Multi-criteria Decision-making Based On Interval Intuitionistic Normal Fuzzy Numbers

Abstract:It is very common to see Fuzzy multiple criteria decision making problems in our daily life. Intuitionistic fuzzy multi-criteria problems, one important branch of Fuzzy multiple criteria decision making problems, has been gained much attention, at the same time, there are many significant progress has been appeared. Owing to the complexity of the environment and the ability defection of the decision maker, it is common to see that decision makers use interval numbers to express the membership and nonmembership but not use real numbers.Based on the research of the intuitionistic normal fuzzy numbers, the definition of interval intuitionistic normal fuzzy number and its related concepts are proposed. With respect to the multiple attribute decision making problems in which the attribute values take the form of interval intuitionistic normal fuzzy numbers, several approaches are developed. The main work are as follows:The first one is the interval intuitionistic normal fuzzy numbers is defined, as well as the Arithmetic operations. At the same time, the scoring function and precise function are given, and the method of comparison of interval intuitionistic normal fuzzy numbers is defined. And the properties of Arithmetic operations are given and been proved. And then several aggregation operators are proposed, namely interval intuitionistic normal fuzzy aggregation operators and interval intuitionistic normal fuzzy point aggregation operators. And the relative properties are proposed. With respect to the multiple attribute decision making problems in which the attribute weights are known and the attribute values take the form of interval intuitionistic normal fuzzy numbers, as well as the attributes are independent or partly being satisfied, several approaches are developed based on the aggregation operators. The second is the definition of distance measure,entropy measure and cross entropy measure of interval intuitionistic normal numbers are proposed.The properties of these measures are given and been proved. With respect to the multiple attribute decision making problems in which the attribute weights are not complete known and the attribute values take the form of interval intuitionistic normal fuzzy numbers,the method are proposed based on distance measure and entropy measure respectively.The last is combined with prospect theory, several approaches are given with respect to two kinds of multiple criteria decision making problems, respectively. The first multi-criteria problem is that in the criteria weights is incomplete and criterion values is given by interval intuitionistic normal fuzzy numbers, a decision method based on prospect theory is proposed. The second type is that stochastic multi-criteria problem in which the criteria weights is incomplete and the criterion values are given by interval intuitionistic normal fuzzy numbers, an approach is proposed.