Evidential reasoning-based nonlinear programming model for MCDA under fuzzy weights and utilities

In a multiple-criteria decision analysis (MCDA) problem, qualitative information with subjective judgments of ambiguity is often provided by people, together with quantitative data that may also be imprecise or incomplete. There are several uncertainties that may be considered in an MCDA problem, such as fuzziness and ambiguity. The evidential reasoning (ER) approach is well suited for dealing with such MCDA problems and can generate comprehensive distributed assessments for different alternatives. Many researches in dealing with imprecise or uncertain belief structures have been conducted on the ER approach. In this paper, both triangular fuzzy weights of criteria and fuzzy utilities assigned to evaluation grades are introduced to the ER approach, which may be incurred in several circumstances such as group decision-making situation. The Hadamard multiplicative combination of judgment matrix is extended for the aggregation of triangular fuzzy judgment matrices, the result of which is applied as the fuzzy weights used in the fuzzy ER approach. The consistency of the aggregated triangular fuzzy judgment matrix is also proved. Several pairs of ER-based programming models are designed to generate the total fuzzy belief degrees and the overall expected fuzzy utilities for the comparison of alternatives. A numerical example is conducted to show the effectiveness of the proposed approach. C © 2009 Wiley Periodicals, Inc.