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Topic: Defuzzification

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	Defuzzification processing - PatentStorm (Site not responding. Last check: 2007-10-17)
		A defuzzification device in which, depending on selection signals (FA1, FA2) and aggregated regulation weights (γ), either in a maximum process a first/last maximum value at which an associated aggregated regulation weight is a maximum is selected as the sharp output value (g) and an activation...
		In a defuzzification system having fuzzy singletons in the consequent, an inference block (1) in each rule includes a device (2) for calculating the maximum value of each fuzzy singleton, devices (3 and 4) for performing weighted and simple additions to each of the inference grades outputted from...
		A defuzzifying apparatus, for a fuzzy inference machine in which the consequent of a fuzzy inference is represented by a fuzzy set or a singleton, comprises a bias impression unit that adds an arbitrary-largeness bias value to each inference output grade, and circuitry a center of gravity of each...
	www.patentstorm.us /class/706/9-Defuzzification_processing.html (1667 words)

	EDN Access -- 04.13.95 ARTICLETITLE
		Its COG is in the neighborhood of 9.
		Because centroid defuzzification calculates system outputs from COG figures, no system output greater than the COG of this function, that is, 9, will be possible-despite the desired maximum being 10.
		With centroid and singleton defuzzification, a fuzzy-rule-based system is nothing more than a representation of a system response function obtained by dividing the input space into crisp, noncontiguous regions, assigning a constant output value to each of these regions, and letting the "fuzziness" provide smooth transitions (an interpolation) between the constant output values.
	www.edn.com /archives/1995/041395/08column.htm (1203 words)

	Fuzzy (Site not responding. Last check: 2007-10-17)
		Defuzzification of the fuzzy terms that appear in the conclusions of rules.
		One method of defuzzification is to place the confidence factors (MV) generated by inference for each fuzzy outcome at the point where the membership function has its highest value.
		Defuzzification of the conditions of each rule and assigning the outcome of each rule the minimum MV of its conditions multiplied by the rule weight.
	www.intellicrafters.com /fuzzy.htm (2052 words)

	Defuzzification - Wikipedia, the free encyclopedia
		Defuzzification is the process of producing a quantifiable result in fuzzy logic.
		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.
		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.
	en.wikipedia.org /wiki/Defuzzification (333 words)

	IEEE TFS: Abstracts of Published Papers, vol. 4, no. 1 (Site not responding. Last check: 2007-10-17)
		Defuzzification is a procedure of crucial importance for fuzzy systems because a final crisp output (control) action is required in many theoretical and practical applications.
		In this paper, the authors introduce two new objective defuzzification strategies, Gaussian distribution transformation-based defuzzification (GTD) and polynomial transformation-based defuzzification (PTD), which are based on a discrete universe of discourse.
		Both strategies include the COA and MOM strategies as special cases, and both are based on parameter learning processes using the extended Kalman filter as their iterative improvement algorithms on sample database containing fuzzy sets and the associate defuzzified values.
	www.ieee-nns.org /pubs/tfs/abstracts/abs4-1.html (1346 words)

	IIIA - CSIC
		Defuzzification is one of the fundamental steps in the development of fuzzy knowledge based systems.
		This is so because defuzzification has been studied as equivalent to the computation of an expected value.
		In this work we present the reversal approach, we study defuzzification procedures for their application to aggregation.
	www.iiia.csic.es /lang-ca/publication_detail.php?pub_id=605 (187 words)

	FuzzyValue
		For example, if the final fuzzy decision were to adjust the temperature setting on the thermostat a ‘little higher’, then it would be necessary to convert this ‘little higher’ fuzzy value to the ‘best’ crisp value to actually move the thermostat setting by some real amount.
		Center of Area (COA) defuzzification finds the x value such that half of the area under the fuzzy set is on each side of the x value.
		However, a place where this defuzzification method is very useful is when the fuzzy set is in fact a series of singleton values.
	ai.iit.nrc.ca /IR_public/fuzzy/fuzzyJDocs/FuzzyValue.html (2787 words)

