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On contra-symmetry and MPT conditionality in fuzzy logic

✍ Scribed by E. Trillas; C. Alsina; E. Renedo; A. Pradera

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 136 KB
Volume: 20
Category: Article
ISSN: 0884-8173
DOI: 10.1002/int.20068

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✦ Synopsis

This article deals with the N-contrapositive symmetry of fuzzy implication operators J verifying either Modus Ponens or Modus Tollens inequalities, in a similar and complementary framework to the one in which Fodor ("Contrapositive symmetry of fuzzy implications." Fuzzy Set Syst 1995;69:141-156) did begin with the subject in fuzzy logic, that is, with the verification of J ~a, b! ϭ J ~N~b!, N~a!! for all a, b in @0,1# and some strong-negation function N. This property corresponds to the classical p r q ϭ ¬q r ¬p. The aim of this article is to study that property in relation to either Modus Ponens or Modus Tollens meta-rules of inference when the functions J are taken among those that belong to the usual families of implications in fuzzy logic. That is, the contra-positive of S implications, R implications, Q implications, and Mamdani-Larsen operators, verifying either Modus Ponens or Modus Tollens inequalities or both, the conditionality's aspect on which lies the complementarity with Fodor. Within this study new types of implication functions are introduced and analyzed.

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