A multi attribute decision making method based on inclusion measure for interval neutrosophic sets

Abstract-In this paper, we introduce an inclusion measure for interval neutrosophic sets, which is one of information measures of interval neutrosophic theory. For this purpose, we first give a system of axioms for inclusion measure of interval neutrosophic sets. Using the concept of distance measure, we develop a simple inclusion measure for ranking the interval neutrosophic sets. Finally, a multi attribute decision making problem is presented to show effectiveness of proposed inclusion measure, and results obtained are discussed. Though having a simple measure for calculation, the inclusion measure presents a new approach for handling the interval neutrosophic information. Index Terms- Fuzzy entropy, distance measure and similarity measure are three basic concepts used in fuzzy sets theory. Usually subsethood measures are constructed using implication operators, t-norms or t-conorns, entropy measures or cardinalities. In classical theory, it is said that a set is a subset of and is denoted by if every element of is an element of , whenever is a universal set and are two sets in . Therefore, inclusion measure should be two valued for crisp sets. That is, either is precisely subset of or vice versa. But since an element in universal set can belong to a fuzzy set to varying degrees, it is notable to consider situations describing as being "more and less" a subset of another set and to measure the degree of this inclusion. Fuzzy inclusion allows a given fuzzy set to contain another to some degree between and . According to Zadeh's fuzzy set containment, a fuzzy set contains a fuzzy set if In this paper, we firstly review the systems of axioms of Young's fuzzy inclusion measure. Then we extend the inclusion measure of single valued neutrosophic sets to interval neutrosophic environment and give a new system of axioms for inclusion measure of interval neutrosophic sets. Moreover, we utilize the neutrosophic inclusion measure to rank the interval neutrosophic sets. To demonstrate the effectiveness of the proposed inclusion measure, we consider a multi attribute decision-making problem. II. RELIMINARIES In the following we give a brief review of some preliminaries. Neutrosophic se