Novel spherical fuzzy aggregation operators and similarity & distance measures

Abstract

Fuzzy Sets theory, developed by Zadeh in (Zadeh, 1965), is one of the most appropriate approaches to deal with the ambiguity of information and uncertain situations (Farrokhizadeh et al., 2021). Since the introduction of fuzzy sets by (Zadeh, 1965), they have been prevalent in almost all branches of science (Gündoğdu & Kahraman, 2019a). Many generalizations for ordinary fuzzy sets have been introduced by different researchers in the literature (K. T. Atanassov, 1986, 1999; Cuong & Kreinovich, 2014; Grattan-Guinness, 1976; Kutlu Gündoğdu & Kahraman, 2018; Smarandache, 1999a; Torra, 2010; Yager, 1986, 2014; Zadeh, 1975). Numerous researchers have utilized these extensions in recent years in the solution of multi-attribute decision-making problems (Gündoğdu & Kahraman, 2019b). These extensions are presented in chronological order, as given in Figure 1.1. One of the latest extensions of fuzzy sets is Spherical Fuzzy Sets (SFSs), recently developed (Gündoǧdu & Kahraman, 2019), where the squared sum of membership, non-membership, and indeterminacy degrees is at most equal to 1. Decision-making is the main aspect of every problem, and selecting the most appropriate alternative is fundamental for those problems and investigated by many researchers. Multi-criteria decision-making (MCDM) methods are among the most applicable and trustfulness methods to select the optimal alternative. MCDM algorithms select the best alternative from a finite set of alternatives based on multiple criteria. MCDM algorithms are methodological tools that deal with many different engineering problems. Some of those complex problems include fields of economy, businesses, insurance, medical and healthcare systems, engineering designs, sustainable supply chain, finance, actuarial, water management, energy management, agriculture and food supply chain, and environmental issues. Uncertainty is another aspect of every real-world problem that should be considered during the decision-making procedure to validate the results. Fuzzy decision-making theories together with different modeling techniques have been studied, and many suitable approaches are introduced and studied through different applications and case studies. Moreover, in every fuzzy MCDM problem expert or decision-maker (DM) is acting a significant role, but it also carries the uncertainty of the environment by itself. So, in most of the fuzzy MCDM problems, there would be a desire to have a number of the DMs which is called fuzzy Multi-criteria group decision-making (MCGDM) problem. A fuzzy MCGDM problem could be considered a high dimensional MCDM problem, therefore, carrying precise assessments for alternatives. One of the primary and significant steps in every fuzzy MCGDM problem is the data fusion stage, which means there is a huge need to combine fuzzy data. Many fuzzy aggregation operators are proposed based on different characteristics for the data fusion stage of fuzzy MCGDM problems. Fuzzy distance and similarity measurements for comparison are also sitting in the framework of fuzzy data fusion, that considered in this thesis. So this manuscript, it is tried to define two main concepts of the data fusion concept: aggregation operators and distance-based similarity measurements in the spherical fuzzy environment. So, the novel concept of Harmonic mean aggregation operator for spherical fuzzy sets (SFSs) is introduced and discussed in all detail. Weighted, order weighted and hybrid order weighted Harmonic Mean operators and using two types of Algebraic and Einstein Strict Archimedean t-norms and t-conorms are types of proposed spherical fuzzy harmonic mean aggregation operators. So, 6 harmonic mean aggregators in the Spherical Fuzzy environment are introduced. Also, this thesis investigated the concept of fuzzy distance and similarity measurements which are other types of fuzzy data fusion methods. I introduced the novel Minkowski and Minkowski-Hausdorff distance measures for spherical fuzzy sets and also studied novel spherical fuzzy f-similarity measures based on Minkowski and Minkowski-Hausdorff distances. So in this thesis, some novel fuzzy MCGDM algorithms for fuzzy data fusion extended to the spherical fuzzy environment. In these extensions, some real-life problems such as air quality evaluation problem and COVID_19 medical diagnosis problem are covered and suggesting other problems like supplier selection, energy source selection, hospital site selection, etc. problems to be covered for future works.