Match List I with List II
| List I (Operations on Fuzzy Sets) |
List II (Description) |
| A. Intersection |
I. μ̃_A(x) + μ̃_B(x) − μ̃_A(x) · μ̃_B(x) |
| B. Bounded Sum |
II. max(0, μ̃_A(x) − μ̃_B(x)) |
| C. Bounded Difference |
III. min(1, μ̃_A(x) + μ̃_B(x)) |
| D. Algebraic Sum |
IV. min(μ̃_A(x), μ̃_B(x)) |
Choose the correct answer from the options given below:
1.A → III, B → I, C → II, D → IV
2.A → III, B → II, C → IV, D → I
3.A → IV, B → III, C → II, D → I ✓ Correct
4.A → II, B → I, C → III, D → IV
Solution
The correct answer is Option 3) A → IV, B → III, C → II, D → I
Match the operations to their standard fuzzy-set formulas
| List I (Operation) |
List II (Description / Formula) |
Match |
| A. Intersection |
IV. min( μ̃_A(x), μ̃_B(x) ) |
A → IV |
| B. Bounded Sum |
III. min( 1, μ̃_A(x) + μ̃_B(x) ) |
B → III |
| C. Bounded Difference |
II. max( 0, μ̃_A(x) − μ̃_B(x) ) |
C → II |
| D. Algebraic Sum |
I. μ̃_A(x) + μ̃_B(x) − μ̃_A(x) · μ̃_B(x) |
D → I |
Why these matches are correct (easy explanations)
- Intersection (A → IV): In fuzzy logic, the “AND” of two memberships is the smaller of the two at each x. Hence
min( μ̃_A, μ̃_B ).
- Bounded Sum (B → III): Sum the memberships but cap at 1 because membership cannot exceed 1. That is
min(1, μ̃_A + μ̃_B).
- Bounded Difference (C → II): Subtract B from A but never go below 0 since membership cannot be negative. So
max(0, μ̃_A − μ̃_B).
- Algebraic Sum (D → I): Also called the probabilistic OR; it ensures no double counting by subtracting the product:
μ̃_A + μ̃_B − μ̃_A·μ̃_B.
Quick mnemonic
- min → Intersection (take the lesser overlap).
- min(1, sum) → Bounded Sum (sum but bounded by 1).
- max(0, difference) → Bounded Difference (difference but not below 0).
- sum − product → Algebraic Sum (probabilistic OR formula).