DECISION MAKING THEORY AND APPLICATIONS USING INTUITIONISTIC FUZZY SET EXTENSIONS

Introduction

The continuous fuzzy logic of Zadeh (1965) is the greatest achievement of multivalued logic. Singletons with a few elements and their degrees of membership to the set serve as representations for the ordinary fuzzy sets (OFS) first established by Zadeh (1965). The complement of the membership degree of this element to one is its non-membership degree. Many researchers objected to this complimentary aspect of regular fuzzy sets. These scholars contend that the requirement for the complimentary feature in OFS should not exist, and that the membership degree of an element should likewise be ambiguous. In order to add fuzziness to membership degrees and/or remove the complimentary feature, OFS has been expanded to a number of new extensions that explain membership functions in greater depth. The development of type-2 fuzzy sets and interval-valued fuzzy sets allowed membership functions to be fuzzy (Zadeh, 1975). Later, Intuitionistic Fuzzy Sets (IFSs) were proposed by Atanassov (1986), which comprise x values with degrees of membership and non-membership whose sum may only be at most equal to 1. The degree of hesitation or indecision of the decision maker is the product of the membership and non-membership degrees to one. In order to deal with a set of potential membership values for an element in a fuzzy set, Torra (2010) proposed hesitant fuzzy sets (HFSs). In his book, Atanassov (1999) developed intuitionistic type-2 fuzzy sets (IFS2), which allowed the squared sum of membership and non-membership degrees to be no greater than one. IFS2 was later referred to as Pythagorean fuzzy sets (PFSs) by Yager (2013). As a generalization of IFSs, Yager (2017) also presented q-rung orthopair fuzzy sets (Q-ROFSs), where the sum of the qth powers of membership and non-membership equals at most one. Neutosophic sets were first introduced by Smarandache (1998), whose degrees of truthiness, indeterminacy, and falsity for each element in the universe can only add up to a maximum of one. Picture fuzzy sets with three parameters—yes, no, and abstain—as well as their complement to one as rejection degree were developed by Coung (2017). In their publication in 2018, Kahraman and Kutlu Gündodu proposed spherical fuzzy sets, where the squared sum of the same parameters as image fuzzy sets can only be one. Later, some more recent extensions were brought to the literature, including continuous intuitionistic fuzzy sets (Alkan and Kahraman, 2023), circular intuitionistic fuzzy sets (Atanassov, 2020), and fuzzy sets that are decomposed (Cebi et al., 2022). All of these expansions aim to provide more details and parameters to explain an element's membership to a fuzzy set. We see that these extensions are frequently used in the literature, especially in the field of decision making. In this thematic issue, it is aimed to include innovative and guiding examples of fuzzy set extensions in decision making theory and practice in various disciplines. The subtopics are • Decision making in finance • Decision making in quality management, • Decision making in statistics, • Decision making in multi-attributes analyses, • Decision making in multi-objective analyses, • Decision making in engineering economics, • Decision making in operations research, • Decision making in the other possible areas Tentative date of submission of the complete thematic issue: • Final date for a full paper submission: November 25, 2023 • Review results of round 1: March 1, 2024 • Resubmission of revsed papers: May 15, 2024 • Notification of final decisions: July 20, 2024

Keywords

extensions of ordinary fuzzy sets, intuitionistc fuzzy sets, Pythagorean fzzy sets, spherical fuzzy sets, decion making, picture fuzzy sets, multi-attribute decision makig, multi-objective decision making