage as the most critical challenges. FF-VIKOR prioritizes Effective Implementation of Existing Policies as the best alternative, followed by Improving Access to Medicines and Vaccines, indicating that governance quality and access-enabling infrastructure are complementary levers for resilience. To further enhance robustness, we embed the VIKOR outcomes into a policy-oriented game-theoretic analysis, where strategic weighting scenarios (e.g., cost-focused, infrastructure-driven, human-capital focused) interact with policy choices. The equilibrium results reveal that a mixed strategy combining Effective Implementation of Existing Policies and Strengthening Distribution and Storage Systems guarantees the best compromise performance across adversarial scenarios. The proposed framework operationalizes systems thinking for uncertainty-aware and strategically robust policy design and can be extended with real-time data integration, scenario planning, and regional replication to guide adaptive supply chain governance. Full article

The concept of Multi Q-Fermatean hesitant fuzzy soft sets (MQFHFSS), derived from the integration of multi-Q fuzzy soft sets and Fermatean hesitant fuzzy sets, can be applied in practice to optimise the resolution of complex multi-criteria decision-making problems. The method exceeds traditional approaches such as Fermatean hesitant fuzzy sets, fuzzy soft sets, and Pythagorean fuzzy sets in enhancing the ability to capture higher levels of uncertainty, hesitation, and symmetry in multi-criteria evaluations, thereby supporting more balanced judgments in complex decision-making situations. In this study, we investigate the novel MQFHFSS concept along with the associated operations. The fundamental characteristics of aggregation operators derived from MQFHFSS have been examined to address some complex decision-making issues. Moreover, we discuss some key algebraic features and their different cases, emphasizing the role of symmetry under the influence of MQFHFSS. Finally, we illustrate some numerical examples and solve the real-world decision-making problem by using the proposed technique. Full article

To assist stakeholders in selecting appropriate social media influencers (SMIs), this study proposes a multi-attribute decision-making framework for influencer evaluation based on their key performance metrics and engagement characteristics. This study introduces a new modification of the Evaluation Based on Distance from Average Solution (EDAS) under an interval-valued Fermatean fuzzy (IVFF) environment, addressing the limitations of the conventional EDAS method. In addition, a conceptual framework for the static and dynamic evaluation of SMIs is developed, integrating various crisp and fuzzy multi-criteria decision-making (MCDM) approaches. Empirical validation through two practical case studies demonstrates the effectiveness and applicability of the proposed framework, resulting in recommendations for marketers seeking to optimize their influencer-based marketing strategies. Full article

Multidimensional clustering of large-scale multi-view data is an important topic because it makes possible to combine a variety of manifestations of a complex information set. Nevertheless, comparing and selecting the most suitable deep clustering method is not an easy task, especially when several opposing criteria are applied. Multi-criteria decision-making (MCDM) techniques provide systematic approaches to making such judgments, although they are often limited in their ability to handle uncertainty, imprecise judgments, and interdependencies in practice. To solve these problems, this paper suggests a circular Fermatean fuzzy technique order preference by similarity to ideal solution (CFF-TOPSIS) method, which combines improved fuzzy modeling with MCDM to make the decision-making process accurate and sound. By exploiting the intrinsic symmetry of TOPSIS, where distances to positive and negative ideal solutions are treated symmetrically, the proposed model integrates five evaluation criteria for assessing clustering adequacy, including clustering accuracy, scalability, computational complexity, robustness, and interpretability, to critically evaluate five alternative clustering methods based on the input of three decision-makers. This measurement is performed efficiently by the CFF-TOPSIS method based on the uncertainty and subjective judgment contained within circular Fermatean fuzzy sets (CFFSs). The model is reliable and superior to existing models, as confirmed by sensitivity and comparative analyses. The suggested approach provides a systematic and flexible method for making decisions in complex big-data settings, while maintaining symmetry in the evaluation of alternatives and criteria. Full article

Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm $\left(D_{tn}\right)$- and Dombi t-conorm $\left(D_{tcn}\right)$-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi’s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab. Full article

