Developing Stochastic Additive Utility Method (UTA) Considering the Possible Dependency among Criteria

One of the well-known methods as to Multi Attribute Utility Theory (MAUT) in the field of decision making is Utility Additive Method (UTA), which has been developed over time. Two main deficiencies of such methods are first, ignoring the uncertainty embedded in the values of different criteria and second, disregarding the possibility of dependencies among various criteria. The uncertainty problem, either fuzzy or stochastic, has been discussed in various developments including, fuzzy UTA and stochastic UTA models, respectively. Although it seems unlikely to apply in real world problems, the criteria independency is the primary assumption of all these models. Thus, this paper is aimed at developing stochastic UTA model so as to consider the possibility of dependency among different criteria. In this paper, conditional probability is applied in developing the UTA model, so that the probability of values of each criterion is considered with respect to probable values of other criteria. The developed model is presented in 12 steps, and its applicability in practice is shown using a real example based upon the data extracted from three main criteria of stock investments for three petrochemical companies. The proposed model addresses the deficiency of ignoring the probable dependencies among criteria in stochastic UTA model, and covers the research gap posed by previous researchers.