On fuzzification of propositional logics
type: Item
instance of: scholarly article
title: On fuzzification of propositional logics
zbMATH Open document ID: 0960.03020
DOI: 10.1016/S0165-0114(97)00369-2
published in: Fuzzy Sets and Systems
publication date: 2001-05-10T00:00:00Z
review text: The paper elaborates the idea of fuzzifying arbitrary crisp logics. The author proposes two different procedures. Due to the first one, the language of the propositional logic \(L\) is extended by a family of unary propositional operators and \(L\) is extended by the list of axioms related to the basic properties of the measure of fuzziness. The new formulas \(\Phi_r A\), \(\Phi^r A\) represent two kinds of propositions, namely ``the measure of fuzziness of a formula \(A\) is at least \(r\)'' and ``\(\ldots\) at most \(r\)'', respectively. The semantics is constructed using Kripke models. The deduction and completeness theorems are proved for such extensions. The second procedure is more abstract considering an algebra of extensions of a crisp logic \(L\). This algebra is proved to be a complete Heyting algebra and taken as fuzzification of \(L\). The extracted membership function is then connected with the deduction relation.
reviewed by: Vilém Novák
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 1369999
zbMATH Keywords: fuzzy logic
zbMATH Keywords: Kripke model
zbMATH Keywords: fuzzification
zbMATH Keywords: measure of fuzziness
zbMATH Keywords: semantics
zbMATH Keywords: Heyting algebra
author: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: s0165-0114(97)00369-2
OpenAlex ID: W2091864044
description: scientific article; zbMATH DE number 1369999