The theory of fuzzy sets was proposed in 1965 by Professor Lotfi Asgarzadeh, an Iranian scientist and professor at Berkeley University in the United States. The word fuzzy in the Oxford Dictionary is defined vaguely, vaguely, and inaccurately. Using this model is suitable for when the data is vague, uncertain, and inaccurate.
Fuzzy theory includes four steps of fuzzy construction, fuzzy law database, fuzzy inference engine, and non-fuzzy construction.
Comparison of fuzzy and logical logic by Professor Lotfi zadeh:
Classic logic is like a person in a black formal dress, white blouse, black tie, shiny shoes, etc. coming to a formal party, and fuzzy logic is somewhat similar to a person in a formal dress, pants, T-shirt, and shoes. Cloth has come to the same party. This dress was not accepted in the past, but today it is different.
Definition of fuzzy systems and their types
The word fuzzy is vaguely defined in the Oxford Dictionary. If we want to define the theory of fuzzy sets, we must say that it is a theory to act in conditions of uncertainty; This theory is able to mathematically formulate many concepts, variables, and systems that are inaccurate and provide the basis for reasoning, inference, control, and decision-making in conditions of uncertainty.
Why fuzzy systems?
Our real-world is too complex to come up with an accurate description; Therefore, for a model, an approximate or fuzzy description must be introduced that is acceptable and analyzable.
As we move towards the information age, human knowledge becomes very important. We, therefore, need a hypothesis that can systematically formulate human knowledge and incorporate it, along with other mathematical models, into engineering systems.
What are fuzzy systems like?
Fuzzy systems are systems based on knowledge or rules; The heart of a fuzzy system is a knowledge base made up of fuzzy if-then rules.
An if-then fuzzy rule is an if-then expression whose words are defined by continuous belonging functions.
If the car speed is high, then apply less force to the accelerator pedal.
The words “high” and “low” are denoted by belonging functions;
Suppose we want to design controllers that control the speed of the car automatically. The solution is to simulate drivers’ behavior; This means turning the rules that the driver uses while driving into an automatic controller.
In colloquial speech, drivers naturally use the following three rules while driving:
If the speed is low, then apply more force to the accelerator pedal.
If the speed is medium, then apply a balanced force to the accelerator pedal.
If the speed is high, then apply less force to the accelerator pedal.
In short, the starting point for building a fuzzy system is to obtain a set of if-then-fuzzy rules from the knowledge of experts or the field; The next step is to combine these rules into a single system.
Types of fuzzy systems
Mamdani fuzzy systems
Takagi-Sugnokang Fuzzy Systems (TSK)
Mamdani fuzzy system
The fuzzy inference engine combines these rules into a mapping from fuzzy sets in the input space to fuzzy sets in the output space based on the principles of fuzzy logic.
The main problem with Mamdani fuzzy systems is that their inputs and outputs are fuzzy sets. In engineering systems, inputs and outputs are variables with real values.
To solve this problem, Takagi Sugeno has introduced another type of fuzzy system whose inputs and outputs are variables with real values.
Takagi-Sugo fuzzy system
Thus the fuzzy rule has become a simple relation from a descriptive expression to linguistic values; For example, in the case of a car, it can be stated that if the speed of the car is X, then the force on the accelerator pedal is equal to Y = CX.
The main problems of TSK fuzzy system are:
The “then” section is the rule of a mathematical formula and therefore does not provide a framework for the representation of human knowledge.
This system does not leave us free to apply the various principles of fuzzy logic, and as a result, there is no flexibility of fuzzy systems in this structure.
To solve these problems, the third type of fuzzy system was used, namely a fuzzy system with fuzzy generators and non-fuzzy generators.
Educational video headlines : (zero to one hundred)
History of fuzzy systems
Where did the fuzzy logical idea start?
What is human reasoning?
The concept of degree and truth table
What does fuzzy logic do?
The concept of rules in fuzzy
Explanation of fuzzy system block diagram
The difference between crisp value and fuzzy value
Description fuzzy inference system (FIS)
A complete description of an example of a fuzzy system
Concept of fuzzy set
Example of a fuzzy set
The difference between classical set and fuzzy set
Reasoning in fuzzy logic
Boolean binary logic
The concept of membership function
Two-tier membership function
Online membership function
Input Interpretation that has several membership functions
Types of MATLAB membership functions
Triangular and trapezoidal membership function and Gaussian and Sigmoid
Input parameters of membership functions
AND and OR and NOT fuzzy
Fuzzy truth table
How are fuzzy rules determined?
The concept of antecedent and consequent
An example block diagram of a fuzzy system
Applications of fuzzy logic
Description of the fuzzy inference system
MATLAB programming of fuzzy systems type 1
A simple example
Steps of designing a fuzzy system
Input change interval
Fuzzy system design through GUI
Types of fuzzy systems
Mamdani and Takagi Sugno
Set up incoming membership functions in MATLAB
Explain the membership functions definition window
Manually set up membership functions
The parametric setting of membership functions
Assign names to inputs and outputs
Adjust the range of range changes
Naming membership functions
Definition of rules
Concept of connection in rule
The concept of not in the rule
The concept of weight in rule
Surface observation in the fuzzy system
Set X input and Y input
Graphical view of a rule in MATLAB
Save a fuzzy system
The fis extension in MATLAB
Open a stored fuzzy system
A variety of other membership functions in the fuzzy system
Three-dimensional surface view
Three-dimensional surface adjustment
Manually change fis file
Add a membership function to the input in the fis file
Explain a fis file line by line
Set the rule as numbers
Build a fuzzy system in MATLAB through coding
Manual definition of rules
Apply input to the fuzzy system
Coding MATLAB membership functions