The Study On Sorting Methods And Applications Of The Uncertain Multi-Attribute Decision Making Based On Interval Rough Numbers

Because of the complexity and uncertainty of the decision-making environ-ment, the classical decision making method can no longer meet the requirement of reality, then the uncertain multi-attribute decision making method was putted forward. Its uncertainty mainly shows up as the uncertainty of weighting and decision-making information. The uncertain multi-attribute decision making method based on interval rough numbers whose research has not yet matured is a new multi-attribute decision making method which was proposed in recent years, and it should be further improved. This paper tries to explore the uncertain multi-attribute decision making method whose attribute values are interval rough numbers.The main research contents and results of this paper are as follows:(1) This paper gives the interpretation about the definition of interval rough numbers and adds the properties of the original distance formula. Then proposes a new distance, and discusses its properties and characteristics;(2) Based on the similarity degree of interval numbers, the definition of interval rough numbers’ similarity degree is given, as well as its properties and theorems, and it puts forward the ideal point method based on the similarity degree of uncertain multi-attribute decision making problems whose attribute values are interval rough numbers, and its effectiveness and practicality are proved by an example;(3) It defines a kind of possible degree of interval rough numbers, then gives a proof of its properties and shows its advantages. Based on the possible degree of interval rough numbers, it structures the variable precision dominance relation and dominance classes of the ordered information systems based on interval rough numbers. By comparing the relative superiority degree between objects based on dominance classes, it builds up objects’comprehensive superiority degree to give a order, then puts forward the sorting method based on the comprehensive superiority degree of uncertain multi-attribute decision making problems whose attribute values are interval rough numbers. At last, an example is given to explain the effectiveness and practicality of it.