"On the Maximum Number of Feasible Ranking Sequences In Multi-Criteria Decision Making Problems"

European Journal of Operational Research Vol. 130, No. 3, (March 2001) pp. 217-230.

Evangelos Triantaphyllou and Bo Shu

In many decision problems the focus is on ranking a set of m alternatives in terms of a number, say n, of decision criteria. Given are the performances values of the alternatives for each one of the criteria and the weights of importance of the criteria. This paper demonstrates that if one assumes that the criteria weights are changeable, then the number of all possible rankings may be significantly less than the upper limit of m! As a matter of fact, this paper demonstrates that the number of possible rankings is a function of the number of alternatives and the number of criteria. These findings are important from a sensitivity analysis point of view or when a group decision making environment is considered.

Key Words:
Deterministic decision making, multi-criteria decision making (MCDM), ranking of alternatives, sensitivity analysis, group decision making, hyperplanes.

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