Two λ -correlation coefficients of q -rung orthopair fuzzy sets and their application to clustering analysis

Abstract

The q-rung orthopair fuzzy set is a significant part of the existing orthopair fuzzy sets, whose advantage is to more comprehensively describe uncertain information. For q-rung orthopair fuzzy sets, the correlation between them is generally measured by the correlation coefficient. In order to express the positive and negative correlations of q-rung orthopair fuzzy sets simultaneously from a statistical perspective, and to reflect the attitude of decision makers, in this paper, two new correlation coefficients of q-rung orthopair fuzzy sets are proposed and investigated. Firstly, a λ-variance-based correlation coefficient of q-rung orthopair fuzzy sets is proposed from the statistical viewpoint. Secondly, a λ-matching-function-based correlation coefficient of q-rung orthopair fuzzy sets is defined from the perspective of vector calculation. In the end, an example of clustering analysis is presented to verify the feasibility and superiority of the proposed correlation coefficients by comparing with other existing correlation coefficient of q-rung orthopair fuzzy sets. It can be seen from the clustering results that the two new λ-correlation coefficients not only consider the positive or negative correlation at the same time, but also can be dynamically adjusted according to the needs of decision makers. Furthermore, clustering results using λ-variance-based and λ-matching-function-based correlation coefficients converge faster than clustering results using the existing correlation coefficient in the q-rung orthopair fuzzy environment.