A new class of fuzzy implications derived from generalized h-generators

  • Authors:
  • Hua-Wen Liu

  • Affiliations:
  • School of Mathematics, Shandong University, Jinan, Shandong 250100, China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2013

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Abstract

A new class of fuzzy implications, called (h,min)-implications, is introduced by means of generalized h-generators. Basic properties of these implications are discussed. It is shown that the (h,min)-implications are really a new class different from the known (S,N)-, R-, QL- and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz., law of importation, contraction law and distributivity over triangular norms (t-norms) and triangular conorms (t-conorms) are investigated. A series of necessary and sufficient conditions are established, under which the corresponding functional equations are satisfied.