DBR ₀ - Algebraic Properties And Related Research

As we all know, 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.and achived series of research results. Algebra of logic as a semantic theory of fuzzy propositional logic system has formed an important branch of algebra and research directions. Professor Wang Guojun established Ro-algebra. Through the research of Ro-algebra by Professor Wu Hongbo, BRo-algebra and WBRo-algebra. have been investigated, Firstly, based to the research in the non-ordered representation of BRo-algebra, and using the characteristics of duality in the logic algebra about Intersection and Unite, and the ideology of dual category theory, a symmetric form of BRo-algebra—DBRo-algebra is established in general set from the perspective of classical algebra. Next, it is proved that DBRo-algebra is another new non-ordered representation of BRo-algebra, in which the order relation of BR0-algebra is contained in the basic operation· andâ†'. Lastly, according to the form of WDBRo-algebra, a new weaken BRo-algebra—LBRo-algebra is proposed, and it is proved that LBRo-algebra and regular FI algebra are the same algebraic structure.The construction and the detailed contents of this paper are as follow:Chapeter1:Preliminaries.In this chapter, we gave the basic concepts of lattice, logic algebra; BRo-algebra; DBRo-algebra; WB Ro-algebra.Chapeter2:The definition of the DBRo-algebra and its properties. discussed the properties of the DBRo-algebra, and proved the equivalence of DBRo-algebras and BRo-algebras.Chapeter3:This chapter first gives the definition of WDBRo-algebra and discussed its independence, Then the definition of WDBRo-algebra is simplified, Then we discussed the properties of WDBRo-algebras. And from the angle that WDBRo-algebra. algebra is a bounded lattice.Chapeter4:This chapter first discussed the difference of the WDBRo-algebra and BRo-algebra. a weaken form of WDBRo-algebra—the LBRo-algebra. and proved that the regular FI-algebra and LBRo-algebra are equivalence.