Co-Authored By: D. Wu and Z.Y. Dong

Multiattribute decision making has progressed in a variety of directions throughout the world. Most models are deterministic, to include multiattribute utility theoryand AHP. Outranking methods from various schools also support deterministic inputs, although methods such as ELECTRE and PROMETHEE have always supported fuzzy input for alternative performances on attributes. We addresses the use of Monte Carlo simulation to this model to reflect uncertainty as expressed by fuzzy input. Simulation has been applied to AHP, generating random pairwise comparison input values. Our paper differs from past papers in that instead of estimating the expected value or extreme performance of alternatives, simulation offers a more complete understanding of the possible outcomes of alternatives as expressed by fuzzy numbers. The focus is on probability rather than on maximizing expected or extreme values. Both weights and alternative performance scores are allowed to be fuzzy. Both interval and trapezoidal fuzzy input are considered