Defuzzifications are has the following types:
1)Centre-of-area/gravity defuzzification.
2)Centre-of-largest-area defuzzification.
3)Mean of maxima.
4)First-of-maxima defuzzification.
5)Middle-of-maxima defuzzification.
6)Height defuzzification
But which method is better???
The center of gravity./ Centroid Method is generally considered.
The Following References may Help.
1. Defuzzification
From Wikipedia, the free encyclopedia
Defuzzification is the process of producing a quantifiable result in fuzzy logic, given fuzzy sets and corresponding membership degrees. It is typically needed in fuzzy control systems. These 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
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. 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). Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value.
There are many different methods of defuzzification available, including the following:
AI (adaptive integration); BADD (basic defuzzification distributions); BOA (bisector of area); CDD (constraint decision defuzzification); COA (center of area), COG (center of gravity); ECOA (extended center of area); EQM (extended quality method); FCD (fuzzy clustering defuzzification); FM (fuzzy mean); FOM (first of maximum);GLSD (generalized level set defuzzification); ICOG (indexed center of gravity); IV (influence value); LOM (last of maximum); MeOM (mean of maxima)
MOM (middle of maximum); QM (quality method); RCOM (random choice of maximum); SLIDE (semi-linear defuzzification), WFM (weighted fuzzy mean)
The maxima methods are good candidates for fuzzy reasoning systems. The distribution methods and the area methods exhibit the property of continuity that makes them suitable for fuzzy controllers.
Link: http://en.wikipedia.org/wiki/Defuzzification
2. Fuzzy Syatems and Sets.
i) Defuzzification: criteria and classification
Werner Van Leekwijck, Etienne E. Kerre
Volume 102,Issue 2, 1 December 1999, Pages 159–178
In this paper, we contribute to the theory and development of defuzzification techniques. First we define the core of a fuzzy set. Then we formulate a set of criteria for defuzzification in arbitrary universes, ordered universes, and the set of the real numbers. Finally, we classify the most widely used defuzzification techniques into different groups and we examine the prototypes of each group with respect to the defuzzification criteria. We show that the maxima methods behave well with respect to the more basic defuzzification criteria, and hence are good candidates for fuzzy reasoning systems. On the other hand, the distribution methods and the area methods do not fulfill the basic criteria, but they exhibit the property of continuity that makes them suitable for fuzzy controllers.
Link: http://www.sciencedirect.com/science/article/pii/S0165011497003370
Keywords
Defuzzification; Fuzzy sets; Operators; Membership functions
ii) Criteria for evaluating fuzzy ranking methods (1991)
by Y Yuan
Venue: Fuzzy Sets and Systems
Ranking and Defuzzification Methods based on Area Compensation.
by Philippe Fortemps, Marc Roubens, Facult'e Polytechnique De Mons, Rue De Houdain - Fuzzy Sets and Systems , 1996
"... : We present some interesting properties related to the area compensation procedure to compare fuzzy numbers. It has been proved that this method produces more than a fuzzy interval order: it induces a ranking of fuzzy numbers. Some further results are given about the transitivity property and about ..."
Link: http://citeseerx.ist.psu.edu/showciting?cid=2080629
P.S.
Regarding to the literature, they cannot recommend one criteria, but we may apply a few. Some criteria for a defuzzification method choice could be:
1)continuity;
2) disambiguity;
3)plausibility;
4)computational complexity.
Continuity, It means that a small change in an input of a fuzzy controller should not result in a large change in the output.
Disambiguity means that a defuzzification method should work in any situation. This is not always the case. For example, the centre-of-largest-area method cannot make a choice when we have two equal areas. Plausibility means that a procedure produces a defuzzified output that lies approximately in the middle of the support of the resulting membership function and has a high degree of membership. The centre-of-area method, for example, does not satisfy these properties: although the centre-of-area output lies in the middle of the support set, its membership degree may be one of the lowest possible.
The computational complexity sometimes depends on the shape of the output
membership functions and whether max–min composition-based inference or scaled inference is chosen. The middle-of-maxima method, for example, is faster with a scaled inference. There is also an issue of representation of the fuzzy sets. In the case of the centre-of-area defuzzification, a tabular representation of the fuzzy sets in combination with clipped fuzzy sets (max–min composition) makes the defuzzification procedure very slow.
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