Quasi-Neighborhoods in Bipolar Fuzzy Topological Spaces

Source abstract

Analogous to fuzzy topology, the concepts of quasi-coincidence and [Formula: see text]-neighborhoods are indispensable tools in exploring many bipolar fuzzy topological properties like convergence of nets, separation axioms, closure and denseness. This paper aims at incorporating quasi-coincidence into bipolar fuzzy context and investigating the properties of [Formula: see text]-neighborhoods in bipolar fuzzy topological spaces. As the system of [Formula: see text]-neighborhoods of a bipolar fuzzy point is found to be not closed under intersections in general, a necessary and sufficient condition for this closure is derived. Also, bases and subbases of bipolar fuzzy topological spaces are characterized in terms of [Formula: see text]-neighborhoods. Further, it is proved that the [Formula: see text]-neighborhoods of bipolar fuzzy points completely determine the open sets in a bipolar fuzzy topological space.