Discrete fuzzy-stochastic multi-criterion decision-making method with incomplete information
REN Jian1,2, GAOYang1
1. Business School, Central South University, Changsha 410083, China;2. Normal School of Science Technology, Hunan Agriculture University, Changsha 410128, China
Abstract：To solve the discrete fuzzy-stochastic multi-criterion decision-making problems with states’ probabilities and criterions’ weights both evaluated interval numbers and some of alternatives’ evaluations on criterions missing, a new method based on the information integration was designed. After distinguishing the types of criterions and determining the risk preference level of decision-makers, the following were these tasks. Firstly, according to the types of criterions, the positive ideal values and negative ideal values of alternatives’ evaluations on criterions in different states were worked out by the maximum operator and minimum operator. Secondly, via the risk preference level of decision-makers, positive ideal values and negative ideal values, the alternatives’ missing evaluations on criterions in different states were filled completely. Thirdly, in the light of the types of criterions and risk preference level of decision-makers, the alternatives’ evaluations in form of trapezoidal fuzzy numbers on criterions in different states were integrated and normalized. Fourthly, with the help of maximizing the entropy and deviation, the programming models were constructed separately to find the optimal state probability distribution and weight vector of criterions. Fifthly, the integrated evaluations of alternatives were worked out. And then, the rank of alternatives was obtained. Finally, a numerical example was given. The result shows the validity and feasibility of the method.
2011, Vol. 31 
