Dissemin is shutting down on January 1st, 2025

Published in

Elsevier, Fuzzy Sets and Systems, 24(159), p. 3297-3312

DOI: 10.1016/j.fss.2008.03.002

Links

Tools

Export citation

Search in Google Scholar

Vagueness evaluation of the crisp output in a fuzzy inference system

Journal article published in 2008 by Michele Lalla, Gisella Facchinetti, Giovanni Mastroleo ORCID
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Orange circle
Postprint: archiving restricted
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO

Abstract

Fuzzy models generally provide an output characterized by vagueness, which is expressed through a solution fuzzy set. In many applications, the response of the model is transformed in a crisp value through some defuzzification methods for solution fuzzy region, thus losing its fuzziness. Only to preserve a few indications of its vagueness, some indices summarizing the spread of the output membership function could be used to associate them with the crisp output, such as its standard deviation, the quartile deviation, the coefficients of skewness and kurtosis. The behaviour of such indices is examined in a large number of possible, though unlikely, output solutions and in an application of a fuzzy inference system for evaluating university teaching activity. The results seem to suggest that the 20–80 mid-percentile range could be a good measure of the vagueness dispersion, while the coefficient of skewness could provide a useful indication about the asymmetry of the solution's shape. Moreover, a rough estimate of dispersion was obtained from a triangle approximating the solution fuzzy region because the results were straightforwardly deduced from formulae involving the abscissae of its vertices. The results generally appear to underestimate the true values of the standard deviations; the 15–85 mid-percentile range of the approximating triangle seemed to be a more suitable rough appraisal of fuzzy output dispersion.