Study On Methods For Multiple Attribute Decision Making Under Interval Uncertainty

This dissertation mainly deals with multiple attribute decision making problems under interval uncertainty as follows.The consistent theories of interval number reciprocal judgment matrix are discussed. The concepts such as perfect consistency, strong consistency, consistency and satisfactory consistency are introduced. Moreover, the relationships between these definitions and the existing ones in some papers are studied. It is also demonstrated that the consistent concept given is sound. The methods for testing strong consistency, consistency, and satisfactory are also proposed, which are illustrated valid and practical by numerical examples.The consistency theories and priority methods of interval number complementary matrix are researched. This paper proposes the additive and multiplicative consistency for interval complementary judgment matrix and correlative definitions as well, such as the complete consistency, the strong consistency, the consistency and the satisfied consistency. At the same time, simple algorithms for testing the strong consistency, the consistency and the satisfied consistency are given. The definition and testing method of the additive satisfied consistency are based on the satisfactory consistency index (CGCI) of the complementary comparison matrix, so it is avoided to presume the thresholds for the tolerance parameter of fuzzy membership function that expresses the decision maker's satisfaction. On the basis of consistency theories, programming models for priorities of interval number complementary judgment matrix are set up, which are examined to show the applications by numerical examples.The group aggregation approach of interval number judgment matrix is studied. The coordinating techniques and aggregation method for the group preference information of interval number complementary judgment matrices are presented. Two models aggregating interval number reciprocal judgment matrix and interval number complementary judgment matrix are given. One is a relative entropy optimal model maximizing the group's overall satisfaction. The other is a programming model based on the satisfactory consistency index CR of reciprocal judgment matrix and the satisfactory consistency index CGCI of complementary judgment matrix.The interval multiple attribute decision making problems are studied. A method is proposed to determine entropy weights based on the midpoint and width of interval numbers under the situations where the decision maker has no preference information on attribute and alternative. Two interval multiple attribute decision making methods with only partial attribute weighting information are present. They are interval multiple attribute decision making method based on ideal incidence degree and superiority and inferiority ranking (SIR) method. As for the decision-making problems with the attribute preference information in the form of interval complementary judgment matrix and alternative preference information in the form of interval reciprocal judgment matrix, the concept of consistency degree for the preference information between attributes and alternatives is set forth. And, a quadratic programming model based on maximal consistency degree of preference information is established. Based on the eigenvector method to derive the priority weights from triangular fuzzy numbers reciprocal judgment matrix, an interval multiple attribute decision making method with attribute weighting information which takes the form of triangular fuzzy numbers reciprocal judgment matrix. Every method is illustrated the validity and practicality by example.