Traffic Control and Transport Planning:: A Fuzzy Sets and by Dušan Teodorović Ph.D., Katarina Vukadinović (auth.)

By Dušan Teodorović Ph.D., Katarina Vukadinović (auth.)

When fixing real-life engineering difficulties, linguistic details is frequently encountered that's usually demanding to quantify utilizing "classical" mathematical innovations. This linguistic info represents subjective wisdom. during the assumptions made by way of the analyst whilst forming the mathematical version, the linguistic info is frequently overlooked. however, quite a lot of site visitors and transportation engineering parameters are characterised by way of uncertainty, subjectivity, imprecision, and ambiguity. Human operators, dispatchers, drivers, and passengers use this subjective wisdom or linguistic info every day whilst making judgements. judgements approximately course selection, mode of transportation, most fitted departure time, or dispatching vans are made via drivers, passengers, or dispatchers. In each one case the choice maker is a human. the surroundings during which a human professional (human controller) makes judgements is generally advanced, making it tricky to formulate an appropriate mathematical version. hence, the advance of fuzzy common sense platforms turns out justified in such events. In yes occasions we settle for linguistic details even more simply than numerical details. within the related vein, we're completely in a position to accepting approximate numerical values and making judgements in keeping with them. In plenty of situations we use approximate numerical values completely. it's going to be emphasised that the subjective estimates of other site visitors parameters differs from dispatcher to dispatcher, driving force to driving force, and passenger to passenger.

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When designing vehicle routes, some models first group the requested rides and then design the routes within each group. Kagaya et al. (1994) developed a model to group the requested rides. The model is based on the concept of fuzzy relations. 20. 20. 20 presents a group of "similar" rides. Kagaya et al. (1994) determined the "similarity" of individual rides according to the following attributes: • • • • Distance between origin of ride ti and origin of ride lj, Distance between destination of ride ti and destination of ride lj, Time difference between pickup time of ride ti and pickup time of ride lj, Time difference between dropoff time of ride Ii and dropoff time of ride lj, Basic Definitions of the Fuzzy Sets Theory • • 23 The difference between the angle that covers rides ti and Ij, and the x (or y) axis, The difference between destination of ride Ii and origin of ride Ij.

The left boundary of the corresponding confidence interval belongs to the first of these two lines. The right boundary of the confidence interval is found in the other line. In other words, the equations of the lines that define the membership function of fuzzy number Ql can be written as follows: a. 111) The left and right boundaries of the confidence interval for the level of presumption a. equal: =SOa. + ISO q~a) I q~a) 2 = -SOa. 112) The confidence interval Qla of fuzzy number Ql with the level of presumption a.

15. , points at square corners, points at line ends represent crisp sets. All other points represent fuzzy sets. The fuzzier things are, the closer we get to the center of a section, square, cube, ... , hypercube in the n-space (in the case of a universe with n elements). As Kosko (1993) noted: "Bivalence holds at cube corners. 16. 13. 19 FUZZY RELATIONS The concept of a fuzzy relation can be explained similarly to that of a fuzzy set. As we have already mentioned, unlike classical sets, where membership functions of set elements can take only the values 0 and 1, membership functions of fuzzy sets can take any value in the interval [0,1].

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