A generalization of Yager's f-generated implications

作者：Xie Aifang; Liu Huawen^*

来源：International Journal of Approximate Reasoning, 2013, 54(1): 35-46.

DOI：10.1016/j.ijar.2012.08.005

• Fuzzy implications
• f-Generators
• Law of importation
• Contrapositive symmetry
• Distributivity of fuzzyimplications

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.

• 出版日期2013-1
• 单位山东大学