on relation between two-criteria user-optimized route choice problem and vector variational inequality problem in fuzzy environment

A two-criteria user-optimized route choice problem is proposed, in which each user of a network system seeks to determine his/her optimal route of travel between an origin-destination (o-d) pair considering two-criteria simultaneously. in this problem, the two-criteria of travel, time and cost, between an o-d pair are fuzzy, in the sense that, time and cost of which links are chosen for traveling are uncertain. applying the concept of alpha-cut level, a fuzzy vector disutility function on a path is computed. furthermore, the fuzzy vector equilibrium principle as a generalization and extension of the wardrop equilibrium principle is defined. finally, by reducing this fuzzy principle to a crisp one, the relationship between the vector equilibrium flow and the solution of a vector variational inequality problem is discussed.