Uncertainty modeling in decision theory and an application with fuzzy set theory

This thesis explores the application of fuzzy set theory to address uncertainty and complexity in decision-making processes. The extended form of fuzzy sets, known as dual hesitant fuzzy sets (DHFSs), effectively captures membership degrees, non-membership degrees, and hesitation degrees in uncertain environments. In the application section, a solution framework is proposed using a multi-criteria decision-making (MCDM) method based on dual hesitant fuzzy information. The study underscores the critical role of uncertainty modeling within fuzzy set theory and demonstrates the applicability of a multi-criteria decision-making method utilizing dual hesitant fuzzy information in a real-world decision theory context. This method facilitates the comparison and ranking of dual hesitant fuzzy evaluations (DHFEs) provided by either a single expert or a group of experts, enabling the identification of the most appropriate alternative. The approach is particularly significant in effectively distinguishing between any two dual hesitant fuzzy elements (DHFEs). This thesis explores the application of fuzzy set theory to address uncertainty and complexity in decision-making processes. The extended form of fuzzy sets, known as dual hesitant fuzzy sets (DHFSs), effectively captures membership degrees, non-membership degrees, and hesitation degrees in uncertain environments. In the application section, a solution framework is proposed using a multi-criteria decision-making (MCDM) method based on dual hesitant fuzzy information. The study underscores the critical role of uncertainty modeling within fuzzy set theory and demonstrates the applicability of a multi-criteria decision-making method utilizing dual hesitant fuzzy information in a real-world decision theory context. This method facilitates the comparison and ranking of dual hesitant fuzzy evaluations (DHFEs) provided by either a single expert or a group of experts, enabling the identification of the most appropriate alternative. The approach is particularly significant in effectively distinguishing between any two dual hesitant fuzzy elements (DHFEs). To address decision-makers' loss aversion tendencies, the full-scale information expressed in the form of dual hesitant fuzzy elements is incorporated into the computational process. To further improve the distinguishability of dual hesitant fuzzy elements, a novel distance measure and a comparison method based on a scoring function have been developed. This approach aligns with human cognitive structures and adheres to the general understanding that hesitation degrees increase as additional potential values are considered within the membership and non-membership functions. Within the extended VIKOR methodology, fuzzy measures are utilized to derive criterion weights, capturing the interactive relationships among criteria. The proposed method is applied to compare Lean and Green production principles using dual hesitant fuzzy information. The findings indicate that Lean production practices represent the best compromise solution.