As a continuation of the first part related to the first and second class o
f ordering approaches this paper deals with the fufilment of reasonable pro
perties in the third class of ordering approaches. To do so we briefly intr
oduce fuzzy relations on which the third class of approaches is based. Then
we recall some transitivity-related concepts and an ordering procedure bas
ed on a acyclic fuzzy relation. Acyclicity is a very weak restriction on a
fuzzy relation. We prove that many fuzzy relations used for the comparison
of fuzzy quantities satisfy some conditions stronger than acyclicity. So we
give a widely applicable formulation to derive a total ranking order from
a fuzzy relation. With our formulation we examine all the ordering indices
in the third class with respect to the proposed axioms in part I. (C) 2001
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