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The main purpose of this paper is to present some fundamental properties of small and large inductive dimensions in intuitionistic fuzzy topological spaces. Our results can be regarded as a study of their properties such as proves subset theorems, zero dimensionality and topological property of an intuitionistic fuzzy small inductive dimension. Furthermore, we introduce a large inductive dimension of intuitionistic fuzzy bi-compact and normal spaces.

In this study, a new concept of generalized intuitionistic fuzzy topological space, called intuitionistic fuzzy b ∼ -door space, is introduced and several characterizations of intuitionistic fuzzy b ∼ -door spaces are analyzed. Many examples were introduced to prove the validity of these concepts. Moreover, certain properties and relationships between intuitionistic fuzzy b ∼ -door spaces and other intuitionistic fuzzy topological spaces were investigated.

In this paper a new concept of generalized intuitionistic fuzzy topological space called intuitionistic fuzzy β generalized α normal space is introduced. Several characterizations of intuitionistic fuzzy β generalized α normal space, intuitionistic fuzzy strongly β generalized α normal and intuitionistic fuzzy strongly β generalized α regular spaces are studied. Moreover, the related intuitionistic fuzzy functions with intuitionistic fuzzy β generalized α normal spaces are investigated.