Residual implications revisited. Notes on the Smets-Magrez Theorem

被引：65

作者：

Baczynski, M ^{[1
]}

机构：

[1] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

FUZZY SETS AND SYSTEMS | 2004年 / 145卷 / 02期

关键词：

functional equations; fuzzy implication; Goguen implication; Lukasiewicz implication; residual implication; triangular norm;

D O I：

10.1016/S0165-0114(03)00245-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

It is well known that continuous residual implications are conjugate with the Lukasiewicz implication. This fact was first obtained by Smets and Magrez (Internat. J. Approx. Reason. 1 (1987) 327). In this paper we show that the assumption of the monotonicity in this theorem can be omitted. We are also interested in the characterization of the other classes of fuzzy implications. As a result, the characterization of fuzzy implications, which are conjugate with the Goguen implication, is obtained. Besides these main results we present some new facts concerning the properties of fuzzy implications. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：267 / 277

页数：11

共 15 条

[1] On a class of distributive fuzzy implications [J].