Measuring Pearson's correlation coefficient of fuzzy numbers with different membership functions under weakest t-norm

Abstract

In statistical theory, the correlation coefficient has been widely used to assess a possible linear association between two variables and often calculated in crisp environment. In this study, a simplified and effective method is presented to compute the Pearson's correlation coefficient of fuzzy numbers with different membership functions using weakest triangular norm (t-norm)-based approximate fuzzy arithmetic operations. Different from previous research studies, the correlation coefficient computed in this paper is a fuzzy number rather than a crisp number. The proposed method has been illustrated by computing the correlation coefficient between the technology level and management achievement from a sample of 15 machinery firms in Taiwan. The correlation coefficient computed by proposed method has less uncertainty and obtained results are more exact. The computed results have also been compared with existing approaches.