How to create complex 'or', 'and' and 'not' operations in fuzzy inference rules

I have a mamdani type 1 system, I want to create two rules

if (a or b) and c then d

if not ((a or b) and c) then e

However, in the fuzzy logic designer the options are use only 'and's or 'or's as connection without the ability to combine them

Answer 1

[Shubham]

Hi Raul,

In Fuzzy Logic Designer, you can implement the desired logic by creating additional variables or breaking the rules into simpler components. Here's how you can achieve this:

Step-by-Step Instructions:

1. Create a Fuzzy Inference System (FIS):

• Open MATLAB and type fuzzy in the command window to launch the Fuzzy Logic Designer.
• Create a new FIS (Mamdani type).

2. Define Input Variables:

• Add input variables a, b, and c.
• Define the membership functions for each input variable according to your system requirements.

3. Define Output Variables:

• Add output variables d and e.
• Define the membership functions for each output variable.

4. Create Intermediate Variable:

• Since you cannot directly combine and and or, create an intermediate output variable x to represent (a or b).
• Define membership functions for x as necessary.

5. Define Rules:

• Intermediate Rules for x:
• Rule 1: If a is high, then x is high.
• Rule 2: If b is high, then x is high.
• Main Rules:
• Rule 3: If x is high and c is high, then d is high.
• Rule 4: If x is not high or c is not high, then e is high.

6. Configure the Rules:

• In the Fuzzy Logic Designer, go to the "Rules" tab.
• Add the rules as described above, using the rule editor to specify the logic.

7. Simulate and Test:

• Use the "View" options to simulate and test your fuzzy logic system.
• Adjust membership functions and rules as needed to achieve the desired behavior.

You can refer to this documentation: https://in.mathworks.com/help/fuzzy/get-started-using-fuzzy-logic-designer.html

Answer 2

[Divyajyoti Nayak]

Hi Raul,

I understand that you want to create complex rules for your Fuzzy Logic System but MATLAB does not support the use of both ‘AND’ and ‘OR’ connections together for the creation of rules in Fuzzy Systems. To make rules that fulfil the given conditions, please make separate rules using only ‘AND’ or ‘OR’ conditions.

I am assuming ‘a’, ‘b’ and ‘c’ are three inputs that can be true or false, and ‘d’ and ‘e’ are the two member functions of the output. The rules for the conditions would look something like this:

%(a OR b) AND c then d
rule1 = "a == true & c == true => output = d";
rule2 = "b == true & c == true => output = d";

%not((a OR b) AND c) then e
rule3 = "a == false & b == false => output = e";
rule4 = "c == false => output = e"

Here's the documentation for adding rules in the 'Fuzzy Logic Designer' app:

https://www.mathworks.com/help/fuzzy/building-systems-with-fuzzy-logic-toolbox-software.html#mw_306b93a6-b253-463f-99c4-84ad90f12d1b

Hope this helps!