The Research Of Nodal Filters And Stabilizers Based On Equality Algebras

Equality algebras have been widely studied by scholars since it was pro-posed,which is an algebraic system corresponding to higher-order fuzzy logic.In the study of logical algebras,filter theory plays an important role.From a logical perspective,it is a set of provable formulas.This thesis will study the theory and application of nodal filter,stabilizers and fuzzy stabilizers on the basis of equality algebras.Firstly,we introduce the concepts of node element,nodal filter,and semin-ode element on equality algebras,and study some related properties and algebra-ic structure.At the beginning of the paper we discuss the relationship between node element and other elements.Then we define operations on NF(E)(the set of whole nodal filters on equality algebras E),and get(NF(E),(?)E)is an equality algebra.Then we explore the relations between nodal filter and(positive)?implication?prime?and boolean filters.The relations between node element and seminode element,and the algebraic structure of all semi node elements are discuss.Under some conditions,all seminode elements are lattice,Heyting algebra and Hertz algebra.Secondly,we introduce the concepts of left(right)stabilizers and fuzzy left(right)stabilizers on equality algebras.We also propose the definition of normal filters and obstinate filters on equality algebras?and discuss the relationship between the stabilizers and normal filters and obstinate filters.Then we study the relations between the stabilizers and several kinds of filters.Finally,we further discuss the relations between the fuzzy stabilizers and the fuzzy filters,and obtain that a fuzzy stabilizer is a fuzzy filter under some conditions.