The Research On Aggregation Operators Based On Interval Neutrosophic Number

Because people’s thinking judgment is often fuzzy and objective thing is complex, it is difficult to use crisp numbers to express the decision-making information given by decision makers in many cases. So the concept of number is expanding constantly by many scholars, which is from the crisp number originally and has extended to fuzzy number, interval number, linguistic variable and intuitionistic fuzzy number and so on. However, it is incomplete, indeterminate or inconsistent for decision-making information which exists commonly in belief systems, and these concepts aforementioned can only process incomplete information but not the indeterminate information and inconsistent information. Therefore, based on the neutrosophy, Smarandache presented the concept of the neutrosophic set(NS) in 1999, which added an independent indeterminacy-membership on the basis of intuitionistic fuzzy set. NS is a generalization of fuzzy set, interval fuzzy set and intuitionistic fuzzy set, and able to depict fuzzy nature of the objective world more exquisitely.The existing researches indicate that NS has an important role in the multi-attribute decision making(MADM), and this is just the preliminary results. So based on the fundamental theory of interval neutrosophic set(INS) and information aggregation operators, this paper is to study the Einstein operational laws of INS, to establish the information aggregation operators with respect to INS which is based on the new operational laws and combines INS with the existing integrated operators, and to provide theory, model and method for MADM problems.The innovation of this paper is:(1) Apply Einstein operator to INS, and define new operational rules of INS.(2) Combine INS with three classical operators likely generalized aggregation operators, power operators and prioritized aggregation operators, use the new operational laws to form new operators based on INS, respectively, and discuss the character and special cases of these operators.(3) Develop the methods of MADM on the basis of these operators to solve the MADM problems in which the values of attributes take the form of interval neutrosophic number.