On interval fuzzy negations

被引:107
作者
Bedregal, Benjamin Callejas [1 ]
机构
[1] Univ Fed Rio Grande do Norte, Grp Log Language Informat Theory & Applicat, Dept Informat & Appl Math, BR-59072970 Natal, RN, Brazil
关键词
Interval representations; Fuzzy negations; Equilibrium point; Automorphisms; T-NORMS; REPRESENTATION;
D O I
10.1016/j.fss.2010.04.018
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
There exist infinitely many ways to extend the classical propositional connectives to the set [0, 1], preserving their behaviors in the extremes 0 and 1 exactly as in the classical logic. However, it is a consensus that this issue is not sufficient, and, therefore, these extensions must also preserve some minimal logical properties of the classical connectives. The notions of t-norms, t-conorms, fuzzy negations and fuzzy implications taking these considerations into account. In previous works, the author, joint with other colleagues, generalizes these notions to the set U = {[a, b]vertical bar 0 <= a <= b <= I}. providing canonical constructions to obtain, for example, interval t-norms that are the best interval representations of t-norms. In this paper, we consider the notion of interval fuzzy negation and generalize, in a natural way, several notions related with fuzzy negations, such as the ones of equilibrium point and negation-preserving automorphism. We show that the main properties of these notions are preserved in those generalizations. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:2290 / 2313
页数:24
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