Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making

The soft set theory can be used as a newly mathematical tool to handle uncertainty. How- ever, the classical soft sets are not appropriate to deal wit h imprecise and fuzzy parameters. In this paper, we propose the interval-valued hesitant fuzzy soft sets which are a combination of the interval-valued hesitant fuzzy sets and soft sets. Then, th e complement, AND, OR, union, inter- section, restricted union, extended intersection, differ ence, average, and geometric operations are defined on the interval-valued hesitant fuzzy soft sets, and some basic properties are also discussed in detail. Finally, by means of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and the maximizing deviation method, an algorithm is presented, and a comprehensive sensitivity analysis is employed, and the effectiveness is proved by a numerical example.