Nonstandard conjunctions and implications in fuzzy logic

J. Fodor, Tibor Keresztfalvi

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for conjunction and disjunction in fuzzy logic. We draw up a general framework for particular investigations, expressed by the so-called closure property. We suggest a constructive approach to the axiomatics of generalized modus ponens (GMP). As a consequence, a system of functional equations is obtained. Idempotent as well as nonidempotent conjunctions fulfilling this system are studied. Three classes of nonstandard conjunctions and implications are formulated so that all of them satisfy the proposed axioms.

Original languageEnglish
Pages (from-to)69-84
Number of pages16
JournalInternational Journal of Approximate Reasoning
Volume12
Issue number2
DOIs
Publication statusPublished - 1995

Fingerprint

Fuzzy Logic
Fuzzy logic
Generalized Modus Ponens
T-conorms
Closure Properties
T-norm
Idempotent
Axioms
Functional equation
Model
Class
Framework

Keywords

  • conjunctions
  • generalized modus ponens
  • R- and S-implications

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Nonstandard conjunctions and implications in fuzzy logic. / Fodor, J.; Keresztfalvi, Tibor.

In: International Journal of Approximate Reasoning, Vol. 12, No. 2, 1995, p. 69-84.

Research output: Contribution to journalArticle

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