Identification and Analysis of Earthquake Risks in Worn-Out Urban Fabrics Using the Intuitionistic Fuzzy Brainstorming (IFBS) Technique for Group Decision-Making

Abstract

This study seeks to advance group decision-making in project management by introducing a hybrid intuitionistic fuzzy brainstorming (IFBS) method tailored for identifying and assessing earthquake risks in worn-out urban fabrics in Iran. By integrating the collaborative ideation of brainstorming with intuitionistic fuzzy sets (IFSs), the IFBS method effectively addresses uncertainties inherent in expert judgments, providing a robust and systematic framework for risk prioritization. Expert opinions, captured as linguistic variables, were transformed into triangular intuitionistic fuzzy numbers using a 5-point Likert scale measurement, enabling precise numerical analysis of 11 identified earthquake risks. Compared to the PMBOK-based qualitative analysis, the IFBS method demonstrates superior accuracy and granularity in risk assessment, as evidenced by its ability to model complex uncertainties and prioritize risks effectively. This study contributes a novel, scalable decision-making tool that enhances precision in urban risk management, offering practical implications for project managers and researchers tackling natural disaster risks. Its primary novelty lies in the innovative combination of IFSs with brainstorming, creating a scientific guide for managing earthquake vulnerabilities in worn-out urban fabrics. This approach not only improves decision-making outcomes but also sets a foundation for future research in hybrid fuzzy methodologies for disaster resilience.

1. Introduction

The rapid advancement of science and technology has profoundly influenced industries, economies, and project management, introducing complexities that challenge decision-making processes. Stakeholders frequently encounter difficulties in making informed choices due to the intricate nature of topics, expansive organizational and operational scopes, and diverse management dynamics [1]. While simple decisions may be straightforward, complex scenarios often demand more robust approaches, as individual expertise may be insufficient to address specialized or multifaceted issues. In such cases, group decision-making emerges as an effective strategy, leveraging collective knowledge to navigate ambiguity and uncertainty.

Group decision-making encompasses various methodologies, including the Delphi method [2], fuzzy Delphi [3,4], brainstorming, and intuitionistic fuzzy brainstorming [5]. Brainstorming, a widely adopted collective approach, fosters the generation of innovative ideas through structured group interactions, guided by specific rules to encourage creativity [6]. Participants collaboratively propose and discuss solutions to specific problems, aiming to reach a consensus [7]. Brainstorming techniques vary, encompassing traditional, face-to-face, and electronic formats [8]. However, despite its widespread use, brainstorming faces challenges due to real-world uncertainties, human cognitive biases, and incomplete data, necessitating advanced methods to enhance decision accuracy.

To address these uncertainties, fuzzy set theory, introduced by Zadeh [9], provides a powerful framework. Unlike classical sets, fuzzy sets allow for graded membership within the interval [0, 1], effectively modeling phenomena with ambiguous parameters [10]. Intuitionistic fuzzy sets (IFSs), an extension proposed by Atanassov [11], further refine this approach by incorporating degrees of membership (μ(x)) and non-membership (γ(x)), offering a nuanced representation of uncertainty. These methods have proven effective across scientific domains, particularly in tackling complex and ambiguous problems [12]. Recent research has advanced fuzzy techniques, with innovations such as the M-TOPSIS method for fuzzy decision-making [13] and intuitionistic fuzzy approaches for transportation problems [14]. Additionally, fuzzy methods have been applied in project and risk management, such as assessing urban earthquake vulnerability using the Analytical Hierarchy Process (AHP) and fuzzy AHP [15,16]. Overall, intuitionistic fuzzy theory is significantly more effective and comprehensible in addressing ambiguities and uncertainties than traditional fuzzy approaches, as it incorporates the features of intuitionistic fuzzy sets in three dimensions. Assessment in logic both methods discussed are convertible; nevertheless, with intuitionistic fuzzy logic, the degree of uncertainty over the accuracy of the propositions renders intuitionistic fuzzy logic distinctly apparent.

Despite the efficacy of these approaches, many project and risk management studies overlook the inherent uncertainties in decision-making processes [17,18,19,20]. Intuitionistic fuzzy sets address this gap by explicitly accounting for ambiguity, enhancing project management outcomes’ precision. The choice of methodology depends on contextual factors, and uncertainties in expert assessments remain a challenge. Incorporating incomplete or uncertain data into decision-making processes is critical, as is mitigating errors from human cognitive biases. Hybrid models, combining artificial intelligence, fuzzy theory, and intuitionistic fuzzy sets, offer promising solutions by producing coherent, accurate, and comprehensible outcomes [21,22].

To overcome these challenges, there is a pressing need for advanced methodologies that can more effectively capture the nuances of uncertainty in group decision-making. This study proposes a hybrid intuitionistic fuzzy brainstorming (IFBS) method to address these shortcomings, integrating brainstorming with IFSs. This dual-parameter approach enables the IFBS method to capture the ambiguity and conflicting perspectives often encountered in group decision-making, particularly in risk assessment for projects such as earthquake vulnerability in urban areas. By combining the creative ideation of brainstorming with the rigorous uncertainty modeling of IFSs, the IFBS method enhances decision accuracy and robustness, significantly improving over previous fuzzy methods. The IFBS technique, based on triangular intuitionistic fuzzy logic, is outlined to demonstrate its application in evaluating and validating risk criteria. This study applies the IFBS approach to identify earthquake risks in worn-out urban fabrics, demonstrating its efficacy in improving decision-making precision and reliability in project and risk management.

The research framework of this study is outlined as follows: The second half of the paper examines the theoretical foundations and contextual background of the investigation. The third section clarifies the research methodology, and the techniques employed to conduct this study. The fourth portion delineates the research findings and the results of statistical analysis, whereas the concluding section provides conclusions and recommendations.

