Correlation Coefficients for Cubic Bipolar Fuzzy Sets With Applications to Pattern Recognition and Clustering Analysis

Cubic bipolar fuzzy set (CBFS) is a powerful model for dealing with bipolarity and vagueness altogether because it contains bipolar fuzzy information and interval-valued bipolar fuzzy information simultaneously. In this article, we define some new notions such as concentration, dilation, support and core of a CBFS. We introduce cubic bipolar fuzzy relations (CBFRs) and some of their types. As in statistics with real variables, we define variance and covariance between two CBFSs. Then, we propose correlation coefficients and their weighted extensions on the basis of variance and covariance of CBFSs. Later on, some properties of these correlation coefficients are discussed. We explore that their values lie in [−1,1]. Moreover, we discuss the applications of the proposed correlation coefficients in pattern recognition and clustering analysis. Numerical examples are provided for better understanding of the applicability and efficiency of proposed correlation coefficients.