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Concept
Defuzzification
Résumé
Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems. These systems will have a number of rules that transform a number of variables into a fuzzy result, that is, the result is described in terms of membership in fuzzy sets. For example, rules designed to decide how much pressure to apply might result in "Decrease Pressure (15%), Maintain Pressure (34%), Increase Pressure (72%)". Defuzzification is interpreting the membership degrees of the fuzzy sets into a specific decision or real value.
The simplest but least useful defuzzification method is to choose the set with the highest membership, in this case, "Increase Pressure" since it has a 72% membership, and ignore the others, and convert this 72% to some number. The problem with this approach is that it loses information. The rules that called for decreasing or maintaining pressure might as well have not been there in this case.
A common and useful defuzzification technique is center of gravity. First, the results of the rules must be added together in some way. The most typical fuzzy set membership function has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal line somewhere between the top and the bottom, and the top portion were to be removed, the remaining portion forms a trapezoid. The first step of defuzzification typically "chops off" parts of the graphs to form trapezoids (or other shapes if the initial shapes were not triangles). For example, if the output has "Decrease Pressure (15%)", then this triangle will be cut 15% the way up from the bottom. In the most common technique, all of these trapezoids are then superimposed one upon another, forming a single geometric shape. Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value.
Source officielle
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Publications associées (1)
Coevolutionary fuzzy modeling
This thesis presents Fuzzy CoCo, a novel approach for system design, conducive to explaining human decisions. Based on fuzzy logic and coevolutionary computation, Fuzzy CoCo is a methodology for constructing systems able to accurately predict the outcome o ...
EPFL2002Concepts associés (1)
Notion à contenu variable
Une notion à contenu variable (anglais : fuzzy concept) est un concept flou qui présente plus d'une solution interprétative possible dans l'interprétation d'un texte. Il s'agit d'un concept à texture ouverte qui présente un noyau de sens clair sur lequel il y a consensus sur le sens ainsi qu'une zone de pénombre sur laquelle il n'y a pas de consensus, d'après le philosophe du droit H.L.A. Hart. En droit, les théoriciens de l'interprétation des lois ont recours à l'idée de notion à contenu variable lorsque le législateur utilise des concepts à contours indéfinis dans la rédaction d'un texte législatif.