	Output Variable Window
		The weighted area defuzzification is analogous to centroid defuzzification, the only difference being that areas shared by two fuzzy sets are counted twice.
		For all fuzzy output defuzzification operators, a correction is applied to the upper bound (resp.
		The threshold parameter is a tolerance threshold associated to a warning message at the defuzzification stage (see the alarm paragraph in section 2.2).
	www.inra.fr /Internet/Departements/MIA/M/fispro/fisprodocen/node5.html (392 words)

	Fuzzy Inference Systems :: Tutorial (Fuzzy Logic Toolbox)
		It enhances the efficiency of the defuzzification process because it greatly simplifies the computation required by the more general Mamdani method, which finds the centroid of a two-dimensional function.
		The input for the defuzzification process is a fuzzy set (the aggregate output fuzzy set) and the output is a single number.
		Perhaps the most popular defuzzification method is the centroid calculation, which returns the center of area under the curve.
	www.mathworks.com /access/helpdesk/help/toolbox/fuzzy/fp351dup8.html (1884 words)

	Red Internacional de Control Automático
		Finally is the (optional) DEFUZZIFICATION, which is used when it is useful to convert the fuzzy output set to a crisp number.
		For this reason, SUM composition is only used when it will be followed by a defuzzification method, such as the CENTROID method, that doesn't have a problem with this odd case.
		Note: Sometimes the composition and defuzzification processes are combined, taking advantage of mathematical relationships that simplify the process of computing the final output variable values.
	www.control-automatico.net /htm/art053.htm (1625 words)

	Dr. Dobb's \| Fuzzy Logic in C \| July 22, 2001
		Fuzzification is the process of assigning or calculating a value to represent an input's degree of membership in one or more qualitative groupings, called "fuzzy sets." Figure 2 shows a system input, temperature, with fuzzy sets cold, cool, warm, and hot.
		Often, more than one rule applies to the same specific action, in which case the common practice is to use the strongest or most true rule; see Figure 4.
		Defuzzification employs compromising techniques to resolve both the vagueness and conflict issues.
	www.ddj.com /184408940?pgno=19 (2880 words)

	[No title]
		It is intuitive that fuzzification and defuzzification should be reversible; that is, if we fuzzifiy a number into a fuzzy set and immediately defuzzify it, we should get the same number back again.
		If defuzzification is to take place, this has implications for the shape of membership functions used to fuzzify input variables into fuzzy sets used in the reasoning process which ultimately results in defuzzifying an output fuzzy set.
		Our first option for defuzzification, maxav or average of maxima, looks at the membership functions for the maximum values, and sees that ZERO reaches its only maximum at OUTPUT = 0; this is selected as the representative value for ZERO.
	members.aol.com /wsiler/chap08.htm (752 words)

	Design of VLSI Systems - Fuzzy Logic Systems (Site not responding. Last check: 2007-10-17)
		The max-min method finally requires a defuzzification stage which is generally performed using the centre of gravity method.
		It can be used with Mamdani'method to simplify considerably the defuzzification stage, whose task is reduced to the calculation of a weighted average with a restricted set of crisp values.
		The truncation of the consequent and the defuzzification pose an important problem as regards the parallelism of the inference engine (especially when the number and size of output sets is large).
	www.vlsi.wpi.edu /webcourse/fuzzy/fuzzy.html (12463 words)

	FuzzyValue
		For example, if the final fuzzy decision were to adjust the temperature setting on the thermostat a ‘little higher’, then it would be necessary to convert this ‘little higher’ fuzzy value to the ‘best’ crisp value to actually move the thermostat setting by some real amount.
		Center of Area (COA) defuzzification finds the x value such that half of the area under the fuzzy set is on each side of the x value.
		However, a place where this defuzzification method is very useful is when the fuzzy set is in fact a series of singleton values.
	www.iit.nrc.ca /IR_public/fuzzy/fuzzyJDocs/FuzzyValue.html (2787 words)

