- The fuzzy logic toolbox does not directly support fuzzy multisets as a seperate data structure or class, and does not provide any built in functionality to create or operate fuzzy multisets.
- However, it is possible to simulate the creation of fuzzy multisets and various operations on them using the already available fuzzy set functionalities.
- Here is an example for the same.
% Define the universe of discourse
universe = (0:1:10);
% Define fuzzy sets
fuzzySet1 = trapmf(universe, [1, 3, 6, 8]);
fuzzySet2 = gaussmf(universe, [5, 2]);
fuzzySet3 = trimf(universe, [3, 6, 9]);
% Define fuzzy membership values for each element
membershipValues1 = [0.8, 0.4, 0.6, 0.2, 0.1, 0.0, 0.3, 0.7, 0.9, 0.5, 0.2];
membershipValues2 = [0.1, 0.3, 0.6, 0.8, 0.9, 1.0, 0.7, 0.4, 0.2, 0.5, 0.8];
In this example, we define fuzzy sets using various membership functions such as trapmf, gaussmf, and trimf for the universe of discourse. Also, we can define the membership values of each element as arrays membershipValues1 and membershipValues2.
- Perform the operations that simulate the multiset operations.
unionSet = max(membershipValues1, membershipValues2);
intersectionSet = min(membershipValues1, membershipValues2);
complementSet = 1 - membershipValues1;
differenceSet = max(membershipValues1 - membershipValues2, 0);
- Display the results which are similar to fuzzy multiset operations, using the disp function.
