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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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