Hypercomplex Neutrosophic Similarity Measure & Its Application in Multicriteria Decision Making Problem

Abstract

Abstract. Neutrosophic set is very useful to express uncertainty, impreciseness, incompleteness and inconsistency in a more general way. It is prevalent in real life application problems to express both indeterminate and inconsistent information. This paper focuses on introducing a new similarity measure in the neutrosophic environment. Similarity measure approach can be used in ranking the alternatives and determining the best among them. It is useful to find the optimum alternative for multi criteria decision making (MCDM) problems from similar alternatives in neutrosophic form. We define a function based on hypercomplex number system in this paper to determine the degree of similarity between single valued neutrosophic sets and thus a new approach to rank the alternatives in MCDM problems has been introduced. The approach of using hypercomplex number system in formulating the similarity measure in neutrosophic set is new and is not available in literature so far. Finally, a numerical example demonstrates how this function determines the degree of similarity between single valued neutrosohic sets and thereby solves the MCDM problem.