INTEGRATION OF LINGUISTIC PROBABILITIES

In a previous study, Zwick, Budescu and Wallsten (1988) found that the membership functions representing the subjective combinations of two independent linguistic probabilistic judgements could not be predicted by applying any dual t- and co-t-norm to the functions of the underlying terms. Their results showed further that judgements involving the "and" connective were best modelled as the fuzzy mean of the two separate components. The present experiment extended those results by manipulating the instructions regarding the "and" connective and also including an additional task in which subjects selected a third phrase to represent the integration of the two independent judgements. Again, no t-norm rule predicted subjects' responses, which were now best modelled by the point-wise arithmetic or geometric means of the functions. In addition, most subjects selected phrases and provided membership functions in response to two identical forecasts that were more extreme and more precise than the individual forecast, a result inconsistent with any t-norm or averaging model. A minority of subjects responded with the same phrase contained in the forecasts. The entire pattern of results in the Zwick et al. (1988) and the present study is used to argue against the indiscriminate application of mathematically prescribed, but empirically unsupported operations in computerized expert systems intended to represent and combine linguistic information. © 1990 Academic Press Limited.