Statistics – Computation
Scientific paper
Oct 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994spie.2353..469l&link_type=abstract
Proc. SPIE Vol. 2353, p. 469-478, Intelligent Robots and Computer Vision XIII: Algorithms and Computer Vision, David P. Casasent
Statistics
Computation
Scientific paper
Imprecision can arise in fuzzy relational modeling as a result of fuzzification, inference and defuzzification. These three sources of imprecision are difficult to separate. We have determined through numerical studies that an important source of imprecision is the defuzzification stage. This imprecision adversely affects the quality of the model output. The most widely used defuzzification algorithm is known by the name of `center of area' (COA) or `center of gravity' (COG). In this paper, we show that this algorithm not only maps the near limit values of the variables improperly but also introduces errors for middle domain values of the same variables. Furthermore, the behavior of this algorithm is a function of the shape of the reference sets. We compare the COA method to the weighted average of cluster centers (WACC) procedure in which the transformation is carried out based on the values of the cluster centers belonging to each of the reference membership functions instead of using the functions themselves. We show that this procedure is more effective and computationally much faster than the COA. The method is tested for a family of reference sets satisfying certain constraints, that is, for any support value the sum of reference membership function values equals one and the peak values of the two marginal membership functions project to the boundaries of the universe of discourse. For all the member sets of this family of reference sets the defuzzification errors do not get bigger as the linguistic variables tend to their extreme values. In addition, the more reference sets that are defined for a certain linguistic variable, the less the average defuzzification error becomes. In case of triangle shaped reference sets there is no defuzzification error at all. Finally, an alternative solution is provided that improves the performance of the COA method.
Buchal Ralph O.
Lapohos Tibor
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