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An investigation into relations between some transitivity-related concepts. (English) Zbl 0917.90025
Summary: There exists a variety of transitivity notions in the literature to eliminate the possible inconsistency adherent to a fuzzy preference relation in ranking fuzzy quantities or alternatives. The relationships among max-min transitivity, restricted max-min transitivity, quasitransitivity, weak transitivity, consistency and acyclicity are investigated. We point out that max-min transitivity and $$\omega$$-transitivity are very strong restrictions on a fuzzy preference relation, and acyclicity is the weakest one. With a certain transitivity condition, an ordering procedure is suggested to obtain a total order relation among fuzzy quantities or alternatives based on a fuzzy preference relation.

##### MSC:
 91B08 Individual preferences 03E72 Theory of fuzzy sets, etc.
##### Keywords:
fuzzy preference relation; ranking fuzzy quantities
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##### References:
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