The impact of alternative distribution channels, such as bank Automated Teller Machines (ATMs), on the financial industry is growing due to technological advancements. Investing in ideal locations is critical for new ATM companies. Due to the many factors to be evaluated, this study addresses the problem of determining the best location for ATMs to be deployed in Istanbul districts by utilizing the multi-criteria decision-making framework. Furthermore, the advantages of fuzzy logic are used to convert expert opinions into mathematical expressions and incorporate them into decision-making processes. For the first time in the literature, a model has been proposed for ATM location selection, integrating clustering and the interval-valued Fermatean fuzzy analytic hierarchy process (IVFF-AHP). With the proposed methodology, the districts of Istanbul are first clustered to find the risky ones. Then, the most suitable alternative location in this district is determined using IVFF-AHP. After deciding the ATM locations with IVFF-AHP, in the last step, a Double Deep Q-Network Reinforcement Learning model is used to optimize the Cash in Transit (CIT) vehicle route. The study results reveal that the proposed approach provides stable, efficient, and adaptive routing for real-world CIT operations. Full article

This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neutrosophic vague soft set (FNVSS), an advanced extension that integrates the concepts of neutrosophic sets with Fermatean membership functions into the framework of vague sets. The FNVSS model enhances the representation of truth, indeterminacy, and falsity degrees, providing greater flexibility and resilience in capturing ambiguous and imprecise information. We systematically develop new operations for the FNVSS, including union, intersection, complementation, the Fermatean neutrosophic vague normalized weighted average (FNVNWA) operator, the generalized Fermatean neutrosophic vague normalized weighted average (GFNVNWA) operator, and an adapted Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. To demonstrate the practicality of the proposed methodology, we apply it to a solar panel selection problem, where managing uncertainty is crucial. Comparative results indicate that the FNVSS significantly outperforms traditional fuzzy and vague set approaches, leading to more reliable and accurate decision outcomes. This work contributes to the advancement of predictive decision-making systems, particularly in fields requiring high precision, adaptability, and robust uncertainty modeling. Full article

This paper aims to effectively tackle decision-making problems on interval-valued Fermatean fuzzy sets; the current research suggested an integrated approach based on the WASPAS method. The criteria weights were determined by combining the objective weights obtained by the similarity measure approach with the subjective weights provided by decision-makers. This combination made achieving more realistic weights possible. Interval-valued Fermatean fuzzy sets were subjected to improved scoring functions and novel similarity measures concerning objective and subjective weights. The application of green supply chain management is discussed to show that the created approach fully applies to multi-criteria decision-making issues in the actual world. Green supply chain management was examined using critical success factors to control and audit enterprises’ processes as a numerical example of the developed method. In the examinations, it was seen that the companies implementing the selected GSC applications achieved close results and thus acted appropriately to the situation. To validate the stability of the developed technique, this study also includes a sensitivity analysis utilizing different weights of criterion and different values of the method’s parameters. According to the investigation, merging subjective and objective weights enhanced the method’s stability created with different criteria weights. The outcomes of the approach developed here were compared with those of other approaches previously put forth in the literature to assess its performance accurately. Full article

To aid in the selection of generative artificial intelligence (GAI) chatbots, this paper introduces a fuzzy multi-attribute decision-making framework based on their key features and performance. The proposed framework includes a new modification of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), adapted for an interval-valued hesitant Fermatean fuzzy (IVHFF) environment. This TOPSIS extension addresses the limitations of classical TOPSIS in handling complex and uncertain data capturing detailed membership degrees and representing hesitation more precisely. The framework is applicable for both static and dynamic evaluations of GAI chatbots in crisp or fuzzy assessments. Results from a practical example demonstrate the effectiveness of the proposed approach for comparing and ranking GAI chatbots. Finally, recommendations are provided for selecting and implementing these conversational agents in various applications. Full article

This study introduces a multi-criteria decision-making (MCDM) framework for optimizing multi-energy network scheduling (MENS). As energy systems become more complex, the need for adaptable solutions that balance consumer demand with environmental sustainability grows. The proposed approach integrates conventional and alternative energy sources, addressing uncertainties through fermatean fuzzy sets (FFS), which enhances decision-making flexibility and resilience. A key component of the framework is the use of stochastic optimization and cooperative game theory (CGT) to ensure efficiency and reliability in energy systems. To evaluate the importance of various scheduling criteria, the study applies the logarithmic percentage change-driven objective weighing (LOPCOW) method, offering a systematic way to assign weights. The weighted aggregated sum product assessment (WASPAS) method is then used to rank potential solutions. The hybrid scheduling alternative, combining distributed and centralized solutions, stands out as the best alternative, significantly improving resource optimization and system resilience. While implementation costs may increase, the hybrid approach balances flexibility and rigidity, optimizing resource use and ensuring system adaptability. This work provides a comprehensive framework that enhances the efficiency and sustainability of energy systems, helping decision-makers address fluctuating demands and renewable energy integration challenges. Full article