Stochastic decision making using multiplicative analytic hierarchy process

The Analytic Hierarchy Process (AHP) has found a number of applications in decision making problems. Its multiplicative version, called the Multiplicative AHP (MAHP), has been proposed to overcome some of the criticisms of the conventional version. Both these methodologies operate by obtaining expert judgements on the ratios of perceived importance of objects under consideration. The literature on MAHP in dealing with these judgements, when they are specified without uncertainty, is well developed. However, stochastic aspects of these judgements have not received much consideration in the literature so far. Stochastic judgements are considered in this paper for use in MAHP. The fact that weight derivation in MAHP can be handled using mathematical programming is exploited and the literature on stochastic programming is adapted to the MAHP context.