Estimating an origin-destination matrix with fuzzy weights. Part I: Methodology

In spite of the extensive amount of work performed on origin-destination (O/D) estimation from link counts, an unresolved problem is the poor quality or the link-count data which are often inconsistent among themselves, resulting in poor quality of the O/D’s estimated and even non-convergence of the algorithm. A method, based on fuzzy mathematics, is outlined here to address this problem. A link count in this case is no longer viewed as a precise, infallible piece of fact. Rather, imprecision is explicitly recognized and is attributable to counting error or causal factors such as obstruction to traffic flow. Such imprecision is modelled by the ‘Subordinate Function’, which quantifies the level of ‘Fuzziness’ about the data. The Fuzzy Weighted Approach (FWA) finally derives a set of ‘Fuzzy Weights’, bound between zero and one in numerical value, for each piece of inconsistent input data, indicating the quality of the data. Thus a larger weight will connote a higher level of confidence in the data input, while a smaller weight will connote the opposite. The inconsistent data set(s) can then be collapsed by these weights to arrive at a consolidated input to the O/D algorithm. Alternatively, the various O/D’s, estimated from each of the inconsistent sets of link counts, can be collapsed to a consolidated set at the conclusion of the algorithm, again via the use of these fuzzy weights. Irrespective of the technical approach, the O/D’s obtained from FWA are found both theoretically and experimentally to be more accurate than those from a regular O/D estimation procedure.