an:00919451
Zbl 0864.26010
Gebhardt, Albrecht
On types of fuzzy numbers and extension principles
EN
Fuzzy Sets Syst. 75, No. 3, 311-318 (1995).
00035389
1995
j
26E50 94D05
fuzzy functions; \(t\)-norm; extension principle; fuzzy numbers
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 \(F\).
S.Gottwald (Leipzig)