	International Technical Working Groups
		Membership grade matrices and membership functions (see figure 2) are then constructed for discrete-valued and continuous-valued features, respectively, and used to fuzzify the decision rules into a set of fuzzy rules.
		Defuzzification is about producing non-fuzzy outputs from the triggered fuzzy rules.
		Because the nature of pattern recognition is quite different from that of fuzzy control where the outputs are real values, we have to develop some new defuzzification methods for fuzzy pattern recognition models.
	www.spie.org /web/oer/april/apr97/eiwg.html (640 words)

	Fuzzy Logic in Autonomous Robot Navigation: Section 2
		The task of the controller is to compute, in state s, the value of Des(s,c) for each control c, and to use these values to choose one control c* for actual execution.
		It should be noted that centroid defuzzification can produce undesired results when the output desirability is not unimodal; for example, the robot, having the option of avoiding an obstacle from the right or from the left, may decide to go straight.
		First, it is essential that defuzzification be performed after combination.
	aass.oru.se /Agora/FLAR/HFC/sec2.html (1341 words)

	Neural Network world
		Defuzzification is a methodology to single out a numerical value v
		In most approaches found in the literature, defuzzification is local, in the sense that V
		They are based on the thresholds and the estimation of the truth value of the answers.
	www.uivt.cas.cz /nnw/contents2001/nnw6_01.htm (1481 words)

	FAQ: Fuzzy Logic and Fuzzy Expert Systems 1/1 [Monthly posting] - [4] What is a fuzzy expert system?
		In SUM composition, the combined output fuzzy subset is constructed by taking the pointwise sum over all of the fuzzy subsets assigned to the output variable by the inference rule.
		Finally is the (optional) DEFUZZIFICATION, which is used when it is useful to convert the fuzzy output set to a crisp number.
		Note: Sometimes the composition and defuzzification processes are combined, taking advantage of mathematical relationships that simplify the process of computing the final output variable values.
	www-2.cs.cmu.edu /Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-4.html (1209 words)

	Design_Details (Site not responding. Last check: 2007-10-17)
		In the case of defuzzification, singleton output membership functions were chosen for their computational expediency.
		The defuzzification process is the most computational intensive portion of the total fuzzy control algorithm (fig 7).
		In the case in which singletons are used for the output membership function, the COG method reduces to a weighted average of the output membership functions (fig.9).
	pasta.union.edu /Projects/Past/Proj97/BillRiley/Design_Details.htm (2076 words)

	An analogue fuzzy logic processor IC
		The major hurdles in designing analogue fuzzy processors have centred on the inefficiency of analogue division techniques, which are needed for the defuzzification stage.
		Analogue division can be avoided using a self normalising loop, but this imposes limitations on the form of defuzzification that can be used.
		], a novel circuit was developed that enables the use of a sophisticated defuzzification method in conjunction with a normalisation locked loop.
	www.eee.bham.ac.uk /QuigleySF/page7.htm (165 words)

	FuzzySet1
		Finds the mean of the maximum values of a fuzzy set as the defuzzification value.
		NOTE: This doesn't always work well because there can be x ranges where the y value is constant at the max value and other places where the maximum value is only reached for a single x value.
		Moment defuzzification defuzzifies a fuzzy set returning a floating point (double value) that represents the fuzzy set.
	ai.iit.nrc.ca /IR_public/fuzzy/fuzzyJDocs/FuzzySet.html (2339 words)

	Output Variable
		The Center of Gravity defuzzification method calculates the center of gravity for the "filled" portions of the sets.
		The Maxima defuzzification method isn't one you find in many of the fuzzy logic "theory and application" books.
		This defuzzification method can be used to create Fuzzy State Machines (FuSMs).
	www.louderthanabomb.com /sparkhelp/output_var.htm (229 words)

	generation5 - Defuzzification Options in Flex
		Note that this means that the defuzzified values of the variable can never reach the extremes of their ranges (0 and 100 in our case).
		The final defuzzification option we have is shrinking versus truncation.
		We need to know two things, the final possibility values for output after all fuzzy rules have fired and the centre points of the base of each of the triangular fuzzy sets which make up the fuzzy variable output.
	www.generation5.org /content/2004/defuzz.asp (1362 words)

