Fuzzy Domain And Its Characterizations

In this paper, we establish a framework of theory of L -Bifuzzy Domain and obtain many equivalent characterizations about L-Bifuzzy Domain and relatednotions by the level cut sets in [2] - [5] through introducing a fuzzy partial order of lattice value defined in [1] ( we denote by L the completely distributive lattice). Furthermore, the L-Bifuzzy continuous domain and L-Bifuzzy algebra domain are also defined, then we prove that they are the promotion of general continuous domain and algebraic domain.The main results are:In Chapter one, we introduce the background and the preliminaryknow ledge of L-fuzzy set and Domain.In Chapter two, some properties of the L-fuzzy mapping defined in [1] and its image and primary image are given. In addition, we define L-Bifuzzy monotonous mapping and obtain a series of equivalent characterizations.In Chapter three, L-Bifuzzy directed subset,directed union, L-Bifuzzy domain,L-Bifuzzy lower set and L-Bifuzzy ideal are introduced, and their characterizations are given.Moreover, the equivalent relation between L-Bifuzzy concepts and classical concepts are proved. Then, we give An example of L-Bifuzzy ideal.In Chapter four, This chapter is divided into two parts.In the first part, L-Bifuzzy Scott closed subset,L- Bifuzzy Scott inverse topology, L-Bifuzzy Scott continuous mapping and L-Bifiizzy Scott continuous mapping of inverse topology are defined on the basis of L-Bifuzzy domain given in the Chapter three and the crresponding characterizations are got. Moreover,we prove the equivalent relation between L-Bifuzzy Scott continuous mapping and L-Bifuzzy Scott continuous mapping of inverse topology. In second part, L-Bifuzzy way-bellow relation is defined and its properties are discussion. Then L-Bifuzzy continuous domain and L-Bifuzzy algebraic domain are defined.