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**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

### MSC:

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) |

### Keywords:

fuzzy weighted average; computational algorithm; combinatorial interval analysis; extension principle; algebraic mappings; weighted average operations; risk and decision analysis; fuzzy sets
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\textit{W. M. Dong} and \textit{F. S. Wong}, Fuzzy Sets Syst. 21, 183--199 (1987; Zbl 0611.65100)

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### References:

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