Probability approximation to multi-attribute decision making method with stochastic attribute values

Abstract

Aiming at the Multiple Attribute Decision Making (MADM) problem that each attribute value is a stochastic variable instead of a real number, this paper develops a probability approximation method to deal with the randomness of the stochastic attribute values. We consider two general cases: (1) the distributions of all stochastic attribute values are known to decision-maker, and (2) the distributions of all stochastic attribute values are unknown, but decision-maker knows the possible value set of each stochastic attribute value. As for each case, firstly, we introduce the probability approach to approximate the stochastic attribute value. Through this approximation, we make sure that the larger the transformed attribute value of one alternative is, the better it is than others. Secondly, a new method is proposed to calculate the weights of stochastic attribute values under the uncertain environment. With this method, we derive the attribute weights from two parts differences: the intra-attributes differences, which denote the weights affected by the uncertainty of the stochastic attributes themselves, and inter-attributes differences which represent the weighted affected by the different attribute differences, and then calculate the two types of attribute weights. Finally, a numerical analysis is used to illustrate the effectiveness of the method proposed.