标题：A generalization of Yager\'s f-generated implications
作者：Aifang Xie;Huawen Liu
作者机构：[Xie, A] School of Mathematics, Shandong University, Jinan, Shandong 250100, China;[ Liu, H] School of Mathematics, Shandong University, Jinan, Shando 更多
通讯作者地址：[Liu, HW]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：International journal of approximate reasoning
关键词：fuzzy implications;f-generators;law of importation;contrapositive symmetry;distributivity of fuzzyimplications
摘要：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, con-trapositive symmetry and distributivity over t-norms or t-conorms) for (f, g)-implications. Characterization of solutions to the corresponding fuzzy functional equations is obtained.