ai-lect12 - This time Fuzzy Logic and Fuzzy Inference Why...

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1 This time: Fuzzy Logic and Fuzzy Inference Why use fuzzy logic? Tipping example Fuzzy set theory Fuzzy inference
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2 What is fuzzy logic? A super set of Boolean logic Builds upon fuzzy set theory Graded truth.  Truth values between True and False.  Not  everything is  either/or, true/false, black/white, on/off  etc. Grades of membership.  Class of tall men, class of far cities, class  of expensive things, etc. Lotfi Zadeh , UC/Berkely 1965.  Introduced  FL to model  uncertainty in natural language .    Tall, far, nice, large, hot, … Reasoning using linguistic terms .  Natural to express expert  knowledge.  If the weather is  cold  then wear  warm  clothing
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3 Why use fuzzy logic? Pros: Conceptually easy to understand w/ “natural” maths Tolerant of imprecise data Universal approximation: can model arbitrary nonlinear functions Intuitive Based on linguistic terms Convenient  way to express expert and common sense knowledge Cons: Not a cure-all Crisp/precise models can be more efficient and even convenient Other approaches might be formally verified to work
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4 Tipping example The Basic Tipping Problem:  Given a number between 0 and 10  that represents the quality of service at a restaurant what should the  tip be? Cultural footnote: An average tip for a meal in the U.S. is 15%,  which may vary depending on the quality of the service provided.
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5 Tipping example: The non-fuzzy approach Tip = 15% of total bill What about quality of service?
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6 Tipping example: The non-fuzzy approach Tip = linearly proportional to service from 5% to 25% tip = 0.20/10*service+0.05 What about quality of the food?
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7 Tipping example: Extended The Extended Tipping Problem:  Given a number between 0 and  10 that represents the quality of service and the quality of the food at a restaurant, what should the tip be? How will this affect our tipping formula?
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8 Tipping example: The non-fuzzy approach Tip = 0.20/20*(service+food)+0.05 We want service to be more important than food quality.  E.g., 80% for  service and 20% for food.
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9 Tipping example: The non-fuzzy approach Tip =  servRatio*(.2/10*(service)+.05) + servRatio = 80%
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ai-lect12 - This time Fuzzy Logic and Fuzzy Inference Why...

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