Fuzzy Logic Evaluator

Synopsis

This project implements a tool written in * Python 3 * that allows the user to:

• Define a diffuse inference system:   - Define the input and output variables, with their respective linguistic values ​​and membership functions   - Define the rules of inference   - Specify the method to be used   - Define the step size to be used in the discretization of the values ​​of the output variables
• Use the defined inference system, to obtain the values ​​of the output variables for different data sets

Input

The program is executed by means of the command:

python main.py <data> .json <rules> .fuz [--step <step_size>]

<data> .json: file in JSON format with the specifications of the input variables and their respective values, as well as the membership functions. An example of a variable and a function would be:

{
  "variables": {
    "input1": 5.3
  }
  "functions": {
    "membership_func1": [
      "Trapezoid", 10, 15, 20, 25
    ]
  }
}

As can be deduced from the example, the functions are specified by a list, whose first element is the type of the function and the rest are the parameters that characterize its behavior; the latter being specific to each type. The types of supported functions are:

• Trapezoid:   - a: Point where the monotony of the function becomes increasing, therefore f (a) == 0. If a == null it is assumed that for any x <= a it is fulfilled that f (x) == 1.   - b: Minor (greater if a == null) value of x for which f (x) == 1.   - c: Greater value of x for which f (x) == 1, if there is no such x finite, then c == null. If a == null, then it is the smallest value of x for which f (x) == 0.   - d: Point where the monotony stops being decreasing. If it does not exist, or a == null, then c == null.
• Triangle: Particular case of trapezoid, with three parameters a, b and c representing the x of its 3 vertices.
• Sigmoid:   - k: Sigmoid width   - x0: Central value
• Gaussian:   - b: Center of the bell   - c: Bell width

<rules> .fuz: file with the specification of the rules and the inference model; Follow the following format:

[model] (Mamdani | Sugeno | Tsukamoto)
[t-norm] (min | product)
[t-conorm] (max | sum)
([defuzzy] (Centroid | Bisecter | Mean_max))?

input1 is val1 or input2 is val2 then output1 is val3

All variables defined to the left of the then must have an associated value in the data file (.json). It also has to happen with the linguistic values used in the rules. In the case of using the model * Sugeno *, the value of the right part of the then will be an arithmetic expression that can use numerical values and input variables. The operators allowed in this case are +, -,*,/and**(power).

In the t-norm and t-conorm fields the operations to evaluate the expressions and and or respectively will be indicated.

Output

The program reports the result of evaluating the specified system. The calculated values for each of the output variables are reported by the standard output, following the format: output1: # .000 \ n