Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment

New vector similarity measures of single-valued and interval neutrosophic sets are proposed by hybridizing the concepts of Dice and cosine similarity measures by determining the similarity measure values between the ideal alternative and each alternative.

Abstract

In this paper, we propose new vector similarity measures of single-valued and interval neutrosophic sets by hybridizing the concepts of Dice and cosine similarity measures. We present their applications in multi-attribute decision making under neutrosophic environment. We use these similarity measures to find out the best alternative by determining the similarity measure values between the ideal alternative and each alternative. The results of the proposed similarity measures have been validated by comparing with other existing similarity measures reported in the literature for multi-attribute decision making. The main thrust of the proposed similarity measures will be in the field of practical decision making, medical diagnosis, pattern recognition, data mining, clustering analysis, etc.