Hesitant fuzzy parameterized soft sets and their applications in decision making

The fuzzy set theory plays an important role in the modeling of the problems involving uncertain data. Some extensions of the fuzzy sets are needed due to the variety of problems encountered in real life. The concept of a hesitant fuzzy set is one of these extensions. Also, soft set theory, which is free from the difficulties of determining the membership function in fuzzy sets, plays an important role in dealing with uncertainty. In this study, we introduce the concept of hesitant fuzzy parameterized soft set as a generalization of the fuzzy parameterized soft sets. Then we define set-theoretical operations of the hesitant fuzzy parameterized soft sets and obtain some of their properties. We also improve a decision-making algorithm under the hesitant fuzzy parameterized soft environment and give an example to show the process of the algorithm. Finally, we compare the proposed decision-making algorithm with methods existing in the literature.