Normal forms and truth tables for fuzzy logics
type: Item
instance of: scholarly article
title: Normal forms and truth tables for fuzzy logics
zbMATH Open document ID: 1027.03023
DOI: 10.1016/S0165-0114(02)00566-3
author: Mai Gehrke
author: Carol Walker
author: Elbert Walker
published in: Fuzzy Sets and Systems
publication date: 2003-09-07T00:00:00Z
review text: Classical representability of logical equivalence by means of (finite) truth tables is discussed. While the Boolean logics (algebras) require 2 truth values only, for the fuzzy logics (algebras) it is shown that 3 truth values are sufficient. Moreover, in the case of interval-valued fuzzy logics (algebras) it is enough to examine the logical equivalence by means of truth tables with 4 truth values. Normal forms in several special algebras (De Morgan, Kleene), fuzzy logics and interval-valued fuzzy logics are presented. The paper extends previous results on universal normal forms and truth tables of \textit{I. B. Türksen} [e.g., IEEE Trans. Fuzzy Syst. 6, 295-303 (1998)] and of the authors [Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, 223-238 (1997)].
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 1975909
zbMATH Keywords: fuzzy connectives
zbMATH Keywords: continuous t-norm
zbMATH Keywords: fuzzy logic
zbMATH Keywords: interval-valued fuzzy logic
zbMATH Keywords: truth tables
zbMATH Keywords: logical equivalence
zbMATH Keywords: normal forms
MaRDI profile type: Publication
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full work available at URL: s0165-0114(02)00566-3
OpenAlex ID: W2008679964
description: scientific article; zbMATH DE number 1975909