Esmat Rashedi Graduate university of advanced technology Kerman

کﻨﺘﺮﻝ ﻓﺎﺯی Esmat Rashedi Graduate university of advanced technology, Kerman, Iran 1

ﺗﺎﺭﻳﺨچﻪ l l In 1965, Lotfi Zadeh published his famous paper “Fuzzy sets”. In 1973, Lotfi Zadeh published his second most influential paper about fuzzy rules. 3

ﻣﺠﻤﻮﻋﻪ ﻫﺎی ﻓﺎﺯی • • • Classic sets Fuzzy sets Types of fuzzy sets Classic set operators (and, or, not) Fuzzy set operators 5

Crisp and fuzzy sets of “tall men”

Defining fuzzy sets for each variable 24

ﺍﺟﺘﻤﺎﻉ ﻓﺎﺯی l Fuzzy union (fuzzy Or) [ A OR B = AÙB = MAX A(x), B(x) ] A B(x) = max [ A(x), B(x)] = A(x) B(x), 27

ﺍﺷﺘﺮﺍک ﻓﺎﺯی l Fuzzy intersection (fuzzy And) [ A and B = A∩B = Min A(x), B(x) ] A B(x) = min [ A(x), B(x)] = A(x) B(x) 28

ﻣکﻤﻞ ﻓﺎﺯی l Fuzzy complement (fuzzy Not) Not A= 1 - A(x) = 1 A(x) 29

Operations of fuzzy sets

Operations of fuzzy sets

ﻗﻮﺍﻧﻴﻦ ﻓﺎﺯی • • IF-then rules Antecedent and consequent Classic rules Fuzzy Rules 32

ﻗﻮﺍﻧﻴﻦ کﻼﺳﻴک . ﻗﺴﻤﺖ ﻣﻘﺪﻡ ﻓﺎﺯی ﻧﻴﺴﺖ ، ﺩﺭ ﻗﻮﺍﻧﻴﻦ کﻼﺳﻴک IF x is a THEN l y is B Rule: 1 IF speed is > 100 THEN stopping_distance is long Rule: 2 IF speed is < 40 THEN stopping_distance is short 34

ﻗﻮﺍﻧﻴﻦ ﻓﺎﺯی . ﻗﺴﻤﺖ ﻣﻘﺪﻡ ﻓﺎﺯی ﺍﺳﺖ ، ﺩﺭ ﻗﻮﺍﻧﻴﻦ ﻓﺎﺯی IF x is A THEN l y is B Rule: 1 IF speed is fast THEN stopping_distance is long Rule: 2 IF speed is slow THEN stopping_distance is short 35

Fuzzy sets of tall and heavy men These fuzzy sets provide the basis for a weight estimation model. The model is based on a relationship between a man’s height and his weight: IF height is tall THEN weight is heavy

ﻗﺴﻤﺖ ﺍگﺮ : ﻗﻮﺍﻧﻴﻦ ﻓﺎﺯی A fuzzy rule can have multiple antecedents, for example: IF AND THEN project_duration is long project_staffing is large project_funding is inadequate risk is high IF service is excellent OR food is delicious THEN tip is generous

ﻣﻨﻄﻖ ﻓﺎﺯی • • AND, OR, NOT Crisp logical functions: o o o AND true is both parameters are true OR true if either parameter is true NOT reverses truth of argument 42

کﻨﺘﺮﻟﺮ ﻣﻨﻄﻖ ﻓﺎﺯی • • Fuzzy logic Controller (FLC) Examples 43

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ﻣﺮﺍﺣﻞ ﺍﺳﺘﻨﺘﺎﺝ ﻓﺎﺯی l l l Fuzzification Fuzzy matching Fuzzy Inference (Implication) Combination (aggregation) Defuzzification (optional) ﻓﺎﺯی کﺮﺩﻥ ﺍﻧﻄﺒﺎﻕ ﻓﺎﺯی ﺍﺳﺘﻨﺘﺎﺝ ﻓﺎﺯی ﺗﺮکﻴﺐ * ﻓﺎﺯی ﺯﺩﺍﻳی l l l 47

ﻣﺮﺍﺣﻞ ﺍﺳﺘﻨﺘﺎﺝ ﻓﺎﺯی l l l Fuzzification Fuzzy matching : Calculation of degree of match for each rule. Fuzzy Inference (Implication) : Inference from each rule. Two methods of ‘clipping’ and ‘scaling’. Combination (aggregation) : Combination of the resultants. Defuzzification (optional) : Two methods of ‘MOM’ and ‘COA’. 48

Inference 52

Defuzzification 53

Defuzzification 54

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ﻗﻮﺍﻧﻴﻦ ﻓﺎﺯی : 1 ﻣﺜﺎﻝ l If (service is poor) or (food is rancid) then (tip is cheap) (1) l If (service is good) then (tip is average) (1) l If (service is excellent) or (food is delicious) then (tip is generous) (1) 63

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Matlab l l l Fuzzy my. FIS=readfis(‘designed. Fis. fis’); Out=evalfis([0. 2 0. 3] , my. FIS); 74