2. Literature Review

2.1. Decision-Making on Project Management Issues

Effective urban risk management and planning to mitigate the destructive impacts of natural disasters, such as earthquakes, and their resultant crises require specialized strategies tailored to the unique characteristics of urban environments [15]. Proactive preparedness, including the development of predetermined response plans, is critical for reducing earthquake risks and minimizing casualties [23]. Urban planning prioritizes reducing vulnerability to the destructive effects of earthquakes, particularly in worn-out urban fabrics, which are disproportionately susceptible due to their degraded physical and functional conditions [24]. Worn-out urban fabrics, characterized by aging, unstable buildings, narrow access paths, and traditional construction materials, often lack robust structural systems [16,25]. These areas typically house low-income communities that receive inadequate urban services and limited post-disaster support, exacerbating their vulnerability [26]. Key characteristics of these fabrics, such as old building stock, low-rise structures, and poor accessibility, amplify their exposure to earthquake hazards [27,28].

Recent advancements in urban risk management have introduced innovative methodologies to address these challenges, particularly for worn-out urban fabrics. The United Nations’ development program’s urban risk management and resilience strategy advocates for risk-informed decision-making, leveraging digital tools like Geographic Information Systems (GIS) and predictive analytics to enhance real-time risk assessment and urban planning. Swaris et al. [29] emphasized collaborative frameworks that integrate disaster risk reduction (DRR) and climate change adaptation (CCA), addressing governance challenges and stakeholder coordination to bolster urban resilience against earthquakes and climate-induced hazards. Additionally, Pu et al. [30] demonstrated the application of machine learning and optimization models in disaster response planning, enabling efficient resource allocation and evacuation strategies in dense urban settings. These modern approaches complement earlier strategies by incorporating data-driven insights and participatory planning to reduce vulnerability and enhance recovery.

The high population density, aging infrastructure, and substandard materials in worn-out urban fabrics necessitate focused crisis management and vulnerability assessments [31]. Identifying critical risk factors and their potential impacts is essential for effective planning. However, uncertainties in these factors, manifested as risks, complicate accurate probability estimation and impact assessment. Traditional risk analysis methods often provide rough estimations of occurrence and impact, failing to explicitly account for ambiguities and complexities [32,33]. This limitation can undermine planning reliability, particularly in dynamic urban environments.

Recent applications of intuitionistic fuzzy sets in urban risk management, such as those by Malibari et al. [34], integrate fuzzy-based decision support systems with deep learning to enhance cybersecurity in smart cities, addressing risks like data breaches that compound disaster vulnerabilities. Similarly, Gavurova et al. [35] proposed fuzzy risk assessment models for smart city components, supporting municipal decision-making during crises like pandemics. These advancements build on foundational fuzzy theories, offering multi-value logic models that improve the accuracy of risk analysis and decision-making.

The integration of intuitionistic fuzzy logic with collaborative techniques, such as brainstorming, further enhances urban risk management. For instance, the IFBS method combines collective ideation with rigorous uncertainty modeling to identify and prioritize earthquake risks in worn-out urban fabrics. Recent studies, such as Xia et al. [36], highlight the efficacy of AI-driven fuzzy models in optimizing emergency medical supplies scheduling, demonstrating the potential of hybrid approaches to manage urban risks under uncertainty. By incorporating stakeholder inputs and advanced computational tools, these methodologies ensure more reliable and resilient urban planning outcomes, minimizing human and economic losses in the face of earthquakes [37,38,39].

2.2. Brainstorming Technique and Intuitionistic Fuzzy Sets

Brainstorming, a widely adopted group decision-making technique, harnesses collective thinking and interaction to generate innovative ideas, facilitate decisions, or address complex problems. The effectiveness of brainstorming sessions hinges on the diversity of participant opinions, group coordination, and the processes employed to achieve desired outcomes [40]. While not always the optimal approach for idea generation, brainstorming seeks to produce a diverse array of solutions by fostering creativity, a key driver of organizational innovation and resilience in addressing challenges [41]. Despite its benefits, real-world decision-making often encounters practical limitations, such as inaccuracies and ambiguities in information, which constrain the generation and evaluation of ideas [27]. The primary challenge lies in managing the uncertainty and ambiguity experienced by group members during idea creation, evaluation, and problem-solving, particularly in complex domains like urban risk management.

Even with expert panels possessing significant scientific and professional expertise, traditional group decision-making methods, including brainstorming, are susceptible to human cognitive biases and ambiguities, ranging from routine to intricate issues [42,43,44,45]. Indeed, the accuracy of brainstorming outcomes is contingent upon the quality of input data, the depth of participant expertise, and the ability to manage ambiguities arising from human judgments. In complex decision-making scenarios, such as urban risk management, these ambiguities can lead to inconsistencies, necessitating advanced methodologies to enhance reliability. Fuzzy set theory, introduced by Bellman and Zadeh [46], addresses these challenges by employing a grading system to model ambiguity, improving computational precision in multi-criteria decision-making [47]. Subsequent research has applied fuzzy sets to diverse decision-making problems, including project and risk management [27]. However, traditional fuzzy methods face limitations when dealing with incomplete data or high levels of uncertainty, prompting the development of more robust frameworks.

To address these challenges, the IFS technique offers a robust framework for handling uncertainties [48,49,50]. IFSs have been effectively applied in multi-criteria decision-making across fields such as engineering, economics, and risk assessment [51,52,53]. Recent advancements have extended IFS applications to urban risk management, enhancing decision-making in complex urban environments. For instance, Malibari et al. [34] integrated IFSs with deep learning to develop decision support systems for smart city cybersecurity, mitigating risks like data breaches that exacerbate urban vulnerabilities during disasters. Similarly, Gavurova et al. [35] employed IFS-based models to support municipal risk assessments in smart cities, addressing crises like pandemics with greater precision.

Contemporary methodologies in urban risk management further augment the efficacy of group decision-making techniques like brainstorming. For example, Xia et al. [36] applied AI-driven intuitionistic fuzzy models to optimize emergency medical supplies scheduling, showcasing the potential of hybrid approaches to manage uncertainties in urban crises. These advancements complement traditional brainstorming by incorporating data-driven insights and computational intelligence, addressing structural, cultural, and economic complexities in urban environments.

