The R0-type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens

Fuzzy modus ponens (briefly, FMP) is the most fundamental form of fuzzy reasoning and has been extensively discussed by diverse researchers. The aim of the present paper is to propose a formalized form of FMP, called generalized modus ponens, in the fuzzy logic system and solve it in , and then provide its numerical version as a new algorithm for solving FMP. As a preparation, some related questions such as what is a fuzzy logic metric space, why is R0-implication operator selected, and what kind of merits does the fuzzy pseudo-metric logic space (F(S),ρ) possess, etc. are analyzed.