An investigation into relations between some transitivity-related concepts

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. (C) 1997 Elsevier Science B.V.