A new class of fuzzy implications. Axioms of fuzzy implication revisited

被引：50

作者：

Turksen, IB

Kreinovich, V ^{[1
]}

Yager, RR

机构：

[1] Univ Texas, Dept Comp Sci, El Paso, TX 79968 USA

[2] Univ Toronto, Dept Ind Engn, Toronto, ON M5S 1A4, Canada

[3] Iona Coll, Inst Machine Intelligence, New Rochelle, NY 10801 USA

来源：

FUZZY SETS AND SYSTEMS | 1998年 / 100卷 / 1-3期

关键词：

basic theory; fuzzy logic; operators;

D O I：

10.1016/S0165-0114(97)00066-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Many different fuzzy implication operators have been proposed; most of them fit into one of the two classes: implication operations that are based on an explicit representation of implication A --> B in terms of &, V, and inverted left perpendicular (e.g., S-implications that are based on the formula B V inverted left perpendicular A), and R-implications that are based on an implicit representation of implication A --> B as the weakest C for which C & B implies A. However, some fuzzy implication operations (such as b(a)) cannot be naturally represented in this form. To describe such operations, we propose a new (third) class of implication operations called A-implications whose relation to &, V, and inverted left perpendicular is described by (implicit) axioms. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

引用

页码：267 / 272

页数：6