Fuzzy inference

the fuzzy logic is very important for any automated or intelligent system.we are training the system with the help of fuzzy logic and fuzzy system so that it can behave and think like human beings. so, in this slide fuzzy inference system has been explained with some numerial problem.

1. BIRLA INSTITUE OF TECHNOLOGY PRESENATION OF SOFT COMPUTING ON FUZZY INFERENCE BY , SWATI SINGH MT/EE/10015/19

2. Contents INRODUCTION PREDICATE LOGIC INFERRING IN FUZZY LOGIC FUZZY LOGIC INFERENCE SOME EXAMPLES ON GMT AND GMP PRACTICAL EXAMPLES CONCLUSION

3. Introduction Fuzzy inference: From a set of fuzzy rules we can infer some other fuzzy rules. Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. There are three types of fuzzy inference system that can be implemented in fuzzy logic tool box: Mamdani-type , Sugeno-type and The Standard Additive Model (SAM). Application of fuzzy inference system (FIS) coupled with Mamdani's method in modeling and optimization of process parameters for biotreatment of real textile wastewater. A fuzzy logic-based diagnosis system was developed to optimize the process parameters for the decolourization of a real textile wastewater .

4. Predicate logic Predicate logic is a two valued logic. Either it is one or zero, True or false. There are some rules with the help of that rule we can infer some other set of rules. Some operations on predicate calculus are: Modus Ponens: P , P Q then, Q It states that if P is the first rule , and P implies Q is the second, then we can infer that the third rule to be Q. Modus Tonens: P Q , NOT Q are the two rules then we can infer that NOT Q is the third rule Chain rule : P Q , Q R are the two rules then, we can infer that P R ( P implies R is the third rule ).

5. Inferring in fuzzy logic Generalized Modus Ponens ( GMP): If x is A ,then y is B …….1 st rule x is A………………………….2 nd rule Then, we can infer that y is B as the 3 rd rule. Generalized Modus Tollens ( GMT): If x is A ,then y is B …….1 st rule y is B………………………….2 nd rule Then, we can infer that x is A as the 3 rd rule. where A, A, B, B are fuzzy sets on the universe of x and y.

6. Fuzzy inferring procedure A, A, B, B are fuzzy sets on the universe of x and y. To compute the membership function of A and B the max- min composition of fuzzy sets A and B, respectively with R(x , y) , where R is the implication relation used .

7. SOME EXAMPLES EXAMPLE OF GMP: P : if x is A , then y is B Where, A = {(x1,0.6),(x2,0.9),(x3,0.7)} We have to derive the conclusion in the form y is B SOL: AXB = AXY =

8. EXAMPLE OF GMT : Assume that a proposition if x is A and y is B is given where, A= {(x1, 0.5), (x2, 1), (x3, 0.6)}, B = {(y1, 1),(y2, 0.4)} And second proposition as y is B is given by, B= {(y1, 0.9), (y2, 0.7)} So, we have to conclude that x is A . Now ,

9. Practical example Apply the fuzzy GMP rule to deduce rotation is quite slow. Given that , If temp is high then rotation is slow Temperature is very high Let, X= {30,40,50,60,70,80,90,100} be the set of temperature. Y ={10,20,30,40,50,60} be the set of rotations per minute. The fuzzy set High (H), Very high (VH), Slow (S) and Quiet Slow (QS) H= {(70,1),(80,1),(90,0.3)} VH = {(80,0.6),(90,0.9),(100,1)} S = {(30,0.8),(40,1),(50,0.6)} QS = {(10,1),(20,0.8),(30,0.5 )}

10. Now, we can solve for if temp is high then rotation is slow R= (H X S) U (H X Y) For temp is very high : To deduce rotation is ‘quite slow’ we make use of QS = VH 0 R (x , y) H X S = H X Y =

11. R = (H X S) U (H X Y) = Q = VH X R (x , y) = [0.6 0.9 1] Q = [ 0.8 0.9 0.7] Hence we derive QS = {(10,0.8),(20,0.9),(30,0.7)}

12. Conclusion We can the steps of fuzzy logic as , firstly forms a rule base with the help of linguistic language. We do the fuzzification of the inputs, by the help of the fuzzified inputs, and the rule base , we infer some of the rules which we wanted. And we analyzed the output of the system. The procedure of doing fuzzy inference is been explained in the slides.

13. THANK YOU