The proposed IFBS method integrates the creative strengths of brainstorming with the analytical rigor of IFSs, offering a robust solution for decision-making in urban risk management. By capturing conflicting expert opinions and incomplete data, the IFBS method is particularly suited for assessing risks in worn-out urban fabrics vulnerable to earthquakes. This approach builds on foundational theories [46,54] while leveraging recent advancements in AI-driven decision support and collaborative frameworks [29,36]. The IFBS method provides a scientifically grounded, probabilistic framework to address ambiguities, ensuring more accurate and reliable outcomes in complex decision-making scenarios, such as urban resilience planning.

3. Research Methodology

This study presented a hybrid method of brainstorming and intuitionistic fuzzy theory for group decisions in project management. Hence, the proposed method was used to identify and analyze the risks of earthquakes in worn-out urban fabrics. Accordingly, the risks identified in the literature were reviewed during brainstorming sessions to determine the final risks. The numerical calculations of the risks were performed based on the intuitionistic fuzzy theory variables after the brainstorming team determined the descriptive expressions, which were then converted into a range of triangular intuitionistic fuzzy numbers. The results of the calculations were used to identify, evaluate, and finally prioritize the risks. Then, the brainstorming method and qualitative analysis were used to review and evaluate the risks to compare the accuracy and validity of the results of the proposed method. At this step, the risks were assessed according to the standard PMBOK method. The score of each risk was calculated by determining its scores in the qualitative method, the consensus of the experts of the brainstorming team, and the result of the qualitative analysis based on linguistic expressions. Finally, the main risks were identified and the results of the two methods were examined and compared. Figure 1 shows the overall research framework for this research.

3.1. Brainstorming Technique

Individual decision-making may not be effective in some specific cases because of the specialized or complicated issues and the lack of individual knowledge and skills, leading to challenges in dealing with problems and necessitating group interaction as an effective solution. There are different methods of group decision-making, one of which is the brainstorming technique developed by Osborn in 1939. In 1953, he provided a comprehensive and detailed description of creative problem-solving methods [55]. This method is a structured process of collecting data and sharing ideas during consecutive sessions, ultimately leading to group consensus. The proposed method follows the following four basic rules [56]:

• Presenting several ideas;
• No criticism of the ideas of others;
• Freedom in expression, participation, and proposing unreasonable or far-fetched ideas;
• Explaining, developing, and improving the existing ideas.

The brainstorming team usually includes 5 to 10 members who follow strict instructions to create ideas [57].

3.2. Fuzzy Set Theory and Intuitionistic Fuzzy Sets

Fuzzy logic was first introduced by Zadeh [9]. Fuzzy logic is a form of many-valued logic with graded membership of each member known as the degree of membership. There are expressions in many linguistic variables called vague, such as intelligence, harvest, and good. A theory of ambiguity must first identify the roots of ambiguity and the logic behind linguistic arguments, including ambiguous expressions, and finally explain the related intuitions. The fuzzy theory explains the ambiguity based on grading and comparative systems using degrees of accuracy [58]. Fuzzy sets were introduced by Zadeh [9]. The membership of each member in these sets is restricted to a closed interval of [0, 1], indicating the membership of each member in a graded set [9]. As a powerful tool, fuzzy sets perform well in describing phenomena influenced by ambiguous parameters and creating non-dual logical models. There is a fundamental concept of membership degrees μ:X → [0, 1] in this theory [10]. Intuitionistic fuzzy sets, introduced by Atanassov [11], are among the most important generalizations of fuzzy sets, expressing the membership in a set by two parameters equal to the degree of accuracy (μ(x)) and the degree of inaccuracy (γ(x)) [11]. A fuzzy set $A$ from the reference set X is defined as follows:

$$A=\left\{<x,{\mu }_A(x)>\mid x\in \mathrm{X}\right\}$$

In which ${\mu }_{A^{\prime }}:X\to [0, 1]$ represents the membership function of $A$ fuzzy set and ${\mu }_A\left(x\right)\in [0, 1]$ indicates the membership degree of $x ϵ X$ in $A$ [59].

Also, an intuitionistic fuzzy set $A$ from reference set X is defined as follows:

$$A=\left\{<x,{\mu }_A(x),{\gamma }_A(x)>\mid x\in X\right\}$$

Functions ${\mu }_A$: X→ [0, 1] and ${\gamma }_A$: X→ [0, 1] are called membership functions if $0\le {\mu }_A\left(x\right)+{\gamma }_A\left(x\right)\le 1$, while ${\mu }_A\left(x\right)$ and ${\gamma }_A\left(x\right)$ that belong to the interval [0, 1] are known as the degree of membership and the degree of non-membership of X to A, respectively.

For each intuitionistic fuzzy set of A from X $=1-\left[{\mu }_A\left(x\right)+{\gamma }_A\left(x\right) \right]$ ${\pi }_A\left(x\right)$ represents the intuitionistic index of $x$ in A, which is in fact the uncertainty degree of $x$ in A. For each $x$ belonging to X, $0\le {\pi }_A\left(x\right)\le 1$ will be held [60,61,62].

3.3. Intuitionistic Fuzzy Brainstorming (IFBS) Technique

This technique is a hybrid method that uses intuitionistic fuzzy set theory to reach a consensus of expert opinions in brainstorming sessions during which the criteria are first examined and evaluated, followed by expressing the opinions of each expert on each criterion as a linguistic variable. Linguistic expressions can be at different ranges based on the field of work or the discretion of the experts. Each linguistic variable is initially considered an intuitionistic fuzzy number to reach a consensus of expert opinions. Confirmation or rejection of criteria or options is performed by the analysis of intuitionistic fuzzy numbers of experts’ opinions on each criterion and their defuzzification. This selection is based on a comparison of defuzzified numbers with a threshold. Finally, the criteria can be prioritized based on their defuzzified values.

