Study On Interval-Valued Intuitionstic Fuzzy Multiple Attribute Decision Making With Incomplete Information

As an important part of the Theory of decision and the important branch of Operations Research and Management Science, multi-attribute decision theory has been widely used in information science, economic management, military, and many other fields. Because of the complexity of the decision environment and the incompleteness of policymakers cognition, fuzzy theories have been proposed and developed rapidly, as an extension of the fuzzy set, interval intuitionistic fuzzy sets becomes a hot direction of the theory of fuzzy decision. Its membership function and membership function are interval types, so its describing the decision-making information is more effective and its expressing the reality on the decision-making information of social, economic and management is more reasonable.This paper made studies on two types of multiple attribute decision problems making of interval-valued intuitionistic fuzzy sets:(1)For multiple attribute decision problems making of interval-valued intuitionistic fuzzy with attribute weights being partially known and property values being interval intuitionistic fuzzy numbers, this paper proposes a new method of calculating attribute weights-two-stage method. Firstly, from partial consideration, we establish multi-objective programming models to make each scheme reach their optimal property values, and calculate the local optimal attribute values of every scheme; Secondly, from the overall consideration, we establish the model of the shortest distance between the local optimum property value and global property value, and calculate the comprehensive property values of each scheme. According to the comparison method of interval intuitionistic fuzzy numbers defined herein which is based on possibility, we make a selection or sort of schemes. Lastly, we verify the effectiveness of the method by an example.(2) For multiple attribute decision problems making of interval-valued intuitionistic fuzzy with attribute weights being partially known or completely unknown and property values being interval intuitionistic fuzzy numbers, policymaker has subjective preferences on alternatives and the preference value is intuitive multi-attribute problem interval fuzzy numbers, this paper proposes two methods: multi-attribute decision making method of interval-valued intuitionistic fuzzy based on gray correlation analysis and projection method. The former established a optimization model of greatest correlation between subjective preference and objective preference; The latter establish a linear programming model of the largest projection of the objective preference to subjective preference. After obtaining attribute weights, we use interval intuitionistic fuzzy weighted average operator to integrate comprehensive property value of the options, and make a selection or sort of schemes by score function or the method mentioned in Chapter Ⅱ. The method is verified its feasibility by an example.