Study On Several Problems Of SS-t-norms Based On Fuzzy Logic UL~*

Since L. A. Zadeh introduced fuzzy sets in 1965, the study on fuzzy systems has developed quickly, and many results in theory and application are gotten. The success in application is evident, especially in fuzzy control.T-norm and residuated lattice are important tools for researching fuzzy logic system. Basic fuzzy logic (BL for short) and BL- algebra are introduced by Hajek in 1998 to cope with the logic of continuous t-norms and their residua This approach to fuzzy logic has been developed by Esteva and Godo in 2001, where the authors introduced the logic MTL which aims at capturing the tautologies of left-continuous t-norms and their residua. There are some interesting schematic extensions of MTL including UL~* by zhangxiaohong, which are added a new involution denial operator "-" and the projection operator "△" in MTL.Constructing UL~* system incarnate the relations between the propositions in the formal system and provides the possible flexible logical foundation. Therefore researching UL~* system is very necessary. As we all know, completeness and axiom-system's independence are two very important logic properties, the former reflects the concordance between syntax and semantics in a fuzzy logic system, the latter reflects a system are pithy and compact. Although UL~* is complete, but it is not standard completeness, axiom-system of UL~* is not independent, too. It is know to the proposition logic reflects parts of logic properties although it have many similarity with predicate logic. For this, we construct the UL~* (?) system in the paper, and prove its completeness.The main content of the present paper as follows:The first part briefly introduces the development of fuzzy logic and the present domestic and foreign research's situation. Preparatory knowledge including some definitions and theorems are given because we will use them next parts. We introduce several common fuzzy logic systems and their schematic extension systems.The second part presents a kind of t-norm with parameter and research from qualitative and quota aspects, which meet with all conditions of t-norm, and build the foundation for the third part of research.In the third part, this paper firstly studies a fuzzy logic system-UL~* from its syntax and semantics, the system possess reliability and completeness but not independent. Finally discusses its application in approximate reasoning.The fourth part discusses the characteristic axiom (L∏G) of L∏G system is a tautology of SS-t-norms and their residuas, but not a theorem of UL~*. This result show that UL~* have not the standard completeness.In the fifth part, to further perfect the reasoning theory in fuzzy logic, research for predicate logic system is necessary. So this paper construct the predicate logic—UL~*(?) system and discuss its completeness initially.The final part summarizes this paper's research work and several questions expected to solve.