The hesitant fuzzy soft set and its application in decision making

Since the appearance of soft set theory, work on fuzzy soft set theory and the extensions of fuzzy soft set theory, known as intuitionistic fuzzy soft set; interval-valued fuzzy soft set; vague fuzzy soft set and multi-fuzzy soft set, is progressing rapidly. Unfortunately, these theories share an intrinsic drawback: all parameters involved in fuzzy soft set based decision making problems must consist of the same number of sub-parameters. In an attempt to circumvent this limitation, we have developed fuzzy soft set theory to a new extension that is referred here to as the hesitant fuzzy soft set theory. In this paper, we first introduce the concept of the hesitant fuzzy soft set using combination of the hesitant fuzzy set and soft set models. Then, we propose an adjustable approach by the use of several kinds of level sets being hesitant fuzzy soft sets to deal with decision making problems.