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 Zadeh’s extension principle has been used by Liu and Kao [Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets and Systems 128 (2002) 267–275], 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 L–R 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 L–R fuzzy numbers. We give the exact solution of a fuzzy correlation coefficient without programming or the aid of computer resources.