Weighted Hesitant Fuzzy Sets and Their Application to Multi-Criteria Decision Making
Zhiming Zhang *
School of Management, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, PR China and College of Mathematics and Computer Science, Hebei University, Baoding 071002, Hebei Province, PR China.
Chong Wu
College of Mathematics and Computer Science, Hebei University, Baoding 071002, Hebei Province, PR China.
*Author to whom correspondence should be addressed.
Abstract
Aims: The aim of this paper is to investigate weighted hesitant fuzzy sets and their application to multi-criteria decision making.
Study Design: This paper puts forward the concept of a weighted hesitant fuzzy set (WHFS), in which several possible membership degrees of each element have different weights. Archimedean t-conorm and t-norm provide a generalization of a variety of other t-conorms and t-norms that include as special cases Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms.
Place and Duration of Study: Hesitant fuzzy set, permitting the membership degree of an element to be a set of several possible values, can be referred to as an efficient mathematical tool for modeling people’s hesitancy in daily life. It is noted that several possible membership degrees of each element in the hesitant fuzzy set are of equal importance, but in many practical problems, especially in multi-criteria decision making, the weights of several possible membership degrees of each element should be taken into account.
Methodology: In this paper, based on Archimedean t-conorm and t-norm, we present some operations on weighted hesitant fuzzy sets (WHESs), and based on which, we develop two weighted hesitant fuzzy aggregation operators for aggregating weighted hesitant fuzzy information. Furthermore, some desired properties and special cases of the developed operators are discussed in detail.
Results: We develop an approach for multi-criteria decision making under weighted hesitant fuzzy environment.
Conclusion: An illustrative example is provided to show the effectiveness and practicality of the proposed operators and approach.
Keywords: Multi-criteria decision making, hesitant fuzzy sets, weighted hesitant fuzzy sets, archimedean t-conorm and t-norm, weighted hesitant fuzzy aggregation operator.