Approaches For Relational Multiple Attribute Decision Making With Interval Neutrosophic Numbers Based On Choquet Integral

Since the interval neutrosophic number adds an independent indeterminacy membership on the basis of intuitionistic fuzzy set, and able to depict fuzzy nature of the objective world more exquisitely. Therefore, the fuzzy multiple attribute decision making problem with interval neutrosophic information has got a great progress and has achieved fruitful researches so far. However, nowadays, most interval neutrosophic multiple attribute decision making methods are based on the implicit assumption that attributes are independent, which is characterized by an independence axiom. For real decision making problems, there is always some degree of inter-dependent characteristics between attributes. Thus, this assumption is too strong to match decision behaviors in the real world. The independence axiom generally can not be satisfied. To overcome these limitations, motivated by fuzzy measure, Choquet integral and generalized Shapley function, this paper shall extend them to accommodate interval neutrosophic environment, and propose some interval neutrosophic Choquet aggregation operators, and establish several models to determine the optimal fuzzy measures on the attribute set, which are the maximization deviation model, the interval neutrosophic cross-entropy model, the interval neutrosophic gray relational model and the interval neutrosophic relative projection model. Further, base on proposed interval neutrosophic Choquet aggregation operators and established models, this paper develops four methods to to deal with interval neutrosophic multiple attribute decision making problems with redundant, complementary or independence condition, in which the information about attribute weights is incompletely known.These four methods have their own advantages and disadvantages. The first method could not only consider the importance of the elements or their ordered positions, but also reflect the correlations among the elements or their ordered positions. However, it only reflects the exist interaction between two adjacent combinations. The second method could global capture the correlative characteristics among elements. However, it is based on fuzzy measure, which is defined on power set, making the problem exponentially complexity. The third method could reduce the computation complexity, and global takes into account the correlative characteristic among elements. However, it is based on λ-fuzzy measure, which could only takes into account one kind of the correlative characteristics among elements. The last method could reduces the computation complexity, and global takes into account the correlative characteristics among two elements. So, the individual can properly select the desirable alternative according to his/her interest and the actual needs.The innovation of the paper is:(1) Extend fuzzy measure, Choquet integral and generalized Shapley function to accommodate interval neutrosophic environment, and propose some interval neutrosophic Choquet aggregation operators;(2) Establish several models to obtain the information about attribute weights;(3) Develop four methods based on the proposed aggregation operators and established models to resolve the interval neutrosophic multiple attribute decision making problems with interactive condition and incomplete weight information.