Fuzzy Logic; Genetic Algorithms

Fuzzy Logic

What is Fuzzy Logic?

"Fuzzy" = vague, not clear, imprecise — real-world characteristics.

Classical (crisp) logic: operates with binary values — True (1) or False (0).

Real life problem: Statements are often neither completely true nor false:

• "This person is tall" — how tall is tall?
• "It is quite hot today" — how hot?
• "The car is moving fast" — how fast?

Fuzzy Logic: allows truth values to be any value between 0 and 1, representing degrees of truth.

Fuzzy vs Classical Logic

Fuzzy Membership Functions

Membership
Degree
  1.0  |   /\          /\
       |  /  \        /  \
  0.5  | /    \      /    \
       |/      \    /      \
  0.0  +--------\--/--------\-----> Temperature
       COLD      WARM        HOT

Each value belongs to multiple fuzzy sets with different degrees.

Fuzzy Logic System

Crisp Input --> Fuzzification --> Fuzzy Inference --> Defuzzification --> Crisp Output
    (e.g., temperature = 35 C)     (Apply rules)         (Convert back)  (e.g., fan speed = 70%)

Use Cases of Fuzzy Logic in AI

1. Engineering decisions with uncertainty / imprecise data (e.g., NLP — "large file", "recent")
2. Regulating and controlling machine outputs with multiple inputs (e.g., temperature control systems)

Additional Applications:

• Air conditioner temperature control
• Washing machine cycle selection (water/dirt level fuzzy)
• Anti-lock Braking System (ABS)
• Camera auto-focus

Medical diagnosis systems

Fuzzy Logic vs Neural Networks

Genetic Algorithms

What are Genetic Algorithms?

Genetic Algorithms (GAs) are search and optimization techniques inspired by natural evolution — specifically Darwin's theory of natural selection.

They are part of Evolutionary Computing — a branch of AI. GAs are effective for:

Complex optimization problems

• Problems where the search space is large
• Problems where traditional methods are too slow

Biological Analogy

Genetic Algorithm Workflow

Step 1: INITIALIZATION
  Create a random initial population of solutions
  Population: [10110010, 01101100, 11001011, 00111010, ...]

Step 2: EVALUATION
  Calculate fitness of each individual (how good is this solution?)
Fitness: [0.82, 0.45, 0.91, 0.33, ...]

Step 3: SELECTION
  Select better-fit individuals for reproduction
  (Methods: Tournament,
Roulette Wheel, Rank-based)

Step 4: CROSSOVER (Recombination)
  Combine two parents to create offspring
  Parent 1: 1 1
0 1 | 0 0 1 0
  Parent 2: 0 1 1 0 | 1 1 0 1
  Child:    1 1 0 1 | 1 1 0 1  (crossover at
position 4)

Step 5: MUTATION
  Randomly flip some bits (small probability)
  Before: 1 1 0 1 1 1 0 1
After:  1 1 0 1 0 1 0 1  (bit 5 flipped)

Step 6: REPLACEMENT
  Replace old population with the new generation

Step 7: TERMINATION
  If best solution found OR max generations reached -> STOP
  Else -> Go to Step 2

Applications of Genetic Algorithms