A characterization of the extension principle
Fuzzy Sets and Systems - Special issue: Dedicated to the memory of Richard E. Bellman
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Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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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 T"W (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 T"W-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.