Fuzzy logic  Inference system
Fuzzy logic tutorial
20201120 00:52:48
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 IFTHEN rules.

Database  It defines the membership functions of fuzzy sets used in fuzzy rules.

Decisionmaking 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.
FIS Methods
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 TakagiSugeno (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 TakagiSugeno (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 TakagiSugeno 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.