Fuzzy weighted averages and implementation of the extension principle. (English) Zbl 0611.65100

From authors’ summary: This paper addresses the computational aspect of the extension principle when the principle is applid to algebraic mappings and, in particular, to weighted average operations in risk and decision analysis. A computational algorithm based on the \(\alpha\)-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 nonlinear programming. The algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers.
Reviewer: G.Alefeld


65C99 Probabilistic methods, stochastic differential equations
65G30 Interval and finite arithmetic
62C05 General considerations in statistical decision theory
03E72 Theory of fuzzy sets, etc.
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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