A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

Abstract

Hesitant fuzzy sets, as an extension of fuzzy sets to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work is focused on the interval-valued hesitant fuzzy sets (IVHFSs) to manage additional uncertainty. Now that distance and similarity as a kind of information measures are essential and important numerical indexes in fuzzy set theory and all their extensions, the present work aims at investigating distance and similarity measures in the IVHFSs and then employing them into multiple attribute decision making application. To begin with, II-type generalized interval-valued hesitant fuzzy distance is firstly introduced in the IVHFS, along with its properties and its relationships with the traditional Hamming-Distance and the Euclidean distance. Afterwards, another interval-valued hesitant fuzzy Lp distance based on Lp metric is proposed and its relationship with the Hausdorff distance is discussed. In addition, different from most of similarity measures with dependent on the corresponding distances, a new similarity measure based on set-theoretic approach for IVHFSs is introduced and its properties are discussed; especially, a relative similarity measure is proposed based on the positive ideal IVHFS and the negative ideal IVHFS. Finally, we describe how the IVHFS and its relative similarity measure can be applied to multiple attribute decision making. A numerical example is then provided to illustrate the effectiveness of the proposed method.

Linguistic Pythagorean Einstein Operators and Their Application to Decision Making

“…Multi-attribute group decision-making is an important component of modern decision making (DM) science, which has been widely considered by multitudinous scholars and has achieved rich research achievements [1][2][3][4][5][6]. Due to the uncertainty and complexity of DM environments, it is arduous to portray the evaluation value of alternatives by precise numerical value.…”

Hesitant Fuzzy Linguistic Hamy Mean Aggregation Operators and Their Application to Linguistic Multiple Attribute Decision-Making

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Multi-attribute Group Decision-making for Online Education Live Platform Selection Based on Linguistic Intuitionistic Cubic Fuzzy Aggregation Operators

“…Therefore, in order to solve these complex DMPs, and to make full use of the original information (in the decision-making process, the lost original information should be as few as possible), scholars have successively proposed interval-valued intuitionistic fuzzy set (IVIFS) [3], hesitation fuzzy set (HFS) [4] [5], dual hesitation fuzzy set (DHFS) [6], interval-valued hesitation fuzzy set (IVHFS) [7], intervalvalued intuitionistic hesitation fuzzy set (IVIHFS) [8], probability hesitation fuzzy set (PHFS) [9], probability interval-valued hesitation fuzzy set (PIVHFS) [10], other forms [11]. The researches and applications of similar AOs have also become a research hotspot [12] [13] [14] [15] [16].…”