Title: Measuring Pearson's correlation coefficient of fuzzy numbers with different membership functions under weakest t-norm
Authors: Mohit Kumar
Addresses: Department of Mathematics, Institute of Infrastructure Technology Research and Management, Ahmedabad-380026, Gujarat, India
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.
Keywords: Pearson's correlation coefficient; fuzzy number; weakest t-norm arithmetic.
International Journal of Data Analysis Techniques and Strategies, 2020 Vol.12 No.2, pp.172 - 186
Received: 27 Sep 2017
Accepted: 25 Oct 2018
Published online: 31 Mar 2020 *