Aggregation of Interacting Criteria in Land Combat Vehicle Selection by Using Fuzzy Measures

We address the problems of multiple criteria decision-making and multiobjective optimization in which the criteria are mutually dependent. A practical application of land combat vehicle selection and its potential extension to force design for Australian Defence is considered. The criteria dependencies are modeled and formalised using the theory of fuzzy measures. The main challenge is an exponentially large set of parameters that quantify all criteria interactions. We develop a number of strategies to 1) simplify the model construction and reduce the number of parameters; 2) elicit preferences from numerical simulations and from decision makers; and 3) translate these preferences into a fuzzy measure learning problem from unlabeled data. We formulate and test a mathematical programming problem to determine fuzzy measure parameters for a relatively large number of decision criteria.