Abstract
Molodtsov’s soft set theory is a newly emerging mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. This paper aims to extend the classical soft sets to hesitant fuzzy soft sets which are combined by the soft sets and hesitant fuzzy sets. Then, the complement, “AND”, “OR”, union and intersection operations are defined on hesitant fuzzy soft sets. The basic properties such as DeMorgan’s laws and the relevant laws of hesitant fuzzy soft sets are proved. Finally, with the help of level soft set, the hesitant fuzzy soft sets are applied to a decision making problem and the effectiveness is proved by a numerical example.
Highlights
In the real world, there are many complicated problems in economics, engineering, environment, social science, and management science
The purpose of this paper is to extend the soft set model to the hesitant fuzzy set, and, we establish a new soft set model named hesitant fuzzy soft set
A hesitant fuzzy set (HFS) on U is in terms of a function that when applied to U returns a subset of [0, 1], which can be represented as the following mathematical symbol: à = {⟨u, hà (u)⟩ | u ∈ U}, (3)
Summary
There are many complicated problems in economics, engineering, environment, social science, and management science. In order to overcome these difficulties, Molodtsov [1] firstly proposed a new mathematical tool named soft set theory to deal with uncertainty and imprecision. This theory has been demonstrated to be a useful tool in many applications such as decision making, measurement theory, and game theory. In order to tackle the difficulty in establishing the degree of membership of an element in a set, Torra and Narukawa [24] and Torra [25] proposed the concept of a hesitant fuzzy set.
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