Typical Hesitant Fuzzy Sets: Evaluating Strategies in GDM Applying Consensus Measures

Abstract

This work studies typical hesitant fuzzy sets (THFS) which can be used in group decision making (GDM) due to the possibility of more flexible values for expressions given by a group of decision makers, instead of using only one value resulting from aggregation expressing their preferences. Besides, formal definitions on fuzzy sets and hesitant fuzzy sets are presented. Moreover, it is considered its relations in THFS and also properties related with consensus measures.

On admissible total orders for typical hesitant fuzzy consensus measures

“…Consider a group of four friends providing ratings for three styles of craft beers (as shown in Table 2) as well as comparing the average, which was firstly introduced in Matzenauer et al 30 One can also see that while everyone partially agrees that the craft beer Sour style is not very good, and the Pale Ale style is not too bad, there is a lack of consensus regarding the Weiss style. See the corresponding preference matrices R F 1 , R F 2 , R F 3 , and R F 4 :…”

On typical hesitant fuzzy automata

“…According to [24,28], a HFS is defined in terms of a function which return sets of membership degrees for each element of their domain U = ∅. In 2014, Bedregal et al [25] introduced a particular case of HFS, called Typical Hesitant Fuzzy Set, or simply THFS, which considers some restrictions.…”

“…The set H 1 = {X ∈ H | #X = 1} is called of degenerate elements set. Several operators on H were proposed in [25,28,29,30,31,32,33]. In particular, Costa and Bedregal [23], have presented the inf-combination and sup-combination.…”

“…Given that hesitant fuzzy set and typical hesitant fuzzy set can deal with problems in which, in addition to uncertainties, there is also hesitation (Chen et al 2019;Deli 2020;Matzenauer et al 2019;Wei et al 2020), in this article, we will use the set of typical hesitant fuzzy elements (Bedregal and Figueira 2008), denoted by H, to establish a mathematical framework for a new extension of notion finite automata (Hopcroft et al 2001;Linz 2011) able to generalize fuzzy automata (Bělohlávek 2002;Cao and Ezawa 2012;Chaud-hari and Komejwar 2011;Das 1999;Farias et al 2016a;Ilie and Yu 2003;Mordeson and Malik 2002;Qiu 2001;Singh et al 2017;Srivastava and Tiwari 2002;Wu et al 2002). Thus in this work, we will first define two operators on H called infcombination and sup-combination.…”