FUZZIFICATION AND DEFUZZIFICATION Principles of Soft Computing 2
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FUZZIFICATION AND DEFUZZIFICATION “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
FUZZY LOGIC Ø Fuzzy logic is the logic underlying approximate, rather than exact, modes of reasoning. Ø It is an extension of multivalued logic: Everything, including truth, is a matter of degree. Ø It contains as special cases not only the classical two-value logic and multivalue logic systems, but also probabilistic logic. Ø A proposition p has a truth value • 0 or 1 in two-value system, • element of a set T in multivalue system, • Range over the fuzzy subsets of T in fuzzy logic. “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
Points to remember In Probability if P(A)=0. 9 then P(A)’=0. 1 In Fuzzy Logic if P(A)=0. 9 then P(A)≠ 0. 1 April 2007 3
Ø Boolean logic uses sharp distinctions. Ø Fuzzy logic reflects how people think. Ø Fuzzy logic is a set of mathematical principles for knowledge representation and reasoning based on degrees of membership. “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
FUZZY vs PROBABILITY Ø Fuzzy ≠ Probability Ø Probability deals with uncertainty and likelihood Ø Fuzzy logic deals with ambiguity and vagueness “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
NEED OF FUZZY LOGIC Ø Based on intuition and judgment. Ø No need for a mathematical model. Ø Provides a smooth transition between members and nonmembers. Ø Relatively simple, fast and adaptive. Ø Less sensitive to system fluctuations. Ø Can implement design objectives, difficult mathematically, in linguistic or descriptive rules. to express “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
CLASSICAL SETS (CRISP SETS) Conventional or crisp sets are Binary. An element either belongs to the set or does not. {True, False} {1, 0} “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
CRISP SETS “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
“Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
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Fuzzy Logic Controller (FLC) Input Fuzzyfication Inference Defuzzyfication Outputs April 2007 11
DEFUZZIFICATION Ø Defuzzification is a mapping process from a space of fuzzy control actions defined over an output universe of discourse into a space of crisp (nonfuzzy) control actions. Ø Defuzzification is a process of converting output fuzzy variable into a unique number. Ø Defuzzification process has the capability to reduce a fuzzy set into a crisp single-valued quantity or into a crisp set; to convert a fuzzy matrix into a crisp matrix; or to convert a fuzzy number into a crisp number. April 2007 12
METHODS OF DEFUZZIFICATION Defuzzification is the process of conversion of a fuzzy quantity into a precise quantity. Defuzzification methods include: Ø Ø Ø Ø Ø Mean of Maxima Centroid method Weighted average method Max Membership Principle Sum of Centers Center of largest area First of maxima Lambda Cut Set “Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.
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