Fuzzy logic - Inference system
Fuzzy logic tutorial
Fuzzy logic - System of inference
The fuzzy inference system is the key unit of a fuzzy logic system having a decision to do as his main job. It uses the “IF… THEN” rules as well as the “OR” or “AND” connectors to draw the essential decision rules.
Characteristics of the fuzzy inference system
Here are some characteristics of the FIS -
The output of FIS is always a fuzzy set regardless of its input which may be fuzzy or sharp.
It is necessary to have fuzzy output when used as a controller.
A defuzzification unit would be there with FIS to convert fuzzy variables into precise variables.
FIS functional blocks
The following five functional blocks will help you understand the construction of the FIS -
Rule base - EIt contains fuzzy IF-THEN rules.
Database - It defines the membership functions of fuzzy sets used in fuzzy rules.
Decision-making unit - It performs rule operations.
Fuzzification UI Unit - It converts qu antities to fuzzy quantities.
Defuzzification interface unit - It converts fuzzy quantities to precise quantities. Here is a block diagram of the fuzzy interference system.
Operation of FIS
Operation of FIS consists of the following steps -
A fuzzification unit supports the application of many fuzzification methods, and converts net input to fuzzy input.
A knowledge base - the collection of rule base anddatabase is formed when converting a clean entry to a fuzzy entry.
The fuzzy input from the defuzzification unit is eventually converted to a clean output.
Now let's talk about the different FIS methods. Here are the two important methods of FIS, having different consequences of fuzzy rules -
- Mamdani 's fuzzy inference system
- Fuzzy model Takagi-Sugeno (TS method)
Mamdani fuzzy inference system
This system was proposed in 1975 by Ebhasim Mamdani. Basically, it was intended to control a combination of steam engine and boiler by synthesizing a set of fuzzy rules obtained from the people working on the system.
Steps for calculating the output
The following steps are needed to calculate the output of this FIS -
Step 1 -The set of fuzzy rules should be determined in this step.
Step 2 - In this step, using the input membership function, the input would be blurred.
Step 3 - Now establish rule strength by combining fuzzy inputs into fuzzy rules.
Step 4 - In this step, determine the consequence of the rule by combining the strength of the rule and the membership function as output .
Step 5 - To get the output distribution, combine all the consequents.
Step 6 - Finally, a defuzzified output distribution is obtained.
Here is a block diagram of Mamdani Fuzzy System Interface.
Fuzzy model Takagi-Sugeno (TS method)
This model was proposed by Takagi, Sugeno and Kang in 1985. The format of this rule isst given as -
IF x is A and y is B THEN Z = f (x, y)
Here, AB are fuzzy sets in the antecedents and z = f (x, y) is a neat function in the consequent.
Fuzzy inference process
The fuzzy inference process under the Takagi-Sugeno fuzzy model (TS method) works in the following way -
Step 1: Input fuzzification - Here the system inputs are blurred.
Step 2: Apply the fuzzy operator - In this step, the fuzzy operators need to be applied to get the output.
Rule format of the form Sugeno
The rule format of the form Sugeno is given by -
if 7 = x and 9 = y then the output is z = ax + by + c
Comparison between the two methods
Now let's understand the comparison between the syMamdani steme and the Sugeno model.
Output membership function - The main difference between them is on the basis of membership function Release. The Sugeno output membership functions are either linear or constant.
Aggregation and defuzzification procedure - The difference between them is also in the consequence of fuzzy rules and due to the same thing, their aggregation and defuzzification procedure also differs.
Mathematical rules - There are more mathematical rules for Sugeno's rule than for Mamdani's rule.
Adjustable parameters - The Sugeno controller has more adjustable parameters than the Mamdani controller.