Method for solving multi-attribute decision-making problems with risk

Multiattribute decision problems with uncertainty exist widely in the real world. A method for solving stochastic multiattribute decision problems is presented. Assuming that the performance probability density function for each alternative on each attribute was known, the probability that one random variable was greater than another was used to compare alternatives with respect to attributes. With the weighting, the local preferences were aggregated to build global preference relationship between each pair. Then, a fuzzy complementary judgment matrix, called possibility degree matrix, was obtained. The ranking of the alternatives could be constructed from the matrix. The new method is intuitionistic and simple. There is no need of normalization of the decision matrix. Finally, the method wwas illustrated by multiattribute decision problems whose evaluations of alternatives were expressed by interval numbers.