Enhancing relative ratio method for MCDM via attitudinal distance measures of interval-valued hesitant fuzzy sets

Abstract

This paper is devoted to develop an enhanced relative ratio (RR) method for tackling with multi-criteria decision making (MCDM) problem in interval-valued hesitant fuzzy setting. First, a hesitant fuzzy COWA operator is defined, based on which we construct an attitudinal distance measure between two IVHFEs and develop subsequently (three) some weighted (including weighted, ordered weighted and synergetic weighted) attitudinal distance measures between two collections of (for) IVHFEs (or two IVHFSs). The measures can not only alleviate the operational load, but also efficiently avoid information loss and distortion, as well as reflect the DMs’ decision attitude in the computing process. Next, under the framework of relative ratio method, we use the attitudinal distance measures to establish an enhanced interval-valued hesitant fuzzy relative ratio method, which adheres to the principle of compromise that the chosen alternative should have the shortest distance from the positive ideal solution and the greatest distance from the negative one simultaneously, to range alternatives. The established method provides us a very flexible and useful way to deal with fuzzy MCDM problems under interval-valued hesitant fuzzy setting for it considers the DMs’ attitudinal character. Moreover, in the methodology, several approaches for determining the interval-valued hesitant fuzzy positive/negative ideal solutions are introduced. Finally, the implementation process and the applicability of our method are illustrated by a real example concerning watershed ecological risk evaluation, and comparisons are made with the four similar methods.