An Analytic Formula for the Weighted Average of Fuzzy Numbers under TW(the Weakest t-norm)-based Fuzzy Arithmetic Operations

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. Recently, T_W-based division was considered by Hong (2006). In this paper, we consider the computational aspect of the extension principle by the use of T_W when this principle is applied to fuzzy weighted average operations. We give the exact solution for the case where the variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources