Multi-criteria decision making method based on improved cosine similarity measure with interval neutrosophic sets

The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem, interval neutrosophic sets (INSs) is a power tool to deal with ambiguous information. Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process, the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs.

Based on an extension of existing cosine similarity, this paper first introduces an improved cosine similarity measure between interval neutosophic numbers, which considers the degrees of the truth membership, the indeterminacy membership and the falsity membership of the evaluation values. And then a multi-criteria decision-making method is established based on the improved cosine similarity measure, in which the ordered weighted averaging (OWA) is adopted to aggregate the neutrosophic information related to each alternative. Finally, an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method.

In the whole process of research and practice, it was realized that the application field of the proposed similarity measure theory still should be expanded, and the development of interval number theory is one of further research direction.

The main contributions of this paper are as follows: this study presents an improved cosine similarity measure under INSs, in which the weights of the three independent components of an interval number are taken into account; OWA are adopted to aggregate the neutrosophic information related to each alternative; and a multi-criteria decision-making method using the proposed similarity is developed under INSs.