Mixed Correlation Coefficient Between Probability Hesitation Fuzzy Sets and Applications

Abstract

Probability hesitation fuzzy sets(PHFSs) have been paid increasing attention in the fuzzy domain nowadays, and correlation coefficient is becoming an important research content in fuzzy data analysis, many scholars have been conducted relevant researches on it. However, the existing correlation coefficients between PHFSs have some limitations, such as not considering the number of membership degrees and having counter-intuitive phenomenon to some extent. Therefore, we propose the mixed correlation coefficient between PHFSs. To begin with, we give the concepts of the average, variance, and length ratio of PHFE to illustrate the integrity, distribution, and length. Then, we define the average, variance, and length three correlation coefficients respectively on the above basic concepts. Furthermore, we construct the mixed correlation coefficient through combining these basic correlation coefficients, and extend to weighted form in addition, which addresses the issues of the available correlation coefficients. Finally, we utilize proposed correlation coefficient to analysis problems of data association and decision making. The effectiveness and rationality of the proposed method is illustrated at length.