Fuzzy measures for a correlation coefficient of fuzzy numbers under TW(the weakest t-norm)-based fuzzy arithmetic operations
Recently, the sup-min convolution based on Zadehs extension principle has been used by Liu and Kao [Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets and Systems 128 (2002) 267275], to calculate a fuzzy correlation coefficient. They used a mathematical programming approach to derive fuzzy measures based on the classical definition of the correlation coefficient. It is well known that TW (the weakest t-norm)-based addition and multiplication preserve the shape of LR fuzzy numbers. In this paper, we consider the computational aspect of the TW-based extension principle when the principle is applied to a correlation coefficient of LR fuzzy numbers. We give the exact solution of a fuzzy correlation coefficient without programming or the aid of computer resources.
correlation fuzzy sets tw based fuzzy arithmetic operations