This repository contains an implementation of a Fuzzy Inference System (FIS), a framework that emulates human reasoning by mapping inputs to outputs using fuzzy logic. The system comprises four main components: a knowledge base, fuzzification module, inference engine, and defuzzification module.
A Fuzzy Inference System is designed to model complex systems by applying a set of fuzzy rules to input data, resulting in outputs that can handle uncertainty and imprecision. This approach is widely used in control systems, decision-making, and pattern recognition.
- Fuzzification: Converts crisp input values into degrees of membership across various fuzzy sets using different membership functions.
- Fuzzy Operations: Supports fundamental operations such as union and intersection on fuzzy sets.
- Inference Engine: Applies a set of fuzzy rules to the fuzzified inputs to derive fuzzy outputs.
- Defuzzification: Transforms the fuzzy outputs into crisp values for practical use.
This component assigns the input variables different degrees of membership in the different classes. For this, the input values are mapped to values from 0 to 1 using a set of membership functions.
The membership functions implemented in our system were:
- Triangular function
- Trapezoidal function
- S function
Each of the membership functions was implemented in membership.py, where each function is a class that receives each of the previously exposed variables as a parameter. They are then evaluated for each of the points other than x.
The three basic operations of fuzzy sets were defined:
- Union
- Intersection
- Complement
Each of this operations is implemented in operators.py
The inference mechanisms relate the input and output fuzzy sets, and represent the rules that define the system. The inputs to this component are fuzzy sets (degrees of membership) and the outputs are also fuzzy sets, associated with the output variable. For the implementation of this inference system, 2 aggregation methods were implemented. For the creation of the system, it receives as input the name of one of these methods
- Mamdani Method
- Larsen Method
These methods are implemented in aggregation.pyas classes that receive the set of rules to analyze, as well as the domain and precision with which the different values of the output fuzzy set are analyzed.
In this stage, the opposite function of the diffuser is performed. The input it receives is the output fuzzy set, the result of the inference stage, and the output is a specific value of the output variable. To obtain, from the output fuzzy set resulting from the aggregation of all the rules, a scalar result, mathematical methods are applied. These algorithms were implemented in defuzzification.py. Here is a summary of them:
- Mean of Maximum (MOM)
- Left of Maximum (LOM)
- Right of Maximum (ROM)
- Median of Maximum (MMOM)
- Centroid of Area (COA)
- Bisector of Area (BOA)
The chosen problem to analyze and validate the proposed system is an autofocus system. To run this example, simply run the file sample.py, where the values of the input variables, the aggregation method to use and the defuzzification method will be requested.
The chosen problem to analyze and validate the proposed system is an autofocus system.
To run this example, simply run the file sample.py, where the values of the input variables, the aggregation method to use and the defuzzification method will be requested.