A Decision-Making Approach Incorporating TODIM Method and Sine Entropy in q-Rung Picture Fuzzy Set Setting

Hindawi Journal of Applied Mathematics Volume 2024, Article ID 3798588, 17 pages https://doi.org/10.1155/2024/3798588 Research Article @) Hindawi A Decision-Making Approach Incorporating TODIM Method and Sine Entropy in g-Rung Picture Fuzzy Set Setting Biisra Aydogan ©,' Murat Olgun ©,' Florentin Smarandache®,” and Mehmet Unver ©’ "Faculty of Science, Department of Mathematics, Ankara University, 06100 Ankara, Tiirkiye ? Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA Correspondence should be addressed to Mehmet Unver; munver@ankara.edu.tr Received 2 November 2023; Revised 26 December 2023; Accepted 5 January 2024; Published 19 January 2024 Academic Editor: Kamal Kumar Copyright © 2024 Biisra Aydogan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decisionmaking) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. 1. Introduction Fuzzy set theory, introduced by Zadeh [1], expands upon classical set theory’s characteristic function with a membership function taking values in the closed interval [0,1]. Atanassov [2] later extended this concept to intuitionistic fuzzy sets (IFSs), which incorporate both membership and nonmembership functions. However, fuzzy sets and IFSs are sometimes insufficient for addressing real-life problems. Yager [3] introduced Pythagorean fuzzy sets (PyFSs) to overcome these limitations, characterized by membership and nonmembership functions with the sum of their squares between 0 and 1. Yager [4] also proposed q-rung orthopair fuzzy sets (q-ROFs) for better modeling real-life applications, characterized by membership and nonmembership functions with the ge power between 0 and 1. q-ROFs are generalizations of IFSs and PyFSs, and some main topological properties of q-ROFs were investigated by Tiirkarslan et al. in [5]. Cuong [6] introduced the notion of picture fuzzy sets (PFSs), characterized by membership, neutral, and nonmembership functions with their sum between 0 and 1. PFSs expand upon fuzzy sets and IFSs. Kutlu Giindogdu and Kahraman [7] and Ashraf et al. [8] later proposed spherical fuzzy sets (SFSs) by generalizing PFSs and PyFSs. Li et al. [9] proposed the notion of q-rung picture fuzzy set (q-RPFS) in 2018, expanding upon PFs, q-ROFSs, and SFSs. All these fuzzy sets provide suitable tools for addressing unexpected Picture fuzzy sets (2014) Buzzy sets Intuitionistic (1965) fuzzy sets (1986) Pythagorean fuzzy sets (2013) Journal of Applied Mathematics q-Rung orthopair fuzzy sets (2016) q-Rung picture fuzzy sets (2018) Spherical fuzzy sets acnsnenssescecceucenscascensssscencscascsecsaccessnuscunee peoeeseouseaseenensssecesneeseesssaecoresscesessssresesseres » timeline FicurE 1: Development network of fuzzy set theory. situations and uncertainties in the input data required for decision-making problems. Several researchers employed these sets in multicriteria decision-making (MCDM). For instance, Seik