Correlation Measures of Dual Hesitant Fuzzy Sets

Abstract

The dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures for dual hesitant fuzzy information and then discuss their properties in detail. One numerical example is provided to illustrate these correlation measures. Then we present a direct transfer algorithm with respect to the problem of complex operation of matrix synthesis when reconstructing an equivalent correlation matrix for clustering DHFSs. Furthermore, we prove that the direct transfer algorithm is equivalent to transfer closure algorithm, but its asymptotic time complexity and space complexity are superior to the latter. Another real world example, that is, diamond evaluation and classification, is employed to show the effectiveness of the association coefficient and the algorithm for clustering DHFSs.

Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making

“…The previously proposed power aggregation operators are not applicable to situations in which the input arguments take the form of dual hesitant fuzzy sets. Some aggregation operations and distance measures have also been developed by researchers [31][32][33][34]. Lei Wang [31], Farhadinia [32], Jun Ye [33] mainly discussed the correlation measures of dual hesitant fuzzy information.…”

“…Some aggregation operations and distance measures have also been developed by researchers [31][32][33][34]. Lei Wang [31], Farhadinia [32], Jun Ye [33] mainly discussed the correlation measures of dual hesitant fuzzy information. Wang proposed some correlation measures of dual hesitant fuzzy elements, obtained several important conclusions, and given an example to illustrate the correlation measures.…”

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

“…Wang et al [162] defined the correlation measures for dual hesitant fuzzy information and then discussed their properties in detail.…”

“…Wang et al [162] defined the correlation measures for dual hesitant fuzzy information and discussed their properties in detail. Qian et al [182] extended hesitant fuzzy sets by intuitionistic fuzzy sets and referred to them as generalized hesitant fuzzy sets and redefined their basic operations.…”

Dual hesitant fuzzy group decision making method and its application to supplier selection

“…Farhadinia [26] studied the correlation coefficient for DHFS and applied it to medical diagnosis. Wang et al [27] defined the correlation measures for DHFS and studied the clustering algorithm for DHFS. Ye [28] proposed the concept of weighted correlation coefficient and the predefined idea alternative and applied it investment management.…”