A novel extension of TOPSIS to MCGDM with bipolar neutrosophic soft topology

Abstract

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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