Q3) c) Define and Explain Classical (Crisp) Set and Fuzzy Set.

📌 1. Classical (Crisp) Set:

A crisp set is a collection of elements where each element either fully belongs (membership = 1) or does not belong (membership = 0) to the set.

Characteristics:

• Sharp boundaries

• Binary membership: either 0 or 1

• No partial membership

• Based on Boolean logic

Example:

Let Set A = {x | x ≥ 18} → If x = 20, then μ_A(x) = 1; if x = 16, μ_A(x) = 0

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📌 2. Fuzzy Set:

A fuzzy set allows partial membership of elements with values between 0 and 1, representing the degree of belonging.

Characteristics:

• Vague boundaries

• Graded membership values

• Models real-world imprecision

• Based on fuzzy logic

Example:

Let Set B = “Young People”

If age = 16 → μ_B = 0.8, age = 25 → μ_B = 0.4

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📊 Comparison Table:

Aspect	Crisp Set	Fuzzy Set
Membership	0 or 1	0 to 1
Boundaries	Sharp	Gradual
Logic	Boolean	Fuzzy
Real-life Suitability	Limited	Better for vague concepts
Example	Adult (Yes/No)	Degree of adulthood

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✅ Conclusion:

Crisp sets are ideal for clear-cut classification, while fuzzy sets handle vagueness and partial truths, making them more suitable for real-life problems in AI and soft computing.