Triangular Intuitionistic Fuzzy Numbers (TIFNs)

A triangular intuitionistic fuzzy number $\overline{a}$ is an intuitionistic fuzzy set on a set of real numbers $\mathrm{R}$ denoted by $TIFN\overline{a}=〈(a_1,a_2,a_3;{\mu }_{\overline{a}},{\gamma }_{\overline{a}})〉$. ${\mu }_{\overline{a}}$ and ${\gamma }_{\overline{a}}$ are the maximum and minimum membership degree and non-membership degree, respectively, on condition that $0\le {\mu }_{\overline{a}}\le 1$, $0\le {\gamma }_{\overline{a}}\le 1$, and $0\le {\mu }_{\overline{a}}+{\gamma }_{\overline{a}}\le 1$.

Moreover, ${\mu }_{\overline{a}}\left(x\right)+{\gamma }_{\overline{a}}\left(x\right)+{\pi }_{\overline{a}}\left(x\right)=1$ is held, in which ${\pi }_{\overline{a}}\left(x\right)$ is the intuitionistic index of element $x$ in $\overline{a}$. Figure 2 shows the triangular intuitionistic fuzzy number $TIFN\overline{a}$.

Definition 1. 

The membership and non-membership functions of the triangular intuitionistic fuzzy number $TIFN\overline{a}$ are defined as follows:

$${\mu }_{\overline{a}}\left(x\right)=\left\{\begin{array}{c}{\displaystyle \raisebox{1ex}{$\left(x-a_1\right){\mu }_{\overline{a}}$}\!\left/ \!\raisebox{-1ex}{$\left(a_2-a_1\right)$}\right.} if a_1\le x<a_2\\ {\mu }_{\overline{a}} if x=a_2\\ {\displaystyle \raisebox{1ex}{$\left(a_3-x\right){\mu }_{\overline{a}}$}\!\left/ \!\raisebox{-1ex}{$\left(a_3-a_2\right)$}\right.} if a_2<x\le a_3\\ 0 if x<a_1 or x>a_3\end{array}\right.$$

(1)

And

$${\gamma }_{\overline{a}}(x)=\left\{\begin{array}{c}{\displaystyle \raisebox{1ex}{$\left[a_2-\right.x+{\gamma }_{\overline{a}}(x-a_1)]$}\!\left/ \!\raisebox{-1ex}{$(a_2-a_1)$}\right.} if a_1\le x<a_2\\ {\gamma }_{\overline{a}} if x=a_2\\ \left[x\right.{-a}_2+{\gamma }_{\overline{a}}(a_3-x)]/(a_3-a_2) if a_2<x\le a_3\\ 1 if x<a_1 or x>a_3\end{array}\right.$$

(2)

$TIFN\overline{a}$ is positive and written in the form of $\overline{a}>0$ if $a_1\ge 0$ has one of the three values of $a_1$, $a_2$, or $a_3$ and is not equal to zero. Also, $TIFN\overline{a}$ is negative and written in the form of $\overline{a}<0$ if $a_3\le 0$ has one of the three values of $a_1$,$a_2$, or $a_3$ and is not equal to zero.

Definition 2. 

If $\overline{\mathrm{a}}=〈{\mathrm{a}}_1{,\mathrm{a}}_2{,\mathrm{a}}_3;{\mathsf{\mu }}_{\overline{\mathrm{a}}}{,\mathsf{\gamma }}_{\overline{\mathrm{a}}}〉$ and $\overline{\mathrm{b}}=〈{\mathrm{b}}_1{,\mathrm{b}}_2{,\mathrm{b}}_3;{\mathsf{\mu }}_{\overline{\mathrm{b}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}〉$ are two triangle intuitionistic fuzzy numbers $\left(TIF{N}_S\right)$, and $\beta$ is a real number, the arithmetic operators are as follows [49]:

$$\overline{\mathrm{a}}+\overline{\mathrm{b}}=〈\left({\mathrm{a}}_1{+\mathrm{b}}_1\right),\left({\mathrm{a}}_2+{\mathrm{b}}_2\right),\left({\mathrm{a}}_3+{\mathrm{b}}_3\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉$$

(3)

$$\overline{\mathrm{a}}-\overline{\mathrm{b}}=〈{(\mathrm{a}}_1-{\mathrm{b}}_3,{\mathrm{a}}_2-{\mathrm{b}}_2,{\mathrm{a}}_3-{\mathrm{b}}_1); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉$$

(4)

$$\overline{\mathrm{a}}\overline{\mathrm{b}}=\left\{\begin{array}{c}〈\left({\mathrm{a}}_1{\mathrm{b}}_1,{\mathrm{a}}_2{\mathrm{b}}_2,{\mathrm{a}}_3{\mathrm{b}}_3\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}>0 and \overline{\mathrm{b}}>0\\ 〈\left({\mathrm{a}}_1{\mathrm{b}}_3,{\mathrm{a}}_2{\mathrm{b}}_2,{\mathrm{a}}_3{\mathrm{b}}_1\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}<0 and \overline{\mathrm{b}}>0\\ 〈\left({\mathrm{a}}_3{\mathrm{b}}_3,{\mathrm{a}}_2{\mathrm{b}}_2,{\mathrm{a}}_1{\mathrm{b}}_1\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}<0 and \overline{\mathrm{b}}<0\end{array}\right.$$

(5)

$${\displaystyle \raisebox{1ex}{$\overline{\mathrm{a}}$}\!\left/ \!\raisebox{-1ex}{$\overline{\mathrm{b}}$}\right.}=\left\{\begin{array}{c}〈\left({\displaystyle \raisebox{1ex}{${\mathrm{a}}_1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_3$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_2$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_2$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_3$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_1$}\right.}\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}>0 and \overline{\mathrm{b}}>0\\ 〈\left({\displaystyle \raisebox{1ex}{${\mathrm{a}}_3$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_3$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_2$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_2$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_1$}\right.}\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}<0 and \overline{\mathrm{b}}>0\\ 〈\left({\displaystyle \raisebox{1ex}{${\mathrm{a}}_3$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_1$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_2$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_2$}\right.},{\displaystyle \raisebox{1ex}{${\mathrm{a}}_1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{b}}_3$}\right.}\right); \min \left\{{\mathsf{\mu }}_{\overline{\mathrm{a}}},{\mathsf{\mu }}_{\overline{\mathrm{b}}}\right\}, \max \left\{{\mathsf{\gamma }}_{\overline{\mathrm{a}}},{\mathsf{\gamma }}_{\overline{\mathrm{b}}}\right\}〉 if \overline{\mathrm{a}}<0 and \overline{\mathrm{b}}<0\end{array}\right.$$

