Computer Aided Decision Making Using Uncertain and Imprecise Information

Abstract

In many decision situations, especially in an uncertain and imprecise decision making environment, the decision criteria, such as objective functions, restrictions or goals are often modeled by means of a concept of a probabilistic set. A probabilistic set C of X is essentially defined by its defining function C: XxΩ→[0,1] where X represents a set of feasible alternatives and Ω stands for a space of elementary events.

Aggregating all decision criteria sets by means of various operations on probabilistic sets (such as triangular norms, compensatory operations, averaging operations and so on) the final decision probabilistic set has to be found.

Taking into account the distribution function description of the probabilistic set, we can obtain the basic characteristics (e.g., mean value, variance, etc.) of each alternative. According to given criteria (e.g., criteria based on the concept of stochastic dominance, mean-variance criterion and others), we can make the final choice of the best alternative.