Abstract
In this paper, we propose three similarity measure methods for single-valued neutrosophic refined (SVNR) sets and interval neutrosophic refined (INR) sets based on Jaccard, Dice, and Cosine similarity measures of SVN-sets and interval neutrosophic sets. Furthermore, we suggest two multicriteria decision-making (MCDM) methods under SVNR environment and INR environment, and give applications of proposed MCDM methods. Finally, we suggest a consistency analysis method for proposed similarity measures between INR-sets and give an application to demonstrate process of the method.
Highlights
To overcome situations containing uncertainty and inconsistency data has been very important matter for researchers that study on mathematical modeling and decision making which is very important in some areas such as operations research, social economics, and management science, etc
Bhowmik and Pal [6] defined concept of intuitionistic neutrosophic set by combining intuitionistic fuzzy set and neutrosophic set, and gave some set theoretical operations of the intuitionistic neutrosophic set such as complement, union and intersection
We propose three similarity measure methods for single valued refined sets (SVNR-sets) and interval neutrosophic refined sets (INR-sets) by extending Jaccard, Dice and Cosine similarity measures under SVN-value and IN-value given by Ye in [28]
Summary
To overcome situations containing uncertainty and inconsistency data has been very important matter for researchers that study on mathematical modeling and decision making which is very important in some areas such as operations research, social economics, and management science, etc. Bromi et al [11] proposed concept of n-valued interval neutrosophic set and set theoretical operations on n-valued interval neutrosophic set (or interval neutrosophic set) such as union, intersection, addition, multiplication, scalar multiplication, scalar division, truth-favorite They developed a multi-criteria group decision making method and gave its an application in medical diagnosis. Mondal and Pramanik [14] introduced cotangent similarity measure of NR-sets and studied on its properties, and applied cotangent similarity measure to educational stream selection They proposed a similarity measure method [15] for NR-sets based on tangent function and gave an application in multi-attribute decision making.
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