(6)

$$\mathsf{\beta }\overline{\mathrm{a}}=\left\{\begin{array}{c} 〈\left(\mathsf{\beta }{\mathrm{a}}_1,\mathsf{\beta }{\mathrm{a}}_2,\mathsf{\beta }{\mathrm{a}}_3\right);{\mathsf{\mu }}_{\overline{\mathrm{a}}}{,\mathsf{\gamma }}_{\overline{\mathrm{a}}}〉 if \beta >0 \\ 〈\left(\mathsf{\beta }{\mathrm{a}}_3,\mathsf{\beta }{\mathrm{a}}_2,\mathsf{\beta }{\mathrm{a}}_1\right);{\mathsf{\mu }}_{\overline{\mathrm{a}}}{,\mathsf{\gamma }}_{\overline{\mathrm{a}}}〉 if \beta <0\end{array}\right.$$

(7)

$${\overline{\mathrm{a}}}^{-1}=〈\left({\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{a}}_3$}\right.},{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{a}}_2$}\right.},{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{a}}_1$}\right.}\right);{\mathsf{\mu }}_{\overline{\mathrm{a}}}{,\mathsf{\gamma }}_{\overline{\mathrm{a}}}〉$$

(8)

3.4. Intuitionistic Fuzzy Brainstorming (IFBS) Technique in Group Decisions to Select Options

The intuitionistic fuzzy brainstorming technique can be used to determine and select the main criteria. The steps to perform the IFBS procedure are as follows: (1) examining and selecting the criteria and determining their linguistic variables in brainstorming sessions; (2) selecting the appropriate range of intuitionistic fuzzy numbers to express linguistic variables; (3) intuitionistic fuzzification of criteria values based on the experts’ opinions resulting from brainstorming; (4) defuzzification of criteria values; (5) selection of a threshold for criteria confirmation or rejection; and (6) selection of criteria and group consensus. This method considers a suitable range of intuitionistic fuzzy numbers to express linguistic variables, which can vary in different methods. For example, the present study has used a 5-point Likert scale measurement to express the criteria.

Table 1. Triangular intuitionistic fuzzy numbers for 5-point Likert scale of measurement.

Triangular Intuitionistic Fuzzy Numbers	Intuitionistic Fuzzy Number	Linguistic Expressions
(0, 0, 0.25; 0.05, 0.90)	1	Very unimportant (VUI)
(0, 0.25, 0.5; 0.35, 0.6)	2	Unimportant (UI)
(0.25, 0.5, 0.75; 0.5, 0.4)	3	Moderately important (MI)
(0.5, 0.75, 1; 0.75, 0.2)	4	Important (I)
(0.75, 1, 1; 0.9, 0.05)	5	Critical (VI)

shows the 5-point Likert scale measurement for triangular intuitionistic fuzzy numbers.

This study used averaging triangular intuitionistic fuzzy numbers to collect expert opinions expressed as triangular intuitionistic fuzzy numbers. The meaning of triangular intuitionistic fuzzy numbers is calculated based on the following relations (Relations (9) and (10)):

$$\mathrm{F}\mathrm{i}={(a}_{1i},a_{2i},a_{3i})$$

(9)

$$f_{ave}={\displaystyle \frac{\sum a_1}{n}}, {\displaystyle \frac{\sum a_2}{n}}, {\displaystyle \frac{\sum a_3}{n}}$$

(10)

Then, according to the parameters of the intuitionistic fuzzy sets of the criteria (${\pi }_A\left(x\right), {\gamma }_A\left(x\right),{ \mu }_A\left(x\right))$, the upper and lower bounds of the criteria are calculated in Microsoft Excel software 2021 using the following relations:

$${\mathrm{L}=\mu }_A\left(x\right)$$

(11)

$${\mathrm{U}=(1-\gamma }_A\left(x\right))$$

(12)

$$\mathrm{U}-\mathrm{L}={\pi }_A\left(x\right)$$

(13)

In which ${\mu }_A\left(x\right)$, ${\gamma }_A\left(x\right)$, ${\pi }_A\left(x\right)$, L, and U indicate the degree of accuracy, the degree of inaccuracy, the degree of uncertainty, the lower bound, and the upper bound, respectively.

A threshold is defined as the median (M) distance of the upper and lower bounds for defuzzification. The following relations are used for defuzzification:

$$\mathrm{If} \mathrm{U}-\mathrm{L}>\mathrm{M},(\mathrm{U}+\mathrm{L})/2$$

(14)

$$\mathrm{If} \mathrm{U}-\mathrm{L} \le \mathrm{M},\mathrm{U}$$

(15)

In which U, L, M, and U−L indicate the upper bound, the lower bound, the median, and the distance between the upper and lower bounds, respectively. A threshold should be defined for the confirmation or rejection of criteria after the defuzzification of intuitionistic fuzzy numbers. This threshold is usually 0.7 but can vary depending on the type of research or field of work. Criteria are selected after a comparison of the defuzzified numbers of the criteria with the threshold. If these numbers are greater than the threshold, the criteria will be confirmed and otherwise rejected [63,64].

