Intelligent Systems II · M2 · mocks

Q4 · Fuzzy defuzzification [3]

M2 mock 3 · 10 marks

Q1(a)+Q1(b) compulsory; any two of Q2–Q4. Answers immediately below each question.

Confirmed M2 pattern: Q1(a) [2] and Q1(b) [2] are compulsory. Attempt any two of Q2, Q3 and Q4, each worth 3 marks. The paper offers 13 marks; you attempt 10. These are newly written practice questions, not claims about the exact upcoming paper. Solutions are directly below each question; the teaching working is deliberately longer than a concise exam answer.

Q4. Using the weighted-average method, combine output representatives [20, 50, 80] % with respective strengths [0.2, 0.6, 0.2]. [3 marks · Practice]

Given

Output representativeStrength
200.2
500.6
800.2

To find

One crisp output by the specified weighted-average method.

Formula and why it applies

Each representative is multiplied by its strength; add these products and divide by the total strength. Here α is a strength and z is a representative value. These are not automatically the full area of a clipped Mamdani set.

z^*=\frac{\sum_i\alpha_i z_i}{\sum_i\alpha_i}LaTeX: z^*=\frac{\sum_i\alpha_i z_i}{\sum_i\alpha_i}

Solution

Step 1. Multiply each value by its strength
Strength × valueProduct
0.2 × 204
0.6 × 5030
0.2 × 8016
Step 2. Add the products
4+30+16=50LaTeX: 4+30+16=50
Step 3. Add the strengths
0.2+0.6+0.2=1LaTeX: 0.2+0.6+0.2=1
Step 4. Divide
z^*=\frac{50}{1}=50LaTeX: z^*=\frac{50}{1}=50
Final answer. 50 %.