The application of FL in choice experiments is still relatively uncommon though increasing examples can be found. One of the early applications of FL in CE can be found in Hoogendoorn-Lanser and Hoogendoorn (2000) who applied the FL technique to analyse travel choice behaviour where the travellers’ perception and appraisal of the trip attributes were considered to be vague. In this case, in-vehicle time, access, egress and waiting times (at first stop and at transfers) formed the main attributes in the choice set while fuzzy utility of the alternative formed the output variable in the FL system. The premise of this paper was that people’s perception of time is subjective and hence FL theory was applied to model the impact of travel time. In order to obtain a rule base that optimises the percentage correct predicted, the authors applied Genetic Algorithm (GA) where the subset of
optimal rules were selected from the total possible rules. The authors found that compared to the logit model, the FL model with GA yielded significantly better model with fewer set of decision rules required to correctly approximate travellers’
choices. Thus in this case, the FL method was found to be a good descriptive tool for human behaviour.
Another application of FL in mode choice analysis was conducted by Mizutani and Akiyama (2001). In this case, the authors developed a multinomial logit model with fuzzy utility function for different mode choices and several explanatory variables. Fuzzy utility which formed the output was classified into ‘positive’ and
‘negative’ values while the effect of each explanatory variable on utility was incorporated into the system through fuzzy rules. Using trial and error as well as GA, the authors estimated the values of the linguistic variables as well as the parameters of the membership function that comprised the FIS. While this approach provided a unique perspective to model travel choice, the authors only related the effect of each input variable on the fuzzy utility. Thus, no rules were developed which incorporated the combined effect of various inputs on respondents’ choice.
In yet another application of the FL method to mode choice analysis, Cantarella and Fedele (2003) developed a fuzzy utility model (FUM) with several attributes where fuzzy utility can be depicted as a choice fraction vector which is a function of the core vector. The core vector in this case reflects the difference between the deterministic utilities of the alternatives. By considering the width of the fuzzy density function, the parameters associated with the core vector were estimated by trying to reproduce the observed choices. The distance between the observed and modelled values provided an estimate on the relative effectiveness of the set of parameters with the minimum of the values leading to the final parameter estimation. While this appears as a plausible method of parameter estimation, the authors do not explicitly specify the method. Moreover, with the trial-and-error procedure, this process can be cumbersome.
Using a neuro-fuzzy method to estimate rule weights and parameters for the fuzzy membership function, Vythoulkas and Koutsopoulos (2003) applied the FL theory
in modelling discrete choice from mode choice. Travel time, travel cost and access/egress time formed the main attributes in the choice experiment which were incorporated in the FIS using the difference method. The output of the FIS comprised of five membership functions reflecting the preference level for each of the alternatives (train and car). The rule base in this study was based on each alternative. By examining the effect of different rules base on the percentage correct predicted, the authors sought to emphasise the importance of optimal weights on correct prediction. It was observed that with the deterministic choice rules, the correct prediction increased from 72.3% in case of equal weights to 77%
when optimal weights were used. While neuro-fuzzy method had been shown to model respondents’ decision-making fairly well, the authors also acknowledged that defining the criteria for calibration, development of rules base and the calibration of parameters posed some difficulty with the implementation of this method.
Though the above examples have revealed increasing applications of FL in choice experiment, it can also be observed that the method of application as well as the output obtained from the FL system has varied with different studies. While some authors have adopted the GA and neuro-fuzzy methods to estimate parameter values as well as to calibrate the membership function and obtain optimal rule weights, little attention has been paid on the type of rules needed to develop the system. Moreover, the applicability of this method has not been examined across different types of input data. This examination along with the number and types of rules required in the FL system for different types of input variables will therefore form an important component of the FL analysis in this research.
While the previous examples of FL application have focussed exclusively on choice experiment and mode choice analysis, some research has also been conducted to apply this method to model noise annoyance.
Botteldooren et al. (2002) conducted an exercise to calculate noise annoyance related to several factors where the respondents were asked to provide a numeric rating from a scale of 0-10 for each linguistic noise annoyance category. Based on the exposure to noise which included the direction of the living room and bedroom
window as well as the distance to the source, level of masking, sensitivity to noise along with other socio-demographic variables, rules were formed to estimate the effect on annoyance level. The authors used the weighted percentage of the correctly predicted noise annoyance response as a measure of the model performance. The authors found that the fuzzy rule base was better at explaining the extreme levels of annoyance than the moderate levels. Considering the same set of explanatory variables, the authors found that the fuzzy rule base system was better at predicting the noise annoyance response than the linear regression model.
However, the authors noted that the theoretical and empirical basis for the expert varies depending on the cause of annoyance.