Use descriptions for each input variable and 5 desc or output variable. Derive a set of rules for control action and defuzzification. The design should be supported by figure whatever possible, clearly indicate that clothes are to a larger degree, the wash time required will be more.

Solution:

Input variables:

Step 1: Dirt = Small Dirt, Medium Dirt, Large Dirt.

= < SD, MD, LD >

Grease = Small Grease, Medium Grease, Large Grease.

= < SG, MG, LG >

Output variable:

Wash time = Very Small, Small, Medium, Long, Very Large.

= < VS, S, M, L, VL >

Step 2: Membership[ function for each i/p and o/p variable.

Fuzzification:

$M_{Dirt} \ ^{(x)} $ = $M_{SD} \ ^{(x)} = \frac{50 – x}{50} \ 0 \leq x \lt 50$

$M_{MD} \ ^{(x)}$ = $\frac{x}{50} \ 0 \leq x \lt 50$

$\frac{100 – x}{50} \ 50 \leq x \lt 100$

$M_{LD} \ ^{(x)} = \frac{x – 50}{50} \ , 50 \leq x \leq 100$

Grease

$M_{Grease}\ ^{(y)}$ = $M_{SG} \ ^{(y)} = \frac{50 – y}{50} , \ 0 \leq y \lt 50$

$M_{MG} \ (y) = \frac{y}{50} , \ 0 \leq y \lt 50$

$\frac{100 – y}{50}, \ 50 \leq y \lt 100$

$M_{LG} \ (y) = \frac{y – 50}{50} , \ 50 \leq y \leq 100$

For wash time:

$M_{vs} \ ^{(z)} = \frac{10 – z}{10} , \ 0 \leq z \lt 10$

$M_S \ ^{(z)} = \frac{z}{10}, \ 0 \leq z \leq 10$

$\frac{25 – z}{15}, \ 10 \leq z \leq 25$

$M_M \ ^{(z)} = \frac{z – 10}{15}, \ 10 \leq z \leq 25$

$\frac{40 – z}{15}, \ 25 \leq z \lt 40$

$M_L \ ^{(z)} = \frac{z – 25}{15}, \ 25 \leq z \lt 40$

$\frac{60 – z}{20}, \ 40 \leq z \lt 60$

$M_{VL} \ ^{(z)} = \frac{z – 40}{20}, \ 40 \leq z \leq 60$

Step 4: Create Rule Base Table.

Describe the Rule in the form of RY else or RF . . . then

Step 5: Design Inference Engine.

Dirt X = 60%, Y = 70%

$M_{MD} \ ^{(x)} = \frac{40}{50} = \frac{4}{5}$

$M_{LD} \ ^{(x)} = \frac{60 – 50}{50} = \frac{10}{50} = \frac{1}{5}$

$M_{MG} \ ^{(x)} = \frac{100 – 70}{50} = \frac{30}{50} = \frac{3}{5}$

$M_{LG} \ ^{(x)} = \frac{70 – 50}{50} = \frac{20}{50} = \frac{2}{5}$