Fuzzy Implication Methods in Fuzzy Logic

The choice of fuzzy implication methods is a significant problem in the theoretical development of fuzzy set and approximate reasoning. Many operation methods on the fuzzy implication were presented. In this research, first we analyze the truth values of the traditional two valued logical implication using sets theory, propose a novel truth table of the two valued logical implication, then acquire the simplification formulas of the expanded two-valued logical implication using the Karnaugh-map tool; Second we explore the relation of the expanded two valued logical implication and existent fuzzy implication operation methods, subsequently we propose two novel operation methods on the fuzzy implication based on the relation. We validate these two methods with mathematical deduction as well as a concrete example. At last, we compare the superiority of various fuzzy implication methods.