The Probability Of Uncertain Random Multi-criteria Decision Making Methods And Applied Research

Random multi-criteria decision-making is an important part of theory of decision-making. It has extensive application prospect in engineering design, economic management and military fields. In the realistic environment, the status of event is influenced by many uncertain facts, due to the complication and uncertainty of the environment. All of the events can not be multi-repeated under the same condition, so the exact probability under ideal experimental condition loses its significance in realistic environment. In fact, during the process of the judgment and decision-making, people preferred to the fuzzy mode of thinking in order to adapt to the complicated and uncertain environment. When decision-maker evaluates the probability of an event, he always estimates it, relying on subjective and intuitive judgment. In a word, it is more effective to describe the probability by uncertain variable instead of exact number. Three different types of uncertain probability random multi-criteria decision-making problems are studied in this paper, and corresponding models have been constructed and then worked out on the basis of the latest optimization theory and optimizing algorithms. And the details are as follows:(1) Random multi-criteria decision-making problems in which the probability and status value are interval numbers are solved effectively. Random variable with interval probability and interval status value, which will be called interval probability interval random variable, is defined. For two kinds of interval probability interval random variables, namely the complete and the incomplete, the corresponding approaches are proposed to resolve the decision-making problems based on them. For the complete one, the algorithm of maximizing deviations is adopted to get the exact probability and the set pair analysis is used to rank the alternatives. For the incomplete one, evidence reasoning is extended to be used. The sorting of alternatives can be get on the basis of the particle swarm optimization combined with penalty function to solve the optimization model.(2) Interval probability fuzzy random multi-criteria decision- making problems are studied. The research is based on the definition of interval probability fuzzy random variable for this kind of problem. Two different ways are put forward to resolve it. The one is on the basis of projection theory. By constructing the optimization model, the optimal relative closeness degree can be computed to rank all the alternatives. The other one is based on the expectation-hybrid entropy. The expected value and hybrid entropy of interval probability fuzzy random variable are defined in this paper. By the linear combination, a new metric for interval probability fuzzy random variable called expectation-hybrid entropy is used to rank the alternatives.(3) The random multi-criteria decision-making problems, in which the probability is in the form of trapezoidal fuzzy number or fuzzy linguistic variable, are researched. For the trapezoidal fuzzy number probability, an approach based on ideal-solution is proposed. In this approach, first the probabilities of combined states are computed. Then through the method of ideal-solution, the relative closeness degrees of combined states are gained. Finally, the expected value of relative closeness degree is obtained to rank all the decision alternatives. For the linguistic probability, two-tuple linguistic processing and PROMETHEE are combined to resolve the problem.