| In this paper, the main purpose is to discuss the properties of fuzzy connectnion and fuzzy (r,s) compactness in intuitionistic I-fuzzy topological spaces, investigate the notion and some results of stratified intuitionistic I-fuzzy topological spaces, lastly discuss the generated intuitionistic I-fuzzy topology and intuitionistic I-fuzzy topological spaces category.The primary studies in this paper are the following:(1)In intuitionistic I-fuzzy topological spaces, the notion of fuzzy (r,s) separated is given by using fuzzy (r,s) closure, besides the notions of fuzzy{r,s) connectedness and fuzzy (r,s) component are also given, discuss the equivalent theorem that intuitionistic I-fuzzy topological spaces is fuzzy (r,s) connectedness and some properites that intuitionistic fuzzy set is fuzzy (r,s) connectedness. We discuss the stratified intuitionistic I-fuzzy topological spaces and show that every fuzzy (r,s) component in an intuitionistic I-fuzzy topological spaces is fuzzy (r,s) component in the stratification of it. Last, we introduce the concepts of fuzzy (r,s) semi-regular, intuitionistic fuzzy weakly open, intuitionistic fuzzy weakly closed in intuitionistic I-fuzzy topological spaces. Fuzzy (r,s) compactness, fuzzy (r,s) almost compactness, fuzzy (r, s) near compactness are studied that related to fuzzy (r, s) semi-regular and intuitionistic fuzzy weakly continuity.(2)In this thesis, we introduce the concept of r level inclusive intuitionistic fuzzy bitopology, study the intuitionistic I-fuzzy topol-ogy generated by inclusive intuitionistic fuzzy bitopology and the intuitionistic I-fuzzy topology generated by the decreasing family of inclusive intuitionistic fuzzy bitopology. last we discuss the relations of generated intuitionistic I-fuzzy topological spaces category, inclu-Sive intuitionistic fuzzy bitopology spaces category, intuitionistic I-fuzzy topological spaces category. |
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