Novel decision-making approach based on hesitant fuzzy sets and graph theory

Abstract

Hesitant fuzzy set is a powerful and effective tool to express uncertain information in multi-attribute decision-making (MADM) process, as it permits the membership degree of an element to a set represented by several possible values in [0,1]. In this paper, we develop a new decision-making approach based on graph theory to deal with the MADM problems, in which the decision information is expressed by hesitant fuzzy elements. Meanwhile, we generalize this approach to make it suitable for processing interval-valued hesitant fuzzy and hesitant triangular fuzzy information. Moreover, we utilize the numerical examples concerning the energy project selection and software evaluation to show the detailed implementation procedure and reliability of our method in solving MADM problems under hesitant fuzzy, interval-valued hesitant fuzzy and hesitant triangular fuzzy environment.