Revising the OWA operator for multi criteria decision making problems under uncertainty

Multi criteria decision making (MCDM) problems are usually under uncertainty. One of these uncertain parameters is the decision maker (DM)'s degree of optimism, which has an important effect on the results. Fuzzy linguistic quantifiers are used to obtain the assessments of this parameter from DM and then, because of its uncertainty it is assumed to have stochastic nature. A new approach, entitled FSROWA, is introduced to combine the Fuzzy and Stochastic features into a Revised OWA operator. If the DM is not aware of the risk in decision, then the decision objective is to maximize the expected combined goodness measure. If the DM cares only about the risk, then minimizing the variance of the combined goodness measure is his/her objective. The results of the FSROWA provide the expected value and the variance of the combined goodness measure for each alternative. In order to combine these two attributes a composite goodness measure is introduced. This measure gives more robust decision outcomes. The theoretical results are illustrated in a watershed management problem.