By Prof. Andrzej Piegat (auth.)
In the final ten years, a real explosion of investigations into fuzzy modeling and its functions up to speed, diagnostics, selection making, optimization, trend attractiveness, robotics, and so forth. has been saw. The appeal of fuzzy modeling effects from its intelligibility and the excessive effectiveness of the versions received. as a result of this the modeling should be utilized for the answer of difficulties that can no longer be solved until now with any identified traditional equipment. The e-book offers the reader with a sophisticated advent to the issues of fuzzy modeling and to at least one of its most vital functions: fuzzy regulate. it's according to the newest and most important wisdom of the topic and will be used not just via regulate experts but additionally by way of experts operating in any box requiring plant modeling, technique modeling, and structures modeling, e.g. economics, company, medication, agriculture,and meteorology.
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Additional resources for Fuzzy Modeling and Control
5 In the case of a triangular membership function, Fig. 34, for a minimal variation of variable x in the neighborhood of the point b an abrupt jump occurs not only in the value but also in the sign of the derivative jJ,(x). The triangular membership function thus represents a very rough approximation of the human manner of evaluation. However, this does not mean that they should not be used in fuzzy models since a model with triangular membership functions can be satisfactorily exact. 000 Axiom 3.
Membership function consisting of straight segments These functions are very often used in practice for their simplicity. 28. The enormous advantage of the polygonal functions is that they can be defined using a minimal amount of information, in comparison with other membership functions. Data relating to the corner points of a function are hereby sufficient. It is of great importance in the case of modeling of systems on which we do not have much data. In practice, to define polygonal membership functions only data concerning their modal values are needed.
27. Such ranges can come into existence during adjusting (adapting) fuzzy models based on input/output data (self-Iearning algorithms). The consequence is that zones arise which are insensitive to a change of the given input variable. 34 2. --,. abc d e abc x de x Fig. 27. Conversion of fuzzy sets not satisfying the condition of a partition of unity (a) into sets satisfying this condition (b) The condition of a partition of unity is sometimes also called the condition of overlapping or covering membership functions to unity.
Fuzzy Modeling and Control by Prof. Andrzej Piegat (auth.)