Construction of New Similarity Measures and Entropy for Interval-Valued Neutrosophic Sets with Applications

Abstract

The concepts of similarity measures and entropy have practical applications in computational intelligence, machine learning, image processing, neural networks, medical diagnosis, and decision analysis. An interval-valued neutrosophic set (IVNS) is strong model for modeling and handling uncertainties by using independent intervals of truthness, indeterminacy, and untruth. We introduce new similarity measures, entropy and inclusion relation for interval-valued neutrosophic sets (IVNSs). We introduce new inclusion relation named as type-f for ordering of interval neutrosophic sets. Additionally, a robust multi-attribute decision-making (MADM) method is developed by making use of proposed measures of similarity for IVNSs. A practical application for ranking of alternatives with newly developed MADM approach is illustrated by a numerical example for the car selection. The validity and superiority of new similarity measures with existing approaches is also given with the help of a comparison analysis.