The image you uploaded contains two questions regarding fuzzy sets and operations on them. Let's break them down step by step.

Q.01:

Two fuzzy sets $\tilde{G}$ and $\tilde{H}$ are given:

• $\tilde{G} = \{(A,1), (B,0.65), (C,0.5), (D,0.35), (E,0)\}$
• $\tilde{H} = \{(A,0), (B,0.35), (C,0.5), (D,0.65), (E,0)\}$

Calculations:

The operations here involve:

• $\cup$: union
• $\cap$: intersection
• $\bar{G}$: complement of $G$
• $\bar{H}$: complement of $H$
• $\oplus$: maximum or t-conorm (sum-based combination)
• $\odot$: minimum or t-norm (product-based combination)

For each operation, you compare the membership values of corresponding elements in $\tilde{G}$ and $\tilde{H}$.

Q.02:

Two fuzzy sets $\tilde{M}$ and $\tilde{N}$ with a universal set $U = \{1, 2, 3, 4, 5, 6\}$ are given:

• $\tilde{M} = \{(1,0.3), (2,0.1), (3,0), (4,0.9), (5,0.1)\}$
• $\tilde{N} = \{(1,0), (2,0.6), (3,0.5), (4,0), (6,0.45)\}$

Calculations:

Again, operations like union, intersection, complement, and specific t-norm or t-conorm calculations need to be performed for each pair of fuzzy sets.

Would you like to go over the step-by-step solution for each of the operations (e.g., union, intersection, complement, etc.)?

Let me know if you have any questions! Here are some related topics to explore:

1. What is the difference between fuzzy set union and intersection?
2. How are fuzzy set complements calculated?
3. What are t-norms and t-conorms in fuzzy logic?
4. How does the universal set affect fuzzy set operations?
5. What are the practical applications of fuzzy set operations?

Tip:

Fuzzy set operations rely heavily on max-min logic rather than traditional binary operations, so pay close attention to how membership values are combined based on the type of operation.