An outranking approach for multi-criteria decision-making problems with interval-valued bipolar neutrosophic sets

In this thesis, various generalizations of the concept of fuzzy set and the concept of intuitionistic fuzzy set, which is an upper generalization of the concept of fuzzy set are examined and their general characteristics(properties) are given. Furthermore, the concepts of neutrosophic set, single valued neutrosophic set, interval valued neutrosophic set and their general properties and operations which are beyond the scope of intuitive fuzzy sets are introduced(defined). Then, the basic definitions, general properties and outranking relations of bipolar neutrosophic sets, which have recently attracted attention with a wide range of applications have been examined. A novel outranking approach for multi-criteria decision-making (MCDM) problems is proposed to address situations where there is a set of numbers in the real unit interval and not just a specific number with a bipolar neutrosophic set. Firstly, the operations of inter-valued bipolar neutrosophic sets and their related properties are introduced. Then some outranking relations for inter-valued bipolar neutrosophic numbers (IVBNNs) are defined based on ELECTRE, and the properties of the outranking relations are further discussed in detail. Additionally, based on the outranking relations of IVBNSs, a ranking approach is developed in order to solve MCDM problems. Finally, three practical examples are provided to illustrate the practicality and effectiveness of the proposed approach.