R < Sub > 0 < / Sub > Residual Lattice Type And Properties

Fuzzy logic as the semantic theory of fuzzy proposition system Has formed an important branch of algebra. The enriched residuated lattice introduced by J.Pavelka is a very important algebraic structure in the classical logic. Lattice implication algebra based on lattice implication algebra by professor XuYang, BL-algebra of the background with MV-algebra, Godel algebra and product algebra established by professor Petr Hajek and R0-algebra for the purpose of revised Kleene logic introduced by professor WangGuojun are logic algebras which are based on the enriched residuated lattice. R0-algebra established by professor WangGuojun which is different from BL-algebra is an important branch of logic algebra.the construction and the detailed contents of this paper are as follows:Chapter1:Preliminaries. In this chapter,we gave the basic concepts of lat-tice.filter, residuate lattice,regular rediduate lattice Ro-algebra,Ro-residuate lattice and generalized Ro-residuate lattice which will be used in this paper.Chapter2:The properties of the Ro-residuate lattice. Firstly, The properties of the Ro-residuate lattice have been discussed. Secondly, it is proved that R0-residuate lattice and MTL-algebra are equivalent.Chapter3:Generalized Ro-residuated lattice. First of all, the definition of generalized Ro-residuated lattice is given and its properties are studied. Then, it is obtained regular generalized Ro-residuated lattice defined on the unit interval is MV-algebra. Finally, some other properties of generalized Ro-residuated lattice are discussed.Chapter4:The filter sets of Ro-residuated lattice. First,filter sets algebra becomes residual lattice with some resultsgiven if V-operation and∧-operation and the adjoint pair((?),â†')in filter sets of Ro-residuated lattice are defined.Then,the properties of this residuated lattice have been studied.Finally,the definition of cop-Ro-residuated lattice and its properties are given. It is proved that filter sets algebra of cop-Ro-residuated lattice is Boole algebra.