Hesitant Fuzzy Soft Sets with Application in Multicriteria Group Decision Making Problems

Abstract

Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy sets. And some operations on hesitant fuzzy soft sets based on Archimedean t-norm and Archimedean t-conorm are defined. Besides, four aggregation operations, such as the HFSWA, HFSWG, GHFSWA, and GHFSWG operators, are given. Based on these operators, a multicriteria group decision making approach with hesitant fuzzy soft sets is also proposed. To demonstrate its accuracy and applicability, this approach is finally employed to calculate a numerical example.

Fuzzy number Intuitionistic fuzzy soft sets and its properties

“…Guan et al (2013) [9] gave a new order relation of fuzzy soft set (FSSs) and Feng et al (2014) [7] studied the decomposition of fuzzy soft sets with finite value spaces. Wang et al (2015) [21] presented hesitant fuzzy soft sets and their corresponding aggregation operators namely hesitant fuzzy soft weighted averaging/geometric operators. Thus, motivated by the theory of intuitionistic fuzzy set and fuzzy soft set, the present paper addressed the new hybrid structure of the set theories called fuzzy number Intuitionistic fuzzy soft set.…”

On Interval-Valued Hesitant Fuzzy Soft Sets

“…In [35,36,43], researchers have introduced the concept of hesitant fuzzy soft sets and developed some approaches to hesitant fuzzy soft sets based on decision making. However, incompleteness and inaccuracy of information in the process of making decision are very important problems we have to resolve.…”

A New Method of Multiattribute Decision‐Making Based on Interval‐Valued Hesitant Fuzzy Soft Sets and Its Application

“…Therefore, the existing methods [15][16][17][18][19][20][21] are inapplicable to solve this problem. Furthermore, it is necessary to evaluate the mud pump from different aspects, since it is a complex system; thus comprehensive opinions by more than one decision-maker are needed, which implies that the existing method [14] considering a decision-maker is not appropriate to deal with this problem, too.…”

“…Wang et al [20] proposed a MADM method based on hesitant fuzzy soft sets. Wang et al [21] proposed a MADM approach based on the aggregation operator to aggregate hesitant fuzzy soft information. Peng and Yang [14], by means of TOPSIS and the maximizing deviation method, presented a MADM method based on interval-valued hesitant fuzzy soft sets.…”