The Study On Some Problems Of Multi-Attribute Decision Making That Based On Interval Rough Numbers

Decision making is to select the best program from the known programs or ranking them. Multi-attribute decision making refers to the decision-making program with multiple attributes. Since the multi-attribute decision making with the effectiveness and practicality in solving practical problems, now it has been widely used in many domains such as project evaluation、economy management,engineering and so on. Scholars have done many in-depth researches of multi--attribute decision making, and have got rich results. Interval rough numbers was proposed in recent years, it is a kind of inaccurate numbers which can describe the objects better as the decision maker known. Now, the study of interval rough numbers is not yet ripe. This article made some researches about multi-attribute decision making that based on interval rough numbers from some aspects as follows:(1) Two kinds of methods of comparing two interval rough numbers are proposed, one is based on possibility degree, the other is by using the possibility of one of the upper or lower approximation of the interval rough number bigger or equal than the other one.(2) Two kinds of methods of algorithm of attribute reduction in ordered information system that based on interval rough numbers is proposed, which is by making use of discernibility matrix and information content, and then an instance is made to demonstrate the feasibility and practicality of the algorithm of attribute reduction.(3) By introducing interval rough numbers into Analytic Hierarchy Process, a judgment matrix whose elements are interval rough numbers is structured. Then study the test method of consistency of the judgment matrix, and then a method of ranking the matrix by optimizing model is proposed. In the end, an example is got to demonstrate that it is feasible to soft multi-attribute decision making by the combine of AHP and interval rough numbers.