Distance and similarity measures of dual hesitant fuzzy sets with their applications to multiple attribute decision making

Abstract

The Dual Hesitant Fuzzy Sets (DHFSs) is a useful tool to deal with vagueness and ambiguity in the multiple attribute decision making (MADM) problems. The distance and similarity measures analysis are important research topics. In this paper, we propose a variety of distance measures for dual hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of dual hesitant ordered weighted distance measures. Finally, we present a TOPSIS approach based on proposed distance measures for the weapon selection problem.

New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making

“…However, it is not allowed to expand the shorter DHFS by increasing the length of the shorter one to the same length in some practical cases. Therefore, Wang et al [9] developed another distance measure as follows:…”

“…As the theoretical basis of DHFSs, the addition, multiplication, union, intersection, exponentiation [5] and other aggregation operators [6,7] were investigated first. Then, the most widely used measures and indexes were developed, such as distance and similarity measures [8][9][10], entropy measures [11], correlation coefficients [12,13] and cross-entropy measures [14] and so forth; (2) Several typical MADM methods were developed. Ren and Wei [15] developed the novel similarity measure and score function, based on which a prioritized MADM method was proposed to handle the problem with DHF assessment.…”

“…Several basic distance measures for DHFSs were developed by Su et al [8] and applied to pattern recognition. A series of distance measures and the relevant similarity measures for DHFSs were first proposed by Wang et al [9] and these distance measures were integrated with a TOPSIS method to evaluate weapon selection problem. A number of normalized generalized distance measures for DHFSs utilizing the set-theoretic and the geometric distance model were defined by Singh [10] and applied in MADM.…”

Decision making with both diversity supporting and opposing membership information

“…Farhadinia (2014) and Tyagi (2015) considered the significant role of correlation in data analysis and studied the correlation model between two DHFSs. Due to the important roles of distance and similarity in decision making and pattern recognition, Wang et al (2014) proposed a variety of distance measures for DHFSs and generated a technique for order preference by similarity to an ideal solution (TOPSIS) method for a weapon selection problem. Su et al (2015) introduced some distance and similarity measures for DHFSs.…”

“…Xu and Xia (2011), Li et al (2015), Zhang et al (2018) and Hu et al (2018) defined distance and similarity measures of HFSs. As an extension of both IFSs and HFSs, Wang et al (2014), Su et al (2015), and Singh (2017) studied the distance measures between DHFSs by ordering the elements in dual hesitant fuzzy elements and extending them to the same length; additionally, based on the Hamming distance, the Euclidean distance and the Hausdorff distance, they defined a dual hesitant normalized Hamming distance, a dual hesitant normalized Euclidean distance, a generalized dual hesitant normalized Hausdorff distance, and a generalized dual hesitant weighted distance. In these distance measures, three points should be considered.…”