A Categorical Property Of (L,M)-fuzzy Convergence Spaces And Determination Of Intuitionistic Fuzzy Topologies

In paper [8],the concept of L-filter is introduced firstly. Then many scholars begin to research the L-filter (such as in the literature [2] and [7] stratified L-filter is studied) and some profound results are obtained. On this basic,in the paper, M-filters on LX are introduced, and intersection, join, and product operations of M-filters on LX are studied. It is proved that the category of (L, M)-fuzzy convergence spaces is a topological construct. Furthermore, the notions of product (L, M)-fuzzy convergence spaces, coproduct (L, M)-fuzzy convergence spaces and quotient (L, M)-fuzzy convergence spaces are defined.Order isomorphism is an important concept in mathematics. For a given set X,the set of all topology on X is written T(X), the set of all Kuratovski closure operator on X is written CL(X). If we can give the partial order relations≤on CL(X) and the isomorphism F:(CL(X),≤)â†'(T(X),(?)), then we can use Kuratovski closure operator to determine the topology. This paper studied determination of intuitionistic fuzzy topologies.The construction and the main contents of this paper are as follow:Chapter1Preliminaries. In this chapter,we gave the basic knowledge of complete Heyting algebra,frame,category, intuitionistic fuzzy set and intuitionistic fuzzy topology.Chapter2A categorical property of (L, M)-fuzzy convergence spaces. In this chapter, M-filters on LX are given and operations of intersection, join, and product. It is proved that the category of (L, M)-fuzzy convergence spaces is a topological construct. At the end, the notions of product (L, M)-fuzzy convergence spaces, coproduct (L, M)-fuzzy convergence spaces and quotient (L, M)-fuzzy convergence spaces are defined.Chapter3The determination of intuitionistic fuzzy topologies. In this chapter, we studied cryptomorphic properties of intuitionistic fuzzy topologies. For an arbi-trary set X, appropriate order relations on IFWCL(X)(the set of all intuitionistic fuzzy weak closure operators), IFWIN(X)(the set of all intuitionistic fuzzy weak interior operators), IFWOU(X)(the set of all intuitionistic fuzzy weak exterior op-erators) and IFWB(X)(the set of all intuitionistic fuzzy weak boundary operators) can be defined respectively, which make IFWCL(X), IFWIN(X), IFWOU(X) and IFWB(X) to be complete lattices that are isomorphic to (IFT(X),(?)), where IFT(X) is the set of all intuitionistic fuzzy topologies on X.