	Prof. P. Matsakis - Journal Paper RSE00
		However, such a partition is often evaluated after “defuzzification”, i.e., it is reduced to a crisp partition.
		This approach is rather drastic and far from satisfactory because the quantitative information is lost after the defuzzification.
		Some methods do not require preliminary defuzzification, but they are not adequate to evaluate non-probabilistic fuzzy partitions (i.e., fuzzy partitions such that the sum of the membership degrees is not necessarily equal to 1).
	www.cis.uoguelph.ca /~matsakis/Publications/rse00.htm (204 words)

	Design of VLSI Systems - Fuzzy Logic Systems
		It can be used with Mamdani'method to simplify considerably the defuzzification stage, whose task is reduced to the calculation of a weighted average with a restricted set of crisp values.
		Their performance is evaluated according to their processing speed (that is the number of fuzzy logic inferences per second (FLIPS)), as to their precision (error and noise generation in analog circuits and number of bit representing fuzzy values in digital ones).
		The truncation of the consequent and the defuzzification pose an important problem as regards the parallelism of the inference engine (especially when the number and size of output sets is large).
	lsiwww.epfl.ch /LSI2001/teaching/webcourse/ch09/fuzzy.html (12463 words)

	A Novel Analogue CMOS Defuzzification Circuit (Site not responding. Last check: 2007-10-17)
		An analogue CMOS circuit technique for the implementation of defuzzification is proposed.
		The defuzzification method is based upon the Normalisation Locked Loop (NLL) method, but with two key improvements: the compact representation of triangular membership functions, and a mechanism to ensure that the relative rule weight proportions are preserved during normalisation.
		Results obtained from the fabricated circuit operating as part of a NLL are presented.
	www.eee.bham.ac.uk /QuigleySF/page19.htm (112 words)

	Defuzzification (Site not responding. Last check: 2007-10-17)
		However, for most applications (in particular in control) there is a need for a single action or `crisp' solution to emanate from the inferencing process.
		Lee [20] describes the three main approaches as the max criterion, mean of maximum and the centre of area.
		Although the process of reducing the final fuzzy set to a crisp value does seem appropriate for control problems much information is lost by doing this and further work needs to be done on how to use the information available in the solution fuzzy set.
	www.cse.dmu.ac.uk /~rij/newrep/node16.html (202 words)

	No Title
		Following [1] the differentiable soft min is used in place of and in the antecedent and the ``Local Mean of Maxima'' or LMOM is used for defuzzification.
		The LMOM is differentiable for use with gradient descent while defuzzification strategies such as center of gravity and mean of maxima are not [1,12].
		The final continuous valued output, call it f, of the set of fuzzy rules for a single cycle of operation is the summation of the values produced from the LMOM defuzzification of the rules that fired.
	seraphim.csee.usf.edu /hallpap/rlshort.html (2395 words)

	Fuzzy Logic: New Feature Documentation
		returns the smallest of maximum defuzzification of fuzzy set A.
		returns the largest of maximum defuzzification of fuzzy set A.
		returns the bisector of area defuzzification of fuzzy set A.
	www.wolfram.com /products/applications/fuzzylogic/newin2/featuredocumentation.html (1397 words)

	Fuzzy Logic Control with the Intel 8XC196 Embedded Microcontroller
		The fuzzy system is associated with Binary Input Output Fuzzy Associative Memories which are used for control.
		This paper discusses the development of a fuzzy inference unit and algorithms for fuzzification, rule evaluation and defuzzification of a fuzzy closed loop control system.
		Tools and techniques to generate optimized fuzzy based real time code in assembly and C, with short development time, are shown for the Intel 8XC196 microcontroller.
	www.intel.com /design/mcs96/papers/esc_196.htm (179 words)

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