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.
Highlights
Since the fuzzy set (FS) was proposed by Zadeh in 1965 [1], it has been widely studied, developed, and successfully applied in various fields, such as multicriteria decision making (MCDM) [2, 3], fuzzy logic and approximate reasoning [4], and pattern recognition [5]
We introduced hesitant fuzzy soft sets, which can be regarded as an extension of both a SS and a hesitant fuzzy sets (HFSs)
hesitant fuzzy soft sets (HFSSs) can describe the real preferences of decision-makers and reflect their uncertainty and hesitancy, which permit the membership degree to have a set of possible values in SSs
Summary
Since the fuzzy set (FS) was proposed by Zadeh in 1965 [1], it has been widely studied, developed, and successfully applied in various fields, such as multicriteria decision making (MCDM) [2, 3], fuzzy logic and approximate reasoning [4], and pattern recognition [5]. Jiang et al [59] presented an adjustable approach to IFSSs-based decision making by using level soft sets of IFSSs. To deal with the problems of subjective evaluation and uncertain knowledge, Xiao et al [60] proposed an evaluation method based on GFSSs and its application in medical diagnosis problem. To deal with the problems of subjective evaluation and uncertain knowledge, Xiao et al [60] proposed an evaluation method based on GFSSs and its application in medical diagnosis problem They [61] extended classical SSs to trapezoidal fuzzy soft sets (TFSSs) and applied them to MCDM problems. The membership degree may be a set of possible values in a SS, so the purpose of this paper is to deal with this situation by combining HFSs with FSSs. To do this, a new kind of SSs, hesitant fuzzy soft sets (HFSSs), can be defined.
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