The brainstorming method, evolved beyond its traditional form, employs a structured and systematic approach by integrating specialized frameworks, such as risk breakdown structures (RBSs) and categorized risk groups, to optimize the identification and assessment of risks in complex scenarios like earthquake risk assessment in worn-out urban fabrics. To enhance the reliability of identified risks, the IFBS method incorporates a structured validation process for expert inputs, combining collaborative ideation with the analytical rigor of IFSs [54]. IFSs model uncertainties in expert opinions by assigning membership (μ(x)) and non-membership (γ(x)) degrees, along with a hesitancy parameter, thereby mitigating subjective biases and improving decision accuracy [48]. The validation process involves iterative expert feedback loops, cross-verification of risk assessments using weighted IFS evaluations, and alignment with predefined risk criteria, ensuring robust and consistent outcomes. By integrating these modern methodologies with structured brainstorming and IFSs, the IFBS method ensures reliable risk identification and evaluation, addressing the complexities of urban resilience planning while minimizing the impact of subjective variability in expert inputs.

While intuitionistic fuzzy sets handle uncertainty better than traditional fuzzy sets, the selection of membership and non-membership functions remain subjective. The defuzzification process may lead to information loss, reducing the precision of results. To address this, the proposed IFBS method integrates structured mechanisms to enhance reliability and precision in urban risk management, particularly for earthquake vulnerabilities in worn-out urban fabrics. The IFBS method mitigates subjectivity by employing a systematic validation process, including iterative expert feedback loops and cross-verification against predefined risk criteria, reducing reliance on subjective judgments [48,54]. To minimize information loss during defuzzification, this method uses advanced techniques like weighted aggregation, preserving the hesitancy parameter of IFSs, and incorporates iterative refinement to adjust fuzzy evaluations before final conversion [53]. Recent advancements, such as IFS-based risk models for smart city crises [35], support these approaches, enhancing decision-making accuracy. An IFS, by using its own parameters and logic and taking advantage of more degrees of freedom, has modeled ambiguities and uncertainties in the real world much better, which has led to higher accuracy outputs. While defuzzification may reduce granularity, it improves result interpretability, and ongoing research aims to further refine its accuracy [30].

Unlike standards like PMBOK, which rely on qualitative and quantitative analyses that may obscure uncertainties, the IFBS method explicitly models ambiguities, providing a foundation for precise, risk-informed decision-making. Indeed, qualitative analysis in these standards is the basis for semi-quantitative and quantitative analyses, which themselves demonstrate the validity of qualitative analyses in comparison with other analyses.

4. Results

4.1. Identification of Earthquake Risks in Worn-Out Urban Fabrics Using the IFBS Technique

The identification and selection of risks based on data and information received from analysis is a crucial stage in the domain of risk management. Any inaccuracies in these analyses present difficulties in the decision-making and risk management process, resulting in time delays and additional costs. The existing literature pertaining to the hazards associated with worn-out urban fabrics caused by earthquakes was initially subjected to meticulous examination to ascertain the potential risks. Subsequently, the technique of brainstorming was employed to screen the risks that had been identified. Accordingly, the experts expressed their opinions on the probability of 11 risks identified from the research literature in the form of linguistic variables to investigate and identify the risks of earthquakes in worn-out urban fabrics.

Table 2. Experts’ opinions based on linguistic variables.

#	Risk	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5
R1	Vulnerability caused by the type of structure	MI	I	I	MI	VI
R2	Vulnerability of infrastructure	UI	MI	VUI	I	MI
R3	Vulnerability due to old buildings	I	VI	MI	VI	I
R4	Lack of access to open space	VUI	MI	UI	MI	UI
R5	Vulnerability caused by the quality of the building	MI	I	MI	VI	I
R6	Building fire	I	UI	I	UI	MI
R7	Obstruction of roads	VI	I	MI	VI	I
R8	Explosion	VUI	MI	UI	VUI	UI
R9	Vulnerability due to environmental and structural conditions	MI	UI	MI	I	MI
R10	Vulnerability caused by non-compliance with construction material standards	I	MI	I	VI	I
R11	Vulnerability caused by aftershocks	VI	I	MI	I	I

indicates these linguistic variables. Then, these variables were then converted to intuitionistic fuzzy numbers based on a 5-point Likert scale of measurement.

Table 3. Triangular intuitionistic fuzzy numbers on a 5-point Likert scale of measurement.

Risk	Expert 1	Expert 2	Expert 3	Expert 4	Expert 5
R1	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.5, 0.75, 1; 0.75, 0.2)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.75, 1, 1; 0.9, 0.05)
R2	(0, 0.25, 0.5; 0.35, 0.6)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0, 0, 0.25; 0.05, 0.90)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)
R3	(0.5, 0.75, 1; 0.75, 0.2)	(0.75, 1, 1; 0.9, 0.05)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)
R4	(0, 0, 0.25; 0.05, 0.90)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0, 0.25, 0.5; 0.35, 0.6)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0, 0.25, 0.5; 0.35, 0.6)
R5	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)
R6	(0.5, 0.75, 1; 0.75, 0.2)	(0, 0.25, 0.5; 0.35, 0.6)	(0.5, 0.75, 1; 0.75, 0.2)	(0, 0.25, 0.5; 0.35, 0.6)	(0.25, 0.5, 0.75; 0.5, 0.4)
R7	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)
R8	(0, 0, 0.25; 0.05, 0.90)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0, 0.25, 0.5; 0.35, 0.6)	(0, 0, 0.25; 0.05, 0.90)	(0, 0.25, 0.5; 0.35, 0.6)
R9	(0.25, 0.5, 0.75; 0.5, 0.4)	(0, 0.25, 0.5; 0.35, 0.6)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)
R10	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.5, 0.75, 1; 0.75, 0.2)	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)
R11	(0.75, 1, 1; 0.9, 0.05)	(0.5, 0.75, 1; 0.75, 0.2)	(0.25, 0.5, 0.75; 0.5, 0.4)	(0.5, 0.75, 1; 0.75, 0.2)	(0.5, 0.75, 1; 0.75, 0.2)

shows the intuitionistic triangular fuzzy numbers of the 5-point Likert scale measurement for linguistic variables.

