Fuzzy.ppt - FUZZY LOGIC Real World Example Parag Jain IT Department Oriental University OVERVIEW Where did it begin What is Fuzzy Logic Fuzzy Logic

Fuzzy.ppt - FUZZY LOGIC Real World Example Parag Jain IT...

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FUZZY LOGIC & Real World Example Parag Jain IT Department Oriental University
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OVERVIEW Where did it begin? What is Fuzzy Logic? Fuzzy Logic Rules and Terminology Fuzzy Logic Development Methodology FuzzyTech Supports Entire Fuzzy Design Methodology Application Fuzzy Logic –Future Standard Conclusion
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ORIGINS OF FUZZY LOGIC Traces back to Ancient Greece Lotfi Asker Zadeh ( 1965 ) First to publish ideas of fuzzy logic. Professor Toshire Terano ( 1972 ) Organized the world's first working group on fuzzy systems. F.L. Smidth & Co. ( 1980 ) First to market fuzzy expert systems.
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Types of Uncertainty Stochastic uncertainty E.g., rolling a dice Linguistic uncertainty E.g., low price, tall people, young age Informational uncertainty E.g., credit worthiness, honesty
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Membership value height 1 0 Linguistic uncertainty A fuzzy function for tall people . a subjective measure. not a probability measure. “tall” in Asia “tall” in USA “tall” in NBA 5’10”
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WHAT IS FUZZY LOGIC? Definition of fuzzy Fuzzy – “not clear, distinct, or real world vagueness ” Definition of fuzzy logic A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts. superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth
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central notion of fuzzy systems is that truth values (in fuzzy logic) or membership values (in fuzzy sets) are indicated by a value on the range [0.0, 1.0], with 0.0 representing absolute Falseness and 1.0 representing absolute Truth.
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TRADITIONAL REPRESENTATION OF LOGIC Slow Fast Speed = 0 Speed = 1 bool speed; get the speed if ( speed == 0) { // speed is slow } else { // speed is fast }
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FUZZY LOGIC REPRESENTATION For every problem must represent in terms of fuzzy sets. What are fuzzy sets? Slowest Fastest Slow Fast [ 0.0 – 0.25 ] [ 0.25 – 0.50 ] [ 0.50 – 0.75 ] [ 0.75 – 1.00 ]
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FUZZY LOGIC REPRESENTATION CONT. Slowest Fastest float speed; get the speed if ((speed >= 0.0)&&(speed < 0.25)) { // speed is slowest } else if ((speed >= 0.25)&&(speed < 0.5)) { // speed is slow } else if ((speed >= 0.5)&&(speed < 0.75)) { // speed is fast } else // speed >= 0.75 && speed < 1.0 { // speed is fastest } Slow Fast
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Terminology: Crisp or Fuzzy Logic Crisp Logic A proposition can be true or false only. Bob is a student (true) Smoking is healthy (false) The degree of truth is 0 or 1 . Fuzzy Logic The degree of truth is between 0 and 1 . William is young (0.3 truth) Ariel is smart (0.9 truth)
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Definition : Fuzzy Sets and Membership Functions If U is a collection of objects denoted generically by x , then a fuzzy set A in U is defined as a set of ordered pairs: ( , ( )) A A x x x U membership function : [0,1] A U U : universe of discourse .
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MF Formulation
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Set-Theoretic Operations A B A B A B A B A A A B A B
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Linguistic Variables Linguistic variable is “a variable whose values are words or sentences in a natural or artificial language”.
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