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.