A generalization of Yager's f-generated implications

Authors:
Aifang Xie;Huawen Liu
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China;School of Mathematics, Shandong University, Jinan, Shandong 250100, China
Venue:
International Journal of Approximate Reasoning
Year:
2013

Citing 28
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Abstract

Since Yager introduced f-generated implications in 2004, this class of fuzzy implications has been extensively investigated. In this paper, we generalize f-generated implications and get a new class of fuzzy implications called (f,g)-implications, which is different from the usual known classes of fuzzy implications. We discuss the basic algebraic properties of (f,g)-implications and study some classical logic tautologies (i.e., law of importation, contrapositive symmetry and distributivity over t-norms or t-conorms) for (f,g)-implications. Characterization of solutions to the corresponding fuzzy functional equations is obtained.