Abstract
Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft sets. By means of level soft sets, we propose an adjustable approach to type-2 fuzzy-soft-set based decision making and give some illustrative examples. Moreover, we also introduce the weighted type-2 fuzzy soft set and examine its application to decision making.
Highlights
Soft set theory 1, firstly proposed by Molodtsov, is a general mathematical tool for dealing with uncertainty
Based on the above discussion, in the following, we point out the differences between type-2 fuzzy soft set and type-2 fuzzy set in detail
Considering that soft set and its existing extension modles cannot deal with the situations in which the evaluations of parameters are fuzzy concepts, we in the current paper introduce the notion of the type-2 fuzzy soft set as an extension to the soft set model
Summary
Soft set theory 1 , firstly proposed by Molodtsov, is a general mathematical tool for dealing with uncertainty. The purpose of this paper is to further extend the concept of soft set theory by combining type-2 fuzzy set and soft set, from which we can obtain a new soft set model: type-2 fuzzy soft sets. We investigate the applications of type-2 fuzzy soft sets and weighted type-2 fuzzy soft sets in decision making problems. Applications of type-2 fuzzy soft sets and weighted type-2 fuzzy soft sets in decision making problems are, respectively, shown in Sections 4 and 5.
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