Fuzzy logic is a form of multi-valued logic that allows reasoning with degrees of truth rather than just true (1) or false (0).
Thank you for reading this post, don't forget to subscribe!- Unlike classical Boolean logic, which operates in a binary manner (yes/no, true/false), fuzzy logic enables handling uncertainty, vagueness, and imprecision in decision-making processes.
Example:
In Boolean logic:
- Temperature ≥ 30°C → “Hot” (True)
- Temperature < 30°C → “Not Hot” (False)
In Fuzzy Logic:
- Temperature = 28°C → “Hot” (0.7), “Warm” (0.3)
This approach makes fuzzy logic useful in real-world applications like control systems, decision-making, and artificial intelligence.
Fuzzy Sets:
A fuzzy set is a mathematical representation of a concept where elements belong to a set with varying degrees of membership (not just fully included or excluded).
Classical (Crisp) vs. Fuzzy Sets:
Crisp Set (Boolean logic):
- An element either belongs (1) or does not belong (0) to the set.
- Example: A set of “Tall People” where height ≥ 180 cm → Tall (1), height < 180 cm → Not Tall (0).
Fuzzy Set (Fuzzy logic):
- Elements belong with a membership degree between 0 and 1.
- Example: A set of “Tall People” where height 170 cm → 0.5, height 180 cm → 0.8, height 190 cm → 1.0.
Example of a Fuzzy Set Representation:
Membership in Fuzzy Sets:
A membership function (MF) assigns a degree of membership (between 0 and 1) to each element in a fuzzy set.
Types of Membership Functions:
- Triangular: Defines membership using a triangular shape.
- Trapezoidal: Uses a trapezoidal shape for smoother transitions.
- Gaussian: Uses a bell curve to define membership.
Example: Membership Function for “Warm Temperature”
If temperature (T) is defined in degrees Celsius:
- Below 15°C → Membership = 0 (Not warm)
- At 20°C → Membership = 0.3 (Slightly warm)
- At 25°C → Membership = 0.7 (Moderately warm)
- At 30°C or above → Membership = 1 (Fully warm)
This allows gradual decision-making rather than binary classification.
Fuzzy Rule-Based Systems:
A fuzzy rule-based system uses fuzzy IF-THEN rules to make decisions based on vague or imprecise inputs. These systems are commonly used in control systems, AI, and expert systems.
Structure of a Fuzzy Rule-Based System:
- Fuzzification: Converts crisp inputs into fuzzy values (e.g., temperature = “warm”).
- Rule Evaluation: Applies fuzzy IF-THEN rules (e.g., “If temperature is warm, set fan speed to medium”).
- Aggregation & Inference: Combines multiple fuzzy rules to get a fuzzy output.
- Defuzzification: Converts fuzzy output into a crisp value (e.g., fan speed = 50%).
Example: Temperature Control System
- Rule 1: If temperature is cold, then heater is set to high.
- Rule 2: If temperature is warm, then heater is set to medium.
- Rule 3: If temperature is hot, then heater is set to off.
Example Applications of Fuzzy Logic:
- Home Automation: Smart thermostats use fuzzy logic to adjust temperature smoothly.
- AI & Expert Systems: Fuzzy logic is used in natural language processing and medical diagnosis.
- Control Systems: Used in washing machines, elevators, and air conditioners for adaptive control.
- Decision Support: Stock market analysis, risk assessment, and business intelligence.