A New Fuzzy Measure for the Analytic Hierarchy Process with the Choquet Integral

A new fuzzy measure is presented in this paper. Using the assumption that the decision maker is able to provide the pairwise additivity degree between attributes, our method uses Zimmerman’s approach to solve the fuzzy multiobjective problem: a simple problem for computing fuzzy density is derived. Having done that, we use this new fuzzy measure to implement an analytic hierarchy process (AHP) with dependent attributes using the Choquet integral. Our identification procedure for fuzzy density is much easier because it reduces the resolution complexity using a linear programming problem rather than the complicated power form used traditionally.