On Relation Between Two-criteria User-optimized Route Choice Problem and Vector Variational Inequality Problem in fuzzy Environment

Document Type : Research Articles

Author

University of Yasouj, Yasouj, Iran

Abstract

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.

Keywords

Caspian Journal of Mathematical Sciences
Volume 11, Issue 1
2022
Pages 334-344

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