Bipolar fuzzy topological spaces
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We define a bipolar fuzzy point and obtain some of its properties. Also we introduce the concepts of a bipolar fuzzy topology, bipolar fuzzy base and subbase and find some properties of each concept. Second, we define a bipolar fuzzy neighborhood and continuity and obtain bipolar fuzzy analogues of many results concerning to classical neighborhood and continuity. Third, we introduce the concepts of a bipolar fuzzy subspace and a bipolar fuzzy quotient space and find some properties of each concept. In particular, we prove the existence of the bipolar fuzzy initial topology Finally, we define a compactness in bipolar fuzzy topological spaces and investigate some of its properties. In particular, we obtain `Alexander Subbase Theorem' in the sense of bipolar fuzzy sets.
Abstract
We define a bipolar fuzzy point and obtain some of its properties. Also we introduce the concepts of a bipolar fuzzy topology, bipolar fuzzy base and subbase and find some properties of each concept. Second, we define a bipolar fuzzy neighborhood and continuity and obtain bipolar fuzzy analogues of many results concerning to classical neighborhood and continuity. Third, we introduce the concepts of a bipolar fuzzy subspace and a bipolar fuzzy quotient space and find some properties of each concept. In particular, we prove the existence of the bipolar fuzzy initial topology Finally, we define a compactness in bipolar fuzzy topological spaces and investigate some of its properties. In particular, we obtain `Alexander Subbase Theorem' in the sense of bipolar fuzzy sets.
참고문헌 (19)
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