6. FUZZY INFERENCES IFK15037, 3 credits. YUITA ARUM SARI, S.Kom, M.Kom

6. FUZZY INFERENCES IFK15037, 3 credits

YUITA ARUM SARI, S.Kom, M.Kom [email protected] 1

HISTORY In 1965, Lo,i A. Zadeh of the University of California at Berkeley published "Fuzzy Sets," which laid out the mathemaJcs of fuzzy set theory and, by extension, fuzzy logic. Zadeh had observed that convenJonal computer logic could not manipulate data that represented subjecJve or vague ideas, so he created fuzzy logic to allow computers to determine the disJncJons Professor LoKi A. Zadeh among data with shades of gray, similar to hNp://www.cs.berkeley.edu/~zadeh/ the process of human reasoning. Yuita Arum Sari, S.Kom, M.Kom

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Example of ApplicaPons •  In the city of Sendai in Japan, a 16-staJon subway system is controlled by a fuzzy computer (Seiji Yasunobu and Soji Miyamoto of Hitachi) – the ride is so smooth, riders do not need to hold straps •  Nissan – fuzzy automaJc transmission, fuzzy anJ-skid braking system •  CSK, Hitachi – Hand-wriJng RecogniJon •  Sony - Hand-printed character recogniJon •  Ricoh, Hitachi – Voice recogniJon •  Tokyo’s stock market has had at least one stock-trading porKolio based on Fuzzy Logic that outperformed the Nikkei exchange average •  NASA has studied fuzzy control for automated space docking: simulaJons show that a fuzzy control system can greatly reduce fuel consumpJon •  Canon developed an auto-focusing camera that uses a charge-coupled device (CCD) to measure the clarity of the image in six regions of its field of view and use the informaJon provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot. Massey University

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IntroducPon of FIS ● A Fuzzy Inference System (FIS) is a way of mapping an input space to an output space using fuzzy logic ● FIS uses a collecJon of fuzzy membership funcJons and rules, instead of Boolean logic. ● The rules in FIS (someJmes may be called as fuzzy expert system) are fuzzy producJon rules of the form: − if p then q, where p and q are fuzzy statements. ● For example, in a fuzzy rule − if x is low and y is high then z is medium. − Here x is low; y is high; z is medium are fuzzy statements; x and y are input variables; z is an output variable, low, high, and medium are fuzzy sets. Indian InsPtute of Technology Delhi

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IntroducPon of FIS (cont.) ● The antecedent describes to what degree the rule applies, while the conclusion assigns a fuzzy funcJon to each of one or more output variables. ● Most tools for working with fuzzy expert systems allow more than one conclusion per rule. ● The set of rules in a fuzzy expert system is known as knowledge base.

Indian InsPtute of Technology Delhi

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Structure of Fuzzy Expert Systems

Knowledge Base

FuzzificaPon

Crisp value

DefuzzficaPon

Crisp value

Inference Engine

Rinaldi Munir STEI ITB

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FuncPonal Process INPUT

FuzzyficaPon

Crisp value à fuzzy membership funcJon

Fuzzy Logic OperaPon

Antecedent may be joined by OR; AND operators

ImplicaPon AgregaPon DefuzzyficaPon OUTPUT Rinaldi Munir STEI ITB

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FuzzyficaPon Fuzzyfikasi : proses memetakan nilai crisp (numerik) ke dalam himpunan fuzzy dan menentukan derajat keanggotaannya di dalam himpunan fuzzy. Hal ini dilakukan karena data diproses berdasarkan teori himpunan fuzzy sehingga data yang bukan dalam bentuk fuzzy harus diubah ke dalam bentuk fuzzy. Rinaldi Munir STEI ITB

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Example : FuzzyficaPon

Rinaldi Munir STEI ITB

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Example : FuzzyficaPon

Sumber: Sri Kusuma Dewi/Aplikasi Logika Fu7zzy

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Fuzzy Membership FuncPon Types of Membership FuncJons • The most commonly used in pracJce are – Triangles – Trapezoids – Bell curves – Gaussian, and – Sigmoidal

Fuzzy Logic with Engineering ApplicaJons: Timothy J. Ross

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Fuzzy Membership FuncPon

Fuzzy Logic with Engineering ApplicaJons: Timothy J. Ross

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Fuzzy Logic:Intelligence, Control, and InformaJon, J. Yen and R. Langari, PrenJceHall

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Fuzzy Logic OperaPon Jika bagian antesenden dihubungkan oleh konektor and, or, dan not, maka derajat kebenarannya dihitung dengan operasi fuzzy yang bersesuaian


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ImplicaPon


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ImplicaPon

Wikipedia

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ImplicaPon


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AggregaPon

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AggregaPon

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AggregaPon

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AggregaPon

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AggregaPon

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AggregaPon

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AggregaPon

Mathworks

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DefuzzyficaPon

Mathworks

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DefuzzyficaPon •  Strategi yang umum dipakai dalam defuzzifikasi adalah menentukan bentuk kompromi terbaik. •  Metode-metode untuk strategi ini adalah: 1.  Metode keanggotaan maximum (max-membership) 2.  Metode pusat luas (Center of Area, CoA). 3.  Metode keanggotaan maksimum rata-rata (Mean- max Membership atau Middle-of-Maxima)

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DefuzzyficaPon

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DefuzzyficaPon

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DefuzzyficaPon

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Thank Yuita Arum Sari, S.Kom, M.Kom

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6. FUZZY INFERENCES IFK15037, 3 credits. YUITA ARUM SARI, S.Kom, M.Kom

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