Factoring fuzzy transitivity

Transitivity of a precise weak preference relation implies that its asymmet ric component (strict preference) and its symmetric component (indifference ) are transitive and conversely the transitivity of strict preference and i ndifference implies that the underlying weak preference relation is transit ive. This paper examines to what extent analogous results may be obtained f or the different transitivity conditions and different methods for deriving strict preference and indifference being used in the literature of choice with fuzzy preferences. (C) 2001 Elsevier Science B.V. All rights reserved.