International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Weighted average of fuzzy numbers under TW(the weakest t-norm)-based fuzzy arithmetic operations

  • Hong, Dug-Hun (Department of Mathematics, Myongji University) ;
  • Kim, Kyung-Tae (Department of Electronics and Electrical Information Engineering Kyungwon University)
  • Published : 2007.03.01
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Abstract

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

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