Fuzzy weighted averages and implementation of the extension principle

This paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and, in particular, to weighted average operations in risk and decision analysis. A computational algorithm based on the α-cut representation of fuzzy sets and interval analysis is described. The method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner. Examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non-linear programming. The algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers.