Two types of implications derived from uninorms
Fuzzy Sets and Systems
On the first place antitonicity in QL-implications
Fuzzy Sets and Systems
QL-implications: Some properties and intersections
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Recent Literature Collected by Didier DUBOIS, Henri PRADE and Salvatore SESSA
Fuzzy Sets and Systems
On two types of discrete implications
International Journal of Approximate Reasoning
On dependencies and independencies of fuzzy implication axioms
Fuzzy Sets and Systems
Solutions to the functional equation I(x,y)=I(x,I(x,y)) for a continuous D-operation
Information Sciences: an International Journal
Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions
Journal of Computer and System Sciences
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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) = 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 → q = ¬q → ¬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. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 313–326, 2005.