m-Polar Neutrosophic Topology with Applications to Multi-criteria Decision-Making in Medical Diagnosis and Clustering Analysis

In this paper, we first introduce novel concepts of m-polar neutrosophic set (MPNS) and topological structure on m-polar neutrosophic set by combining the m-polar fuzzy set (MPFS) and neutrosophic set. Then, we investigate several characterizations of m-polar neutrosophic set and establish its various operations with the help of examples. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). We establish m-polar neutrosophic topology and define interior, closure, exterior, and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results with counter examples, which hold for classical set theory, but do not hold for m-polar neutrosophic set theory. We introduce a cosine similarity measure and a set theoretic similarity measure for m-polar neutrosophic sets (MPNSs). Furthermore, we present three algorithms for multi-criteria decision-making (MCDM) in medical diagnosis and clustering analysis under uncertainty by using m-polar neutrosophic sets (MPNSs) and m-polar neutrosophic topology. Lastly, we present advantages, validity, flexibility, and comparison of our proposed algorithms with the existing techniques.