Contrapositive symmetry of fuzzy implications

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Abstract

Contrapositive symmetry of R- and QL-implications defined from t-norms, t-conorms and strong negations is studied. For R-implications, characterizations of contrapositive symmetry are proved when the underlying t-norm satisfies a residuation condition. Contrapositive symmetrization of R-implications not having this property makes it possible to define a conjunction so that the residuation principle is preserved. Cases when this associated conjunction is a t-norm are characterized. As a consequence, a new family of t-norms (called nilpotent minimum) owing several attractive properties is discovered. Concerning QL-implications, contrapositive symmetry is characterized by solving a functional equation. When the underlying t-conorm is continuous and the t-norm is Archimedean, the t-conorm must be isomorphic to the Lukasiewicz one, while the t-norm must be isomorphic to a member from the well-known Frank family of t-norms. Finally, contrapositive symmetry for some new families of fuzzy implications is investigated.

Original languageEnglish
Pages (from-to)141-156
Number of pages16
JournalFuzzy Sets and Systems
Volume69
Issue number2
DOIs
Publication statusPublished - Jan 27 1995

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Contrapositive
Fuzzy Implication
T-norm
Symmetry
T-conorms
Residuation
Isomorphic
Strong Negation
Symmetrization
Functional equation

Keywords

  • Contrapositive symmetry
  • Fuzzy implications
  • Nilpotent minimum
  • Strong negations
  • t-conorms
  • t-norms

ASJC Scopus subject areas

  • Artificial Intelligence
  • Logic

Cite this

Contrapositive symmetry of fuzzy implications. / Fodor, J.

In: Fuzzy Sets and Systems, Vol. 69, No. 2, 27.01.1995, p. 141-156.

Research output: Contribution to journalArticle

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