Foundations of Generic Optimization pp 403-431 | Cite as

# A Consistency Criterion for Optimizing Defuzzification in Fuzzy Control

## Abstract

Throughout the literature about fuzzy control, various defuzzification methods have been proposed, as well as been classified according to their properties, such as continuity, scale-invariance, core consistency and much more. However, the choice of a suitable defuzzification operator still remains an arbitrary one. We do not claim to have found the “perfect defuzzifier”, but in this article, we would like to add one particular new criterion, that we would like to call the Consistency Criterion, which can be used to measure the suitability of a certain defuzzification process, or at least compare several defuzzification operators, even parametric classes with infinitely many members, that contain some very commonly used ones, such as D.P. Filev and R.R. Yager’s BADD-defuzzification ([3]) as the most commonly used class throughout this text. A surprising result is that the minima of a measure of non-consistency yielded with respect to the parameters occurring in the rule base or other parameters of the problem, are certainly not reached in the most “natural” choice values for the parameters, but for some surprising, transcendent numbers.

## Keywords

fuzzy control defuzzification consistency antecedent rule base## Preview

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