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 TW (the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. Recently, TW-based division was considered by Hong (2006). In this paper, we consider the computational aspect of the extension principle by the use of TW 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