Multi Criteria Decision Making Method Based On A Cross Entropy With Interval Neutrosophic Sets

In this paper, two optimisation models are established to determine the criterion weights in multi-criteria decision-making situations where knowledge regarding the weight information is incomplete and the criterion values are interval neutrosophic numbers.

Multi-attribute decision-making refers to the decision-making problem of selecting the optimal alternative or sorting the scheme when considering multiple attributes, which is widely used in engineering design, economy, management and military, etc. But in real application, the attribute information of many objects is often inaccurate or uncertain, so it is very important for us to find a useful and efficient method to solve the problem.

With respect to multi-criteria decision-making (MCDM) problems in which the criteria denote the form of single-valued neutrosophic sets (SVNSs), and the weight information is also fully unknown, a novel MCDM method based on qualitative flexible multiple criteria (QUALIFLEX) is developed. Firstly, the improved cosine measure of the included angle between two SVNSs is defined.

Fuzzy sets (FSs), which were proposed by Zadeh (1965), are regarded as a comprehensive tool for solving multi-criteria decision-making(MCDM)problems(Bellman&Zadeh,1970).

The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties.

The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set.

In this paper, we propose three similarity measure methods for single-valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single-valued neutrosophic sets and interval neutrosophic sets.

This book is a printed edition of the Special Issue "Neutrosophic Multi-Criteria Decision Making" that was published in Axioms