Qbl Algebra And Imtl Algebra And Systems

Recently, wide interests have arisen from the study of fuzzy logic and many-valued logic, these interests not only have greath'promoted development of all lcinds of logic systems and logic algebras, but also have acquired delightful research results. Professor Hdjek established basic logic algebra which is matched with basic propo-sitional logic system BL and has the basic structure-residuated lattice. The IMTL system and IMTL algebra are constructed by Esteva and Godo, and the IMTL sys-tem is the model extension of system MTL. which is pointed out. The basic fuzzy propositional calculus system BL* which is proposed by professor Wu hongbo. he proved out that propositional calculus system L* and Lukasiewicz system are the extension of the system BL* respectively.Based on the research of the above theories, the construction and the main contents of this paper are as follows:Chapter 1:Preliminaries. In this chapter, the basic concepts and results of residuated lattice, BL algebra, and BL* system which will be used in this paper are given out.Chapter 2:The QBL-algebra. First of all, a new algebra structure-QBL-algebra is proposed, and the properties of QBL-algebra are investigated. Secondly, the relation between Q.BL-algebra and.BL-algebra is discussed. Finally, the result of the equivalence about the two kinds of algebras is pointed out.Chapter 3:Prime boolean fuzzy ideal of IMTL algebra. First of all, the prime boolean fuzzy ideal of IMTL algebra is denned. Next its equivalence is given out. Finally, some new fuzzy sets based on fuzzy ideal are introduced, and the properties of them are discussed.Chapter 4:The relationship between IMTL system and BL* system. Firstly, some properties of BL* system are studied, and it proved that the axioms of IMTL system hold in BL* system. Secondly, so do the axioms of BL* system in IMTL system. Finally, we get the equivalnee of the two systems.