![FUZZY SET
LET X BE A NON EMPTY SET , A FUZZY SET A IN X IS
CHARACTERIZED
BY ITS MEMBERSHIP FUNCTION 𝜇𝐴: 𝑋 -> [0,1] ,
WHERE 𝜇𝐴(𝑋) IS
THE DEGREE OF MEMBERSHIP OF ELEMENT X IN
FUZZY SET A FOR EACH
x 𝜖 X](https://image.slidesharecdn.com/fuzzylogic-151231085451/85/Fuzzy-logic-7-320.jpg)
Fuzzy logic
- 1. FUZZY LOGIC THIS POWER POINT PRESENTATION IS PRESENTED TO YOU BY KUNAL YADAV IX-B 18
- 2. FOUNDER OF FUZZY LOGIC = LOTFI A. ZADEH
- 3. WHAT IS FUZZY LOGIC • Fuzzy logic is a method of performing conditional logic test based on input that are not "crisp". • Fuzzy logic is based on fuzzy set theory which is a type of set theory developed to deal with sets with the property that objects can be partially obtained in a set. • Fuzzy logic is applicable to AI programming since it's a way to describe the types of conditionals that we would really like to ask in a conditional logic chain.
- 4. FUZZY LOGIC ALLOWS US TO: • Ask general questions and get general or specific answers. • Handle inputs that aren't exactly what we were expecting and do the right thing. • Use very high level rules that ultimately result in either a crisp or fuzzy output.
- 6. FUZZY LOGIC VS BIVALUED LOGIC • BIVALUED LOGIC CAN DE HAVE ONLY 2 POSSIBLE VALUES AS 1/0 , YES / NO , RIGHT / WRONG . • FUZZY LOGIC CAN BE MULTI VALUED . IT CAN HAVE RELATION VALUES LIKE YES , NO , NOT SO MUST , A LITTLE BIT . SEE FIGURE ….
- 7. FUZZY SET LET X BE A NON EMPTY SET , A FUZZY SET A IN X IS CHARACTERIZED BY ITS MEMBERSHIP FUNCTION 𝜇𝐴: 𝑋 -> [0,1] , WHERE 𝜇𝐴(𝑋) IS THE DEGREE OF MEMBERSHIP OF ELEMENT X IN FUZZY SET A FOR EACH x 𝜖 X
- 8. MEMBERSHIP FUNCTION • MAPS ELEMENT OF FUZZY SET TO REAL NUMBERED VALUES IN THE INTERVAL 0 TO 1 . • THE CURVE REPRESENTING THE MATHEMATICAL FUNCTION IS A MEMBERSHIP FUNCTION THAT DETERMINES THE DEGREE OF BELONGING OF MEMBER X TO THE FUZZY SET T .
- 9. FUZZIFICATION • THE PROCESS OF TRANSFORMING CRISP (BIVALUED) INPUT VALUES INTO LINGUISTIC VALUES IS CALLED FUZZIFICATION • STEPS OF FUZZIFICATION : - 1. INPUT VALUES ARE TRANSLATED LINGUISTIC CONCEPTS , WHICH ARE PRESENTED BY FUZZY SET. 2. MEMBERSHIP FUNCTION ARE APPLIED TO THE MEASUREMENT AND THE DEGREE OF MEMBERSHIP IS DETERMINED .
- 10. DEFUZZICATION • IT CONVERT THE FUZZY VALUES INTO CRISP (BIVALUED) VALUE. • EXAMPLES METHODS OF DEFUZZICATION :- 1. MAX MEMBERSHIP METHOD :- THIS METHOD CHOOSES THE ELEMENTS WITH MAXIMUM VALUES . 2. CENTROID METHOD :-THIS METHOD FINDS THE CENTRE POINT OF THE TARGETED FUZZY REGION BY CALCULATED THE WEIGHTED MEAN OF THE OUTPUT FUZZY REGION . 3. WEIGHTED AVERAGE METHOD :- ASSIGNS WEIGHT TO EACH MEMBERSHIP FUNCTION IN THE OUTPUT BY ITS RESPECTIVE MAXIMUM MEMBERSHIP VALUES .
- 11. OPERATIONS ON FUZZY SET • INTERSECTION OF FUZZY SET • THE INTERSECTION OF A & B IS DEFINED AS ( A ∩ B ) (X) = MIN • {AS(X) , B (X) } = A (X) ∩ B (X) , ∀ 𝒙 𝝐 𝑿 , AS DEMONSTRATED IN FIGURE
- 12. UNION OF FUZZY SET THE UNION OF A & B IS DEFINED AS ( A ∪ 𝐵) (X) = MAX { A (X) , B(X) } = A (x) U B (X) , ∀ 𝑥 𝜖 𝑋 , AS DEMONSTRATED IN FIGURE
- 14. APPLYING VALUES