On triangular norm-based propositional fuzzy logics

Dan Butnariu; Erich Peter Klement; Samy Zafrany

doi:10.1016/0165-0114(94)00172-4

On triangular norm-based propositional fuzzy logics

Dan Butnariu, Erich Peter Klement, Samy Zafrany

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given. Tautologies, contradictions and contigencies with respect to such fuzzy logics are studied, in particular for the important cases of min-max and Łukasiewicz logics. Finally, fundamental t-norm-based fuzzy logics are shown to provide a gradual transition between min-max and Łukasiewicz logics.

Original language	English
Pages (from-to)	241-255
Number of pages	15
Journal	Fuzzy Sets and Systems
Volume	69
Issue number	3
DOIs	https://doi.org/10.1016/0165-0114(94)00172-4
State	Published - 10 Feb 1995

Keywords

Fuzzy logics
Min-max logic
Satisfiability
Triangular norms
Łukasiewicz logic

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/0165-0114(94)00172-4

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title = "On triangular norm-based propositional fuzzy logics",

abstract = "Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given. Tautologies, contradictions and contigencies with respect to such fuzzy logics are studied, in particular for the important cases of min-max and {\L}ukasiewicz logics. Finally, fundamental t-norm-based fuzzy logics are shown to provide a gradual transition between min-max and {\L}ukasiewicz logics.",

keywords = "Fuzzy logics, Min-max logic, Satisfiability, Triangular norms, {\L}ukasiewicz logic",

author = "Dan Butnariu and Klement, {Erich Peter} and Samy Zafrany",

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AU - Zafrany, Samy

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N2 - Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given. Tautologies, contradictions and contigencies with respect to such fuzzy logics are studied, in particular for the important cases of min-max and Łukasiewicz logics. Finally, fundamental t-norm-based fuzzy logics are shown to provide a gradual transition between min-max and Łukasiewicz logics.

AB - Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given. Tautologies, contradictions and contigencies with respect to such fuzzy logics are studied, in particular for the important cases of min-max and Łukasiewicz logics. Finally, fundamental t-norm-based fuzzy logics are shown to provide a gradual transition between min-max and Łukasiewicz logics.

KW - Fuzzy logics

KW - Min-max logic

KW - Satisfiability

KW - Triangular norms

KW - Łukasiewicz logic

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JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

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ER -

On triangular norm-based propositional fuzzy logics

Abstract

Keywords

ASJC Scopus subject areas

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