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On types of fuzzy numbers and extension principles. (English) Zbl 0864.26010
A real function $$f$$ often is fuzzified into a fuzzy function $$F$$ in such a way that the arguments of $$F$$ become fuzzy numbers and its values are determined from $$f$$ via the extension principle $$EP$$. In general, $$EP$$ depends on a $$t$$-norm $$T$$. Restricting furthermore the input fuzzy numbers to symmetric $$LR$$-fuzzy numbers with $$L=R$$, the fuzzification of $$f$$ depends of the pair $$(L,T)$$.
The author discusses the problem whether different such fuzzifications may yield the same fuzzy function $$F$$.

MSC:
 26E50 Fuzzy real analysis 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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References:
 [1] Bandemer, H.; Näther, W., Fuzzy data analysis, (1992), Kluwer Academic Publishers Dordrecht · Zbl 0758.62003 [2] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049 [3] Otto, K.N.; Lewis, A.D.; Antonsson, E.K., Approximating α-cuts with the vertex method, Fuzzy sets and systems, 55, 43-50, (1993) · Zbl 0931.26010
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