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.
Highlights
Correlation indicates how well two variables move together in a linear fashion
Hung and Wu [17] proposed a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of “centroid.” Xu [18] gave a detailed survey on association analysis of intuitionistic fuzzy sets and pointed out that most existing methods deriving association coefficients cannot guarantee that the association coefficient of any two intuitionistic fuzzy sets equals one if and only if these two intuitionistic fuzzy sets are the same
They further indicated that dual hesitant fuzzy sets (DHFSs) can better deal with the situations that permit both the membership and the nonmembership of an element to a given set having a few different values, which can arise in a group decision making problem
Summary
Correlation indicates how well two variables move together in a linear fashion. In other words, correlation reflects a linear relationship between two variables. The motivation to propose the DHFSs is that when people make a decision, they are usually hesitant and irresolute for one thing or another which makes it difficult to reach a final agreement They further indicated that DHFSs can better deal with the situations that permit both the membership and the nonmembership of an element to a given set having a few different values, which can arise in a group decision making problem. We mainly discuss the correlation measures of dual hesitant fuzzy information.
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