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

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

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

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

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

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

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

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 &

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

“Principles of Soft Computing, 2 nd Edition” by S. N. Sivanandam & SN Deepa Copyright 2011 Wiley India Pvt. Ltd. All rights reserved.

April 2007 10

April 2007 10

Fuzzy Logic Controller (FLC) Input Fuzzyfication Inference Defuzzyfication Outputs April 2007 11

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

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

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.