Research On Methods For Interval Multi-criteria Decision Making And Their Applications

Multiple criteria decision making is an important research topic of operational research and modern decision-making science, whose theory and methods are widely used in economics, management, social, engineering, military and medicine, and many other areas. Because of the complexity and uncertainty of the problem and the limited cognitive ability and information processing capacity of decision maker, the data is often represented by interval numbers. On the other hand, the decision makers are sometimes more easily or willing to express their subjective preferences in the form of interval numbers. Therefore, the decision problems are usually the multi-criteria decision making problems under interval uncertainty. In this dissertation, the multiple criteria decision making problems in the performance evaluation of county-level power grid are studied, where the weights or criteria values are represented by interval numbers. For the different situation or information of decision making, some methods are proposed to determine the weight intervals and rank all decision alternatives, which enrich the existing theory and methods for the multi-criteria decision making under interval uncertainty. The main research works are as follows:Firstly, several basic problems of the multi-criteria decision making under interval uncertainty are reviewed and extended, which include the comparison approaches of two interval numbers, the transition techniques of other types of uncertainty into the interval numbers, the mathematical description of multi-criteria decision problems under interval uncertainty, and several formulas for normalizing the interval decision matrix. These methods are the basis for the study later.Secondly, the multiple criteria decision making under interval uncertainty is investigated according to quantitative information. The issue is studied how to determine the weight intervals from different preference information. In a multi-criteria decision making problems, the approaches to determinate weights include the subjective methods, the objective methods, and their combination methods. In this paper, several mathematical programming models are presented to check the consistency and calculate the weight intervals of different types of pairwise comparison matrix (judgment matrix), which is subjective and given by the decision makers. In addition, two objective methods (maximizing deviation method and entropy-based approach) are compared by the decision matrixes generated randomly, and the maximizing deviation method is extended to integrate easily the subjective preference information. Based on the Credal network, a combination method is proposed to integrate the subjective and objective information on weights. Additionally, a simple incomplete enumeration method is developed for the inference of Credal network.Thirdly, the multiple criteria decision making is studied, in which the weights are represented by interval numbers. Taking into account too much alternatives in the performance evaluation of power grid, a combined TOPSIS and PROMETHEE method is provided to overcome the full compensatory and avoid the phenomenon of reverse ranking. In addition, for the missing multiple criteria decision making under interval uncertainty, some formulas are given to compute the basic probability assignment of each focal element, and a DS-PROMETHEE method is developed to combine with D-S evidence theory.Next, the interval multiple criteria decision making methods are studied, where the weight information is incomplete or linguistic variables, represented by trapezoid fuzzy numbers. For the interval multiple criteria decision making problems with incomplete information on weights, a pair of fractional programming models are constructed to calculate the overall ranges (interval numbers) of each alternative. By comparison analysis, it shows that there are the same ranking results, but our models are more direct and simple. For the interval multiple criteria decision making problems with language variable on weights, the language variables are represented by trapezoid fuzzy numbers and then transmitted into the interval numbers usingα-cut. According to the degree of uncertainty of interval number, a method is proposed by controlling the maximum degree of uncertainty, which is the threshold given by the decision makers. The method can reflect the preferences and risk attitude of decision makers and can further be applied into the interval multiple criteria decision making problems where the weights are general fuzzy numbers.At last, the applications of interval multiple criteria decision making are studied for the comprehensive performance assessment of county-level power grid. Based on the principles of the evaluation, the overall evaluated criteria are established, and the methods previously mentioned are applied to the comprehensive evaluation of economic performance for county-level power grids in Henan Province, the selection of better county-level power grids is determined for investment.