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Research on Consistency and Priority of Judgment Matrix in Interval Attribute Group Decision Making and Its Application

Author: TianWenQian
Tutor: ChenYiHua
School: Chongqing University
Course: Applied Mathematics
Keywords: Multiple attribute decision making (MADM) Interval number Judgement matrix Consistency Linguistic variables County economy
CLC: N945.25
Type: Master's thesis
Year: 2009
Downloads: 147
Quote: 1
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Abstract


Multiple attribute decision making (MADM) addresses the problem of choosing an optimum choice that has the highest degree of satisfaction from a set of alternatives that are characterized in terms of their attributes. It is a great branch of operational research and management science and information science. When we make decisions, it often involves uncertainty with objective nature or subjective nature. Uncertainty is represented by randomness, fuzziness and roughness. Multiple attribute decision making under uncertainty is an extension and development of classic precise numerical decision making methods. In this thesis, based on interval approach, some new approaches are put forward. We obtained the following results.Firstly, we propose a new consistency definition of interval number reciprocal judgment matrices and interval number complementary judgment matrices. The conception of interval number is introduced and the deficiency of the interval number reciprocal judgment matrices and interval number complementary judgment matrices’consistency definition in the present papers. Based on it, the operation rule of interval number are redefined and a new consistency definition of interval number reciprocal judgment matrices and interval number complementary judgment matrices are given.Secondly, we discuss the MADM problems with preference on alternatives, in which the attribute values take the form of interval number variables and the preference on alternatives is interval number preference relation, which mainly is sorting problems. An expectation-variance method has been proposed for the sorting problems of interval reciprocal judgment matrices. We analyze and correct a error in a lecture which could bring on the mistake of decision-making based on the definition and properties of the consistency complementary judgment matrix and gives a ranking method for interval number complementary judgment matrix. A priority method based on possibility and error analysis for interval number complementary judgement matrix is proposed. An example is presented to illustrate the proposed method.Finally, to construct the evaluation index system and corresponding model of county economy, from the aspects of economic strength wealth and development speed factor, a county economy lever indexes system is presented. An evaluate model named the multi-level grey synthesis judgment model is established based on the analytic hierarchy process and the grey related analysis method. The model is applied to evaluate the county economy lever of 40 cities in Chongqing. Some suggestions are given to enhance the county economy lever of Chongqing County.

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