The Wbr <sub> 0 </ Sub> Algebra

With the development of electronic technique and the appearance of artifical intelligence, the study of fuzzy logic and logic algebra has become one of the hot topics in the field. Many scholars have achived a series of research results. Pro-fessor Wang Guojun established R0-algebra.Through the research of R0-algebra, by Professor Wu Hongbo, BR0-algebra and WBRo-algebra have been introduced. The properties of WBR0-Algebra have been investigated, the equivalent relationship be-tween WBR0-algebra and regular residuated lattice has been obtained in this article,the construction and the detailed contents of this paper are as follows:Chapter 1:Preliminaries. In this chapter,we gave the basic concepts of lat-tice,regular rediduate lattice,BR0-algebra,WBRo-algebra which will be used in this paper.Chapter 2:The properties of the WBR0-Algebra.Firstly.the independence of the conditions of WBRo-Algebra has been studied, and the definition of WBR0-Algebra has simplified in some extent. Secondly, the properties of WBR0-Algebra have been investigated, then it was proved to be a bounded lattice by the way of algebra method.Finally,thc filter and ideal of WBR0-algebra have been introduced.Chapter 3:The equivalent relationship between Regular rediduate lattice and the WBR0-algebra. The properties of Regular residuated lattice have been inves-tigated, the equivalent relationship between WBR0-algebra and Regular residuated lattice has been obtained.Chapter 4:Construction of WBR0-Algebra.First of all.an construction of WBR0-algebra and non-BR0-algebra has been established which explains WBR0-algebra is actually different from BR0-algebra. Moreover, this construction also shows that WBR0-algebra dosen t satisfy distributive law of lattices.Secondly, the other example explains the diffence between WBR0-algebra and other common al-gebras. At last,the relationship of some common logic algebras has been displayed through a graph.