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Vertex method for computing functions of fuzzy variables. (English) Zbl 0634.94025
The calculation of (fuzzy) values of functions of fuzzy variables is considered. A so-called vertex method is proposed which is based on interval analysis, discretization, extension principle and alfa-cuts of the respective fuzzy sets. The method is easily implementable, and yields normal fuzzy sets, without widening of the resulting function value set.
Reviewer: J.Kacprzyk

##### MSC:
 94D05 Fuzzy sets and logic in connection with communication
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##### References:
 [1] Baas, S.; Kwakernaak, H.: Rating and ranking of multiple-aspect alternatives using fuzzy sets. Automatica 13, 47-58 (1977) · Zbl 0363.90010 [2] Dubois, D.; Prade, H.: Fuzzy sets and systems. (1980) · Zbl 0444.94049 [3] Mizumoto, M.; Tanaka, K.: Some properties of fuzzy numbers. Advances in fuzzy sets theory and applications (1979) [4] Moore, R. E.: Interval analysis. (1966) · Zbl 0176.13301 [5] Nakamura, Y.: Extension of algebraic calculus on fuzzy numbers using ${\alpha}$-level sets. Paper presented at fuzzy information processing (FIP-84) symposium (1984) [6] Schmucker, K. J.: Fuzzy sets, natural language computations, and risk analysis. (1984) · Zbl 0552.90025 [7] Dong, W. M.; Wong, F. S.: Fuzzy weighted averages and implementation of the extension principle. Fuzzy sets and systems 21, 183-199 (1987) · Zbl 0611.65100 [8] Zadeh, L. A.: Fuzzy sets. Inform. and control 8, 338-353 (1965) · Zbl 0139.24606 [9] Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning. Inform. sci. 8, 199-249 (1975) · Zbl 0397.68071