Br <sub> 0 </ Sub> - Algebra And Wbr <sub> 0 </ Sub> - Algebra

With the development of information science and artifical intelligence, the study of fuzzy logic and many-valued logic has achived plentiful important results. As the semantic theory of proposition logic system, logic algebras have become an important logic branch and study field. After Professor Wu Wangming proposed FI-algebra. Professor Xu Yang defined Lattice implication algebra, and Professor Wang Guojun established R0-algebra. Through the research about R0-algebra by Professor Wu Hongbo, BR0-algebra and WBR0-algebra were introduced.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, we give the basic concepts and results of lattice,∧-semi-lattice, FI-algebra, regular FI-algebra, Lattice implication algebra, BR0-algebra and WBR0-algebra which will be used in this paper.Chapter 2:Regular FI-algebra and WBR0-algebra. Firstly, regular FI-algebra is studied in depth, and its original definition is transformed. Secondly, the basical properties of WBR0-algebra are given. Finally, the relation between regular FI-algebra and WBR0-algebra is discussed. It points out that WBR0-algebra must be regular FI-algebra, and under certain conditions, regular FI-algebra can be WBR0-algebra.Chapter 3:BR0-algebra, WBR0-algebra and Lattice implication algebra. Firstly, the∧-semi-lattice form of BR0-algebra is given. And, some conditions of the∧-semi-lattice form are weakened, so a very simplified form of BR0-algebra is obtained. Secondly, a simplified∧-semi-lattice form of WBR0-algebra is introduced. Thirdly, according to the simplified form, an example of WBR0-algebra which is not a BR0-algebra is constructed. Finally, CBR0-algebra and CWBR0-algebra is introduced, and the relation between them and lattice implication algebra is discussed.