Fuzzy Set Approach in Mass Transit Mode Choice

In, Calcutta, one of the largest metropolis of the world, the mass transportation has already reached alarming situation. All the major forms of metro, railways, roads and waterways are available to provide mass transport services to this city. An attempt has been made to use non-conventional abstract mathematical theory to solve multimodal mass transport system. Fuzzy functions have been used here as an analytical tool, to express the "satisfaction-level" of attributes as viewed by different interest groups. The central concept of fuzzy set theory is the membership function which represents numerically the degree to which an element belongs to a set. This function takes values from 0 to 1. Synthesizing information, rating matrices have been constructed with different alternative modes as columns against various attributes/factors as rows. Each rating matrix represents the evaluation made by respective interest group. Having identified the corridor and selective modal characteristics, the most preferred mode may be choosen by this method. Additionally, when the need for introducing some new mode or increasing the services of some old mode are felt, this procedure may be used as a simplified tool. 1: Introduction Demand for movement is a basic need in human life. This is not only felt in modern days, but also from the prehistoric time. All the human settlements grew near the water bodies during the olden days. The reason behind was that in ancient times water was the only natural medium of movement due to the lack of technological development of road, rail, air, etc. based transportation. So, it is evident that choice of mode always used to play a key role while performing a movement. Still today the appropriate answer for 'How to move? i.e. 'which mode is to be used?' has remained unsolved. The reason lying may be that: (1) users and transport modes have their own diversified characteristics; (2) transportation system are overloaded with high trip demand against limited supply; (3) constraints of environment on the complex network. How the transport system serves the various users is the assumption that travel is used primarily as a linkage between locations at which particular activities are carried out. So problem arises out of lack of system supply which will only be important where problems occur in fulfilling activity requirements. The mode choice problem is not same all over the world. In economically sound society the transport problem is to bring commuters from personalised vehicles to mass transit. But in poor society, where people can not afford for their own car, the main objective is to provide cheap, comfortable and reliable journey by subsidized transport supply. Sociology explains that migration in developing countries occur not due to the pull factor of the city but due to the push factor of the hinterland. So the cities of the developing countries are generally over spill by population. In turn a large number of commuters are creating a high demand on urban transportation. Most of such commuters are not in a position to afford for car (auto) and motorcycle/scooter. Additionally the resources available with such countries are very limited to provide proper infrastructure facilities for private modes. It has, already, been felt by all over the world that to improve urban mobility, emphasis on mass transportation is inevitable. This issue is more crucial for developing countries. Considering this aspect seriously, it is assumed that such countries will design its urban transportation structure consisting of the mass transit only. So, it is evident that choice of mode is a major criteria while implementing decision by public bodies. So, people's travel behaviour, their liking, affording capacity and requirements have to be given due importance as far as feasible against the conflicting situation of the constraints arising from the limited supply of the system and also the limited capacities ofits implementing and operating authorities. In mode-choice problem generally, the competition between the different modes are not studied. The reason may be that their utility is limited or not clearly defined. In an integrated multimodal system the competing modes have many attributes common in nature. Assumptions considered by the analyst influence the structure of the model to a great extent. System characteristics, trip characteristics, and zonal characteristics may be taken into account to relate mode choice in a multicriteria decision problem. The abstract characteristics of the mode are seldom used in trip estimation. Detailed studies for improvement havealready been achieved to overcome the general tendency of trip-end type modal-split models to emphasise transit captive, and of the trip interchange modal-split models to emphasise choice-transit riders, a twostage modal split model. In this process, first, the trip ends between captive and choiceriders are determined followed by synthesis of O-D patterns of the two groups separately. Secondly, the probable split between the public and private transport is estimated. Statistical models, Economic models, and Behavioural models are generally used in mode choice problem. In statistically developed models the relationship is associative in nature since certain variables are connected with others. Such an empirical model is simple, but a confusion may prevail in the causal relationship between variables. Diversion curve is one of the most commonly used tools, where the percentage of trips via public transport is assumed to be related to the difference (or ratio) of travel time or generalised cost of the alternative modes. Economic models are generally based on utility theory or demand. Utility theory leads to the selection of one item between two items, available to an individual or a group. The selection is made, considering the greatest utility or least generalised cost. Cost or travel time is generally taken as the factor for evaluating the choice of mode. In the second type of economic model (i.e. demand model), the travel is considered as a function of demand. Generally, the price of a particular mode, price of the competing modes, and the willingness or ability to pay by the commuters are regarded as factors in the demand model. Attitudinal models, Individual choice models, and Activity based models are the three types of Behavioural travel demand modelling. Three principal methods are available in attitudinal modelling. In one of the methods, the psychometric scaling defines system element for users' selection [e.g. McMillan and Assael 1968]. hi the second method, two-component model of attitudes is constructed. In this, the performance of an alternative is considered as a function of satisfaction achieved by various attributes of that alternative. Various models proposed in this method have been discussed by Golob [1973]; and Golob and Bobson [1974]. The Gestalist concept has been used in the third method [Richardson 1980]. Emphasis is laid on the additive nature of two component theories and then attempt is made to measure either of the components separately [e.g. Levin 1979 and Louviere, Wilss and Piccolo 1979]. The arrangement is based on the overall utility itself; and the concepts of information itergration theory [Anderson 1974] and functional measurement [Anderson 1970] are taken to construct the model. Behavioural models take into account the commuters' behaviour along with their psychological and social motivation. The basic fact underlying this is that a commuter makes a mode choice on the basis of a set of subjectively evaluated and compared to arrive at maximum satisfaction or utility. Binary mode choice models are generally formuleted using such subjective judgement [Richardson 1980]. Multiple choice models using arithmetic approximation can be classified in terms of two criteria: the form of the uderlying cost distribution and the hierarchical structure of the calculation of choice probabilities. The Gumbal (Weibull) and normal distribution are the most commonly used cost distribution. These lead respectively to the logit and probit mode-choice models. Logit model, being a simpler formula, is used for two choice alternatives. Normal distribution model is helpful in multi-choice alternatives. Lace's axiom, composite cost structure and the separated split model are the three fundamental structure for calculating choice probabilities. The most widely used multiple choice model is the multinomial logit model [Benakiva et al. 1975 and Domencich et al 1975]. Modal split in India has been on ah adhoc basis only. For tackling the metropolitan transport problem, the modal split manipulation in favour of public transport is a must. Adequate appropriate technology needs to be developed to take care as to why the travel occurs. The approach needs to consider the behavioural aspect and should not only be city specific. The forecasting models should guide the planner about the level of public transport that must be raised for mass transit [Sarna, 1984]. The traditional mode choice decision was dealt by Reddy [1984] for different users characteristics like family size, vehicle ownership, income level, and trip length. But the qualitative attributes of the modes were not explicitly considered. In the study (Chari et al 1981) on Ahmedabad city as aggregate binary mode choice models between the commuter's own mode and the mass transit, the factors considered were travel time, cost, and socio-economic variables. It was observed by them from the