Correlation coefficients of hesitant multiplicative sets and their applications in decision making and clustering analysis

Hesitant multiplicative set (HMS) can reflect the preferences of decision makers objectively for the reason that it uses the unsymmetrical scale to express the preferences about two alternatives. Considering that there is still no research on correlation coefficients between HMSs, in this paper, we propose some correlation coefficient formulas to measure the relationship between two HMSs. Firstly, we improve the addition and multiplication operations of Hesitant multiplicative elements (HMEs) to avoid the increasing of values in the derived HME. Then a series of new concepts related to the HME and the HMS are defined. Then, some correlation coefficient formulas between two HMSs are defined, and the weighted forms of the correlations and correlation coefficients between HMSs are developed. Finally, we provide two practical examples (online car selling, and star-classification of cities' happiness by clustering analysis) to validate the validity and usability of the correlation coefficients. (C) 2017 Elsevier B.V. All rights reserved.