"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
Abstract:
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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