The document presents a comprehensive overview of fuzzy inference systems, including the introduction of fuzzy logic, types of fuzzy inference systems (Mamdani-type, Sugeno-type, and the standard additive model), and their applications in optimizing process parameters for textile wastewater treatment. It further explains predicate logic, generalized modus ponens, and generalized modus tollens, along with practical examples illustrating the application of these principles in fuzzy inference. The conclusion emphasizes the step-by-step process of fuzzy logic, starting from rule formation to output analysis.

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 …….1st rule
x is A………………………….2nd rule
Then, we can infer that y is B as the 3rd rule.
 Generalized Modus Tollens ( GMT):
If x is A ,then y is B …….1st rule
y is B………………………….2nd rule
Then, we can infer that x is A as the 3rd 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 =

9.  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 ,

11. PRACTICAL EXAMPLE
 Apply the fuzzy GMP rule to deduce rotation is quite slow.
 Given that ,
1. If temp is high then rotation is slow
2. 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)}

12.  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 =

13.  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)}

14. 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.

15. THANK YOU