A new fuzzy approach to estimate the O--D matrix from link volumes

<title>Abstract</title> Estimation of the origin--destination (O--D) trip demand matrix plays a key role in travel analysis and transportation planning and operations. Many researchers have developed different O--D matrix estimation methods using traffic counts, which allow simple data collection as opposed to the costly traditional direct estimation methods based on home and roadside interviews. In this paper, we present a new fuzzy model to estimate the O--D matrix from traffic counts. Since link data only represent a snapshot situation, resulting in inconsistency of data and poor quality of the estimated O--Ds, the proposed method considers the link data as a fuzzy number that varies within a certain bandwidth. Shafahi and Ramezani's fuzzy assignment method is improved upon and used to assign the estimated O--D matrix, which causes the assigned volumes to be fuzzy numbers similar to what is proposed for observed link counts. The shortest path algorithm of the proposed method is similar to the Floyd--Warshall algorithm, and we call it the Fuzzy Floyd--Warshall Algorithm. A new fuzzy comparing index is proposed by improving the fuzzy comparison method developed by Dubois and Prade to estimate and compare the distance between the assigned and observed link volumes. The O--D estimation model is formulated as a convex minimization problem based on the proposed fuzzy index to minimize the fuzzy distance between the observed and assigned link volumes. A gradient-based method is used to solve the problem. To ensure the original O--D matrix does not change more than necessary during the iterations, a fuzzy rule-based approach is proposed to control the matrix changes.