In this paper, we bring out the idea of bipolar neutrosophic soft topology based on bipolar neutrosophic soft set (BNS-set). We study the properties of classical topology under bipolar neutrosophic soft (BNS) vagueness. The BNS-topology is the generalization of the fuzzy topology. We discuss certain properties of BNS-topology including, BNS-closure, BNS-interior, BNS-exterior and BNS-frontier by utilizing BNS-points. We also study the concept of BNS-subspace, BNS-neighborhoods and BNS-base for BNS-topology with the help of detailed examples and theorems. Furthermore, we propose: Technique for Order Preferences by Similarity to an Ideal Solution (TOPSIS) method under BNS-topological environment to deal with similarities in medical diagnosis. We see the importance of BNS-topology in multi criteria group decision making (MCGDM) as well. We present a numerical example with real background to demonstrate the validity of our model. Finally, we make a method-based and set-based comparison analysis of proposed method with some existing methods. Compared with existing MCGDM models, this study provides a flexible framework to form an approximate decision model to real-world MCGDM problems.
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