At this step, the opinions of experts about each risk were averaged from triangular intuitionistic fuzzy numbers, leading to a triangular intuitionistic fuzzy number for each risk. Intuitionistic fuzzy parameters of each risk were then calculated, the results of which are presented in

Table 4. Triangular fuzzy numbers and intuitionistic fuzzy parameters of the criteria.

Risk	a1	a2	a3	${\mathit{\mu }}_{\mathit{A}}\left(\mathit{x}\right)$	${\mathit{\gamma }}_{\mathit{A}}\mathit{\left(}\mathit{x}\mathit{\right)}$	${\mathit{\pi }}_{\mathit{A}}\left(\mathit{x}\right)$
R1	0.45	0.7	0.9	0.683	0.267	0.05
R2	0.25	0.45	0.65	0.45	0.45	0.1
R3	0.55	0.8	0.95	0.766	0.184	0.05
R4	0.1	0.3	0.55	0.32	0.63	0.05
R5	0.5	0.75	0.85	0.7	0.25	0.05
R6	0.25	0.5	0.75	0.5	0.4	0.1
R7	0.55	0.8	0.95	0.77	0.18	0.05
R8	0.05	0.2	0.45	0.233	0.717	0.05
R9	0.35	0.6	0.85	0.6	0.35	0.05
R10	0.5	0.75	0.95	0.733	0.217	0.05
R11	0.5	0.75	0.95	0.733	0.217	0.05

.

In the final step, the upper and lower bounds of the intuitionistic fuzzy parameters were calculated and defuzzified, followed by the comparison of the resulting numbers with the threshold, identification (selection) of risks, and their prioritization. Given the sensitivity of earthquake events, a threshold of 0.5 was considered in this study to identify (select) more important risks.

Table 5. Scores of risks and their identification (selection/confirmation or rejection).

Risk	L	U	Defuzzy	Result
R1	0.683	0.733	0.733	Confirmation
R2	0.45	0.55	0.5	Confirmation
R3	0.766	0.816	0.816	Confirmation
R4	0.32	0.37	0.370	Rejection
R5	0.7	0.75	0.750	Confirmation
R6	0.5	0.6	0.550	Confirmation
R7	0.77	0.82	0.820	Confirmation
R8	0.233	0.283	0.283	Rejection
R9	0.6	0.65	0.650	Confirmation
R10	0.733	0.783	0.783	Confirmation
R11	0.733	0.783	0.783	Confirmation

shows the results of this step.

According to Table 5, risks 7 and 3 had the highest score and probability of risk with scores of 0.82 and 0.816, respectively, while criteria 8 had the lowest score and probability of risk with a score of 0.283. Of the 11 risks studied, numbers 4 and 8 were rejected and others were confirmed. The results show that out of nine confirmed risks, only one was moderate and the other eight were important or critical.

The brainstorming technique is one of the most widely used methods for the identification and evaluation of risks and a powerful tool for integrating the project team. The results of this method are obtained from the cooperation and consensus of the group panel, whose members have full commitment. The second part of this research used the qualitative method of project risk management in the PMBOK standard to identify, confirm, or reject risks. The results of the brainstorming sessions concerning risks were provided through descriptive expressions (Table 2). This method uses descriptive expressions to achieve consensus among the members of the brainstorming team. It is noteworthy that the score of linguistic expressions in this method is considered equal to the intuitionistic fuzzy number in the IFBS method, and the mean of expert opinions forms the basis of the score of linguistic expressions. The threshold of this study included moderate and higher levels of risk to establish the same conditions for the comparison of the two methods.

Table 6. Identification (selection) of risks using a brainstorming technique and PMBOK-based qualitative analysis methods.

Risk	Score of Linguistic Expression	Result of Qualitative Analysis	Selection/Confirmation or Rejection
R1	4	I	Confirmation
R2	3	MI	Confirmation
R3	4	I	Confirmation
R4	2	UI	Rejection
R5	4	I	Confirmation
R6	3	MI	Confirmation
R7	4	I	Confirmation
R8	2	UI	Rejection
R9	3	MI	Confirmation
R10	4	I	Confirmation
R11	4	I	Confirmation

indicates the results of this analysis.

The results show the rejection of two risks (numbers 4 and 8) and the confirmation of others. In addition, out of nine confirmed risks, three were moderate and six were significant or critical.

4.2. Comparison of the Results Between the IFBS Technique and the PMBOK-Based Qualitative Analysis Method

A comparison of the results obtained from both IFBS- and PMBOK-based methods shows their consistency in the number and type of criteria rejected. The difference in the results can be due to the higher accuracy of the IFBS method because it has used the range of numerical analysis while also introducing ambiguities and uncertainties in the computational analysis. Both methods evaluated the risk of R₂ at a moderate level, while the risks of R₆ and R₉ were reported to be critical in IFBS and moderate in PMBOK brainstorming. Therefore, the brainstorming method with PMBOK qualitative analysis is not accurate enough and cannot determine the exact probability of risk within the range of its descriptive expression. On the other hand, numerical analysis based on the range of intuitionistic fuzzy numbers provided suitable numerical estimation in each region of the selected range. Finally, these numbers not only facilitate the selection of risks (criteria) but also ensure good estimation of the probability of risk occurrence.

