Correlation Coefficient of Complex Interval-Valued Intuitionistic Fuzzy Sets and Their Applications in Pattern Recognition

Complex interval-valued fuzzy sets are powerful tools for representing uncertainty and periodicity that occur in many real-life problems. They not only take both periodicity semantics and uncertainty into account but also describe the information using interval-valued membership grades, which gives experts more freedom to solve complex real-life problems effectively. Complex interval-valued fuzzy sets have been successfully employed many times in medical diagnosis and pattern recognition problems. In this article, two novel methods for computing the correlation coefficient and weighted correlation coefficient of complex interval-valued fuzzy sets are proposed. The methods employed fuzzy statistical parameters such as mean, variance, and covariance of complex interval-valued fuzzy sets. Several important mathematical properties are rigorously established. In order to establish the efficacy and implementation of the methods, a real-life application related to pattern recognition for mineral identification is discussed in detail. Furthermore, based on the proposed correlation and weighted correlation, a classification algorithm is developed. The time and space complexities of the proposed algorithm are analyzed. The proposed algorithm is validated through experiments conducted on two real benchmark datasets. The results demonstrate that the proposed approaches are more reliable and accurate than several existing approaches by achieving classification accuracies exceeding 98%.