Random Multi-attribute Decision-making And Applied Research

Stochastic multi-attribute decision-making is an important research branch of uncertain multi-attribute decision-making, and it's also a kind of common questions in the social and economic activities. In brief, what it handles is the problem of selecting, ranking or classifying alternatives when their evaluations are random variables on multiple attributes. Because of the complexity and indeterminacy of the problems in the real practice of decision-making, it is normal that the evaluations of alternatives are random variables and some information of the decision-making factors, such as the weights and the preference given by the decision-maker, may be incomplete. As far as these problems are considered, few literatures are focused. Therefore, the academic value of systemic research on theories or methods for stochastic multi-attribute decision-making is great. In practical application, those methods are applied to social life, economic activities or administration departments in enterprises and they assist relevant managers in decision making in order to reduce the decision-making risk and improve decision-making quality. They hereby have important theory significance and appliance value.At first, the paper is based on comprehensive research on the current domestic and international situation of stochastic multi-attribute decision-making research. Secondly, according to the properties of stochastic evaluations of alternatives with respect to attributes, the latest achievement of research on theories or methods for multi-attribute decision-making is put to use in the domain of stochastic multi-attribute decision-making, and some corresponding models are created. Finally, they are worked out on the basis of the latest optimization theories and the popular optimizing algorithms. And the main productions are organized as follows:(1)An improved PROMETHEE method is developed in order to deal with stochastic multi-attribute decision-making problems. Based on expected utility theory, the method combines the advantage of stochastic dominance relation and current PROMETHEE method together. And the different preference levels of the decision makers are considered with the help of two kinds of thresholds. The method effectively handles stochastic multi-attribute decision-making problems, and extends the application of PROMETHEE method.(2)With respect to discrete stochastic multi-attribute decision-making problems with incomplete certain information of the evaluations of alternatives on attributes, the evidential reasoning and possibility matrix are put to use. In the method, firstly, the incomplete certain information of each alternative on all attributes is aggregated by evidential reasoning. Secondly, the utility interval of each alternative is gotten. Thirdly, according to the possibility matrix, the ranking vector comes up. Finally, ranking alternatives is finished by it.(3)Concerning stochastic multi-attribute decision-making problems with uncertain information on weights of the attributes, the favourable close-degree is considered. In the method, firstly, the problem of normalization of attributes is discussed. Secondly, based on uncertain information on weights of the attributes, two single-goal programming models are given in order to positive favourable point and negative favourable point. Thirdly, the favourable weight vector of the attributes is got according to the favourable close-degree of all the alternatives. Finally, ranking alternatives is finished by it.(4)With regard to multi-attribute decision-making problems with incomplete certain information of the weights on attributes and normal distributed evaluations of alternatives on attributes, a new method based on WC-OWA operator is proposed. Firstly, according to 3σprinciple of normal distribution, the evaluations of alternatives on attributes are transformed into interval numbers. Secondly, interval numbers are aggregated by C-OWA operator. With the help of ideal close degree and WC-OWA operator, a nonlinear programming model is constructed. Finally, it is worked out by genetic algorithms.(5)As for stochastic multi-attribute decision-making problems with reference set, a method based on rough sets is improved. In the method, firstly, the number of attributes is reduced by the constructed theory of attributes' reduction on preference information system. Secondly, the net flow score of each alternative is gotten. Finally, the order of alternatives is given by the size of net flow scores.(6)Based on probability of converse order, a stochastic multi-objective DEA method is amended. In the method, stochastic evaluations of alternatives with respect to attributes are denoted by the evaluations of DMU (Decision-making Unit) on input indices and output indices with certain probability distribution functions. After the model constructed by stochastic multi-objective DEA method is worked out by Monte Carlo method, the analysis based on probability of converse order is carried on.Some instances in the domain of investment projects' appraisement and selection have been indicated and verified the feasibility, effectiveness and scientific of the above methods. It offers one for similar decision question in other relevant fields and disciplines to consult helpfully.