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Neural approach to linguistic approximation of fuzzy sets

In many practical implementations involving fuzzy systems, a numerical value is delivered to the user as the output of the system. Nevertheless, there are applications where such a numeric value is of little interest for the user, which, in turn, demands a linguistic output. In these cases, the linguistic approximation of the output has to be performed. This is not a simple problem, since often the application of approximate reasoning leads to very irregular non-normal, possibly non-convex output fuzzy sets. This paper shows that linguistic approximation can be approached in a more traditional way as a problem of compatibility between fuzzy sets, but also as a pattern classification problem. Several possible solutions are presented and discussed. Emphasis is put on a neural-based pattern classification approach. In order to comparatively evaluate the performances of all considered solutions, each one was integrated within an expert system dedicated to coronary heart disease diagnosis. The performance of the whole system was then evaluated using clinical data from 152 patients, by comparing the linguistic output of the expert system to the results of the gold standard of coronary angiography.