an:00890912
Zbl 1018.03511
Hong, Dug Hun; Hwang, Seok Yoon
On the compositional rule of inference under triangular norms
EN
Fuzzy Sets Syst. 66, No. 1, 25-38 (1994).
00033615
1994
j
03B52 03E72
compositional rule of inference; Archimedean t-norm; membership function
Summary: The aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under an Archimedean t-norm, where both the observation and the relation parts are given by Hellendoorn's \(\phi\)-function [\textit{H. Hellendoorn}, Fuzzy Sets Syst. 35, No. 2, 163-183 (1990; Zbl 0704.03006)]. In particular, if the left and right spreads of the observation part are the same as those of the relation part, then this upper bound is the exact membership function, which generalizes the earlier result of \textit{R. Full??r} and \textit{H.-J. Zimmermann} [Fuzzy Sets Syst. 51, No. 3, 267-275 (1992; Zbl 0782.68110)] in that the assumption of twice differentiability is deleted.
Zbl 0704.03006; Zbl 0782.68110