4.3. Research Limitations and Future Research Directions

This research provides a novel approach to assessing earthquake risks in worn-out urban fabrics using a hybrid method combining brainstorming and IFSs. However, this study acknowledges several limitations that impact its applicability and generalizability, and it suggests directions for future research to address these shortcomings. This study identifies several limitations inherent in its methodology and scope, which are critical for understanding the boundaries of its findings:

• Reliance on expert opinions: The IFBS technique heavily depends on the subjective judgments of experts during brainstorming sessions, which can introduce biases and inconsistencies. Despite structured validation processes, such as iterative feedback loops, the variability in expert expertise and cognitive biases may affect the reliability of risk assessments, particularly in diverse urban contexts.
• Subjectivity in IFS function selection: The selection of membership and non-membership functions for TIFNs involves subjective expert judgment, which can compromise objectivity. Although the IFBS method employs standardized guidelines, the lack of fully objective criteria for function assignment remains a challenge.
• Information loss during defuzzification: The defuzzification process, which converts fuzzy numbers into crisp values, may lead to information loss, potentially reducing the precision of risk prioritization. While weighted aggregation techniques are used, the granularity of uncertainty representation may still be compromised.
• Expertise requirements for TIFNs conversion: Converting linguistic expressions into TIFNs requires specialized knowledge, limiting the method’s accessibility to non-specialists. Despite efforts to simplify this process with predefined scales, the technical complexity may restrict broader adoption.
• Computational complexity: The IFBS method’s computational demands increase with the number of criteria and experts, posing scalability challenges for large-scale urban risk assessments. This complexity can hinder practical implementation in resource-constrained settings.
• Context-specific application: This study focuses on worn-out urban fabrics in Iran, which may limit the generalizability of findings to other geographic or socio-economic contexts. Variations in urban infrastructure, cultural factors, and disaster preparedness levels may require methodological adaptations.
• Limited validation scope: The comparison between the IFBS method and PMBOK-based qualitative analysis is confined to a single case study, which may not fully validate the method’s superiority across diverse risk management scenarios. This study lacks broader empirical testing to confirm its robustness.

To address these limitations and enhance the IFBS method’s applicability, this study proposes several directions for future research, which are elaborated here based on the manuscript’s conclusions and context:

• Enhancing bias mitigation: Future research should explore advanced techniques to further reduce biases in expert opinions, such as integrating artificial intelligence (AI) algorithms to detect and correct cognitive biases during brainstorming sessions [21]. Developing automated validation tools could enhance objectivity in IFS function selection, building on Gavurova et al.’s [35] work on smart city risk models.
• Improving defuzzification techniques: Investigating novel defuzzification methods that minimize information loss, such as machine learning-based approaches, could improve the precision of risk prioritization [36]. Research could focus on adaptive defuzzification algorithms that retain the hesitancy parameter’s granularity, as suggested by Pu et al.’s [30] optimization models.
• Increasing accessibility for non-specialists: To broaden the IFBS method’s adoption, future studies should develop user-friendly interfaces and training modules that simplify TIFNs conversion for non-specialists. Collaborative frameworks, as proposed by Swaris et al. [29], could inform the design of inclusive decision-making platforms that empower diverse stakeholders.
• Optimizing computational efficiency: Research should focus on scalable algorithms to reduce the computational complexity of the IFBS method, particularly for large-scale urban risk assessments. Leveraging AI-driven optimization, as demonstrated by Xia et al. [36], could streamline calculations and enhance applicability in resource-constrained environments.
• Expanding contextual applicability: Future studies should test the IFBS method across diverse geographic and socio-economic contexts to validate its generalizability. Comparative studies in different urban settings, such as those with varying infrastructure resilience or disaster preparedness levels, could refine the method’s adaptability [26].
• Broader validation and comparative analysis: Conducting extensive empirical validations across multiple case studies and risk management scenarios would strengthen the IFBS method’s credibility. Future research could compare the IFBS method with other advanced decision-making frameworks, such as deep learning-based risk models, to establish its relative advantages [35].
• Integration with emerging technologies: Exploring the integration of the IFBS method with emerging technologies, such as GIS and real-time data analytics, could enhance its applicability in dynamic urban risk management. This could involve developing hybrid models that combine IFBS with predictive analytics for proactive disaster planning.

5. Conclusions

A decision is hindered by the absence or insufficiency of comprehensive and precise information. This predicament poses a significant obstacle for professionals and practitioners in diverse domains, as it hampers their ability to make well-informed decisions, both individually and collectively. The primary objective of both individual and group panels is to achieve the most favorable conclusion. The ultimate decision consensus is significantly influenced by two crucial factors: the knowledge derived from data analysis and the input of human judgments. One primary component pertains to the manner in which incomplete and ambiguous information is included into the analysis, while a second aspect relates to errors stemming from human cognition and judgment. Hence, the utilization of non-deterministic approaches is of utmost significance when making decisions that encounter unpredictable circumstances. The utilization of fuzzy theory and its generalizations is a commonly employed approach across several domains of decision-making to address these issues. By using these theoretical frameworks, one has acquired the capacity to construct models that yield outcomes that are both more precise and coherent.

This study proposed a hybrid method, including brainstorming and intuitionistic fuzzy theory, to address group decision-making problems through a case study. Brainstorming is a collective method to create novel ideas and various topics, solve problems, and make decisions about them to increase accuracy and efficiency. Although this method is a powerful tool in group decision-making, it sometimes faces problems and challenges. For example, this technique does not have enough accuracy when more complexities, ambiguities, or uncertainties enter human thoughts and judgments. The combination of this method with intuitionistic fuzzy logic and sets and the development of a hybrid method can increase the accuracy of calculations and decisions while also converting human thoughts and judgments into numerical methods. The IFBS technique covers ambiguities and uncertainties arising from decision-making in the brainstorming method using intuitionistic fuzzy theory. This technique presents the properties of the variables as triangular intuitionistic fuzzy sets. The accuracy and inaccuracy degrees of each variable in a set of criteria are expressed by triangular intuitionistic fuzzy sets, respectively. The degree of uncertainty of brainstorming decision-makers regarding each criterion or issue can be considered through the degree of uncertainty of each variable, enabling decision-makers to make better decisions. This technique can be widely used in different fields of research, industry, and economics. Comparison of the two methods performed in this study showed higher accuracy and intuition of the IFBS method. Future studies can focus on the application of intelligent methods related to complex issues and ambiguities of brainstorming and intuitionistic fuzzy theory to improve this method for indefinite decisions, experts’ linguistic ambiguities, and correction and revision of criteria or options. Some examples include issues related to potential risk assessment, risk management, crisis management, natural hazard prediction, and types of financial decisions. The proposed method can be a useful tool for project managers to make sensible decisions in various areas of project management to improve the results of group decisions. It can also contribute as a scientific guide for researchers in the field of project management.