Q4) a) List Fuzzy Logic Operations and Explain in Detail.

✅ Fuzzy Set Operations:

Fuzzy logic operations are extensions of classical set operations, applied using membership functions (μ).

---

1. Union (OR Operation)

Combines membership of two sets using maximum value.

Formula:

\mu_{A \cup B}(x) = \max[\mu_A(x), \mu_B(x)]

Example:

μ_A(x)=0.6, μ_B(x)=0.8 ⇒ μ_A∪B(x)=0.8

---

2. Intersection (AND Operation)

Commonality between two sets using minimum value.

Formula:

\mu_{A \cap B}(x) = \min[\mu_A(x), \mu_B(x)]

Example:

μ_A(x)=0.6, μ_B(x)=0.8 ⇒ μ_A∩B(x)=0.6

---

3. Complement (NOT Operation)

Represents non-membership.

Formula:

\mu_{A{\prime}}(x) = 1 - \mu_A(x)

Example:

μ_A(x)=0.7 ⇒ μ_A’(x)=0.3

---

4. Algebraic Sum

Alternative to union.

Formula:

\mu_{A \oplus B}(x) = \mu_A(x) + \mu_B(x) - \mu_A(x) \cdot \mu_B(x)

---

5. Algebraic Product

Alternative to intersection.

Formula:

\mu_{A \cdot B}(x) = \mu_A(x) \cdot \mu_B(x)

---

6. Bounded Sum & Difference

• Bounded Sum:

\mu_{A + B}(x) = \min[1, \mu_A(x) + \mu_B(x)]

• Bounded Difference:

\mu_{A - B}(x) = \max[0, \mu_A(x) - \mu_B(x)]

---

7. Drastic Union & Intersection

• Drastic Union: If either μ=0 → result = other; else = 1

• Drastic Intersection: If either μ=1 → result = other; else = 0

---

📌 Conclusion:

Fuzzy operations help manipulate fuzzy sets in decision-making systems by using min-max or algebraic methods, making them suitable for real-world uncertain environments.