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 \(F\).
The author discusses the problem whether different such fuzzifications may yield the same fuzzy function \(F\).
Reviewer: S.Gottwald (Leipzig)
MSC:
| 26E50 | Fuzzy real analysis |
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
References:
| [1] | Bandemer, H.; Näther, W., Fuzzy Data Analysis (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0758.62003 |
| [2] | Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: 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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