Fuzzy Logic

What I do

• Design fuzzy inference systems
• Implement membership functions
• Create fuzzy rules
• Handle uncertainty and imprecision
• Build expert systems with fuzzy logic
• Control systems with fuzzy rules

When to use me

Use me when:

• Building control systems
• Working with imprecise inputs
• Expert system development
• Pattern recognition with uncertainty
• Decision support with vague criteria

Key Concepts

Fuzzy Logic Basics

Classical: Temperature > 30 → Hot (true/false)
Fuzzy:    Temperature 28 → Hot (0.6), Warm (0.4)

Fuzzy Control Example

import numpy as np
import skfuzzy as fuzz
from skfuzzy import control as ctrl

# Define universes
temperature = ctrl.Antecedent(np.arange(0, 41, 1), 'temperature')
fan_speed = ctrl.Consequent(np.arange(0, 101, 1), 'fan_speed')

# Membership functions
temperature['cold'] = fuzz.trimf(temperature.universe, [0, 0, 20])
temperature['cool'] = fuzz.trimf(temperature.universe, [10, 25, 30])
temperature['hot'] = fuzz.trimf(temperature.universe, [25, 40, 40])

fan_speed['low'] = fuzz.trimf(fan_speed.universe, [0, 0, 50])
fan_speed['medium'] = fuzz.trimf(fan_speed.universe, [25, 50, 75])
fan_speed['high'] = fuzz.trimf(fan_speed.universe, [50, 100, 100])

# Rules
rule1 = ctrl.Rule(temperature['cold'], fan_speed['low'])
rule2 = ctrl.Rule(temperature['cool'], fan_speed['medium'])
rule3 = ctrl.Rule(temperature['hot'], fan_speed['high'])

# Control system
fan_ctrl = ctrl.ControlSystem([rule1, rule2, rule3])
fan_sim = ctrl.ControlSystemSimulation(fan_ctrl)

# Input and compute
fan_sim.input['temperature'] = 28
fan_sim.compute()
print(fan_sim.output['fan_speed'])

Key Concepts

• Membership functions: Triangular, trapezoidal, Gaussian
• Fuzzy operators: AND (min), OR (max), NOT (1-x)
• Defuzzification: Centroid, bisector, MOM
• Inference: Mamdani, Sugeno

Applications

• Control: AC, washing machines, autofocus
• Decision: Credit scoring, medical diagnosis
• Pattern: Image processing, recognition