Mathematical analysis demonstrates the behavior of quasi-neighbourhoods in bipolar fuzzy topological spaces, suggesting a complete determination of open sets.
Analogous to fuzzy topology, the concepts of quasi-coincidence and Q-neighbourhoods are indispensable tools in exploring many bipolar fuzzy topological properties like convergence of nets, separation axioms, closure and denseness. The present paper aims at incorporating quasi-coincidence into bipolar fuzzy context and investigating the properties of Q-neighbourhoods in bipolar fuzzy topological spaces. As the system of Q-neighbourhoods 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 Q-neighbourhoods. Further, it is proved that the Q-neighbourhoods of bipolar fuzzy points completely determine the open sets in a bipolar fuzzy topological space.
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Mohan et al. (2026) studied this question.
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