Correlation measure of hesitant fuzzy soft sets and their application in decision making

Hesitant fuzzy soft set (HFSS) allows each element to have different number of parameters and the values of those parameters are represented by multiple possible membership values. HFSS is considered as a powerful tool to represent uncertain information in group decision-making process. In this study, we introduce the concept of correlation coefficient for HFSS and some of its properties. Using correlation coefficient of HFSS, we develop correlation efficiency which shows the significance of the HFSS. We also propose an algorithm to apply correlation coefficient in decision-making problem, where information is presented in hesitant fuzzy environment. In order to extend the application of HFSS, we propose correlation coefficient in the framework of interval-valued hesitant fuzzy soft set (IVHFSS). We also introduce correlation efficiency in the context of IVHFSS. Then the proposed algorithm is extended using IVHFSS for solving decision-making problems. Finally, two examples that are semantically meaningful in real life are illustrated to show the effectiveness of the proposed algorithms.