Some properties of fuzzy reasoning in propositional fuzzy logic systems

In order to analyze the logical foundation of fuzzy reasoning. this paper first introduces the concept of generalized roots of theories in Lukasiewicz propositional fuzzy logic Luk. Godel propositional fuzzy logic God. Product propositional fuzzy logic II. and nilpotent minimum logic NM (the R(o)-propositional fuzzy logic L*) Next, it is proved that all consequences of a theory r named D(r). are completely determined by its generalized root whenever r has a generalized root Moreover. it is proved that every finite theory r has a generalized root, which can be expressed by a specific formula Finally, we demonstrate the existence of a non-fuzzy version of Fuzzy Modus Ponens (FMP) in Luk, God, II and NM (L), and we provide its numerical version as a new algorithm for solving FMP (C) 2010 Elsevier Inc All rights reserved