Simplest Introduction to Fuzzy Logic?


Predicate Logic used for representing human knowledge. But limitation is that, the knowledge should contains statements which are either true or false. It fails to represent knowledge which is uncertain or vague or partially true. Fuzzy Logic is one of the Artificial Intelligence technique, which overcomes the limitation of Predicate Logic. It can represent and reason even if knowledge is uncertain or vague. This article gives brief introduction to Fuzzy Logic, key applications, advantages and its limitations.

Article Content

1. What and Why of Fuzzy Set? [ Back]

Prof. Lotfi A. Zadeh introduced Fuzzy set theory in 1965, to deal with the vagueness and ambiguity in complex systems [2]. Fuzzy is an extension of classical set. Classical sets are mutually exclusive. Means data element can belong to one and only one set. Hence, crisp set can’t be used to solve problems when elements partially belong to more than one set.


Let us take a problem of vehicle speed control. Generally we speak about speed of vehicle as slow, medium or fast. Now let us represent these three speeds using three classical set. We have an Universal set for vehicle speed = {0, 1, .., 120}, and three sets named slow = {0, 1, .., 40}, medium = {41, 42, .., 80} and Fast = {81, 82, .., 120}. Figure-1 shows how to represent these sets diagrammatically . Not a single element of set slow or medium can belong to set Fast, as they are mutually exclusive.

Fuzzy Logic
Figure-1: Crisp Sets Near (Slow), Medium, and Far (High) for Input Variable Speed

But, now just look at a scenario where speed of vehicle is 79 KMH. With our commonsense, can’t we say that speed is between medium to high? Means the data element 79 belongs to both sets medium as well as set fast with some degree. Classical set can’t be used for representing this scenario. But fuzzy set can easily represent this scenario.

Fuzzy Logic
Figure-2: Fuzzy Sets Near (Slow), Medium, and Far (High) for Input Variable Speed

Figure-2: Fuzzy Sets Near (Slow), Medium, and Far (High) for Input Variable Speed


Fuzzy set is defined as a collection of data elements where each element belongs to a set fully or partially with some degree of membership which varies from 0 to 1. In fuzzy sets theory, an element of a set medium may belong to more than one set with some degree of membership, which may vary between 0 and 1, that is it may partially belong to slow and/or fast set. For example as shown in figure-2, data element 40 equally belong to set slow (with 0.5 degree of membership) and similarly, element 85 belong to Medium and fast set.

2. What is Fuzzy Logic? [ Back]

Fuzzy logic is a form of multi-valued logic to deal with reasoning that is approximate rather than exact. One can arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing (incomplete) input information. It has emerged as a profitable tool for the controlling of systems and complex industrial processes. Household equipment, entertainment electronics, diagnosis systems and expert systems are also using Fuzzy Logic.

3. How to Develop Fuzzy System [ Back]

To easily understand how to develop Fuzzy Logic System (FLS), let us take an example of vehicle speed control.

1. Determine fuzzy sets for input and output variables

For speed control system some of the variable are:

input variable = {speed and acceleration}
output variable = {Speed-Control}

Sets for input variable are low, medium, high. Similarly set for acceleration and speed-control. Here we taken three variables but for real time vehicle speed control, more number of variables may be used.

2. Decide fuzzy membership functions and their range for each sets determined in step-1.

Membership functions map crisp value of variable to fuzzy value. Triangular, Trapezoidal, Gaussian, and Bell-Shaped functions are example of different membership functions. Figure-2 shows triangular membership functions for each of the low, medium and high sets.

3. Define rules that maps input variable values to output variable values

Fuzzy rules are defined based understanding the problem. For speed control of a vehicle say car, truck, bus, rules may be defined as follow:

a. If speed is high and acceleration is medium then speed-control medium
b. If speed is low and and acceleration is medium then speed-control low

Such all the possible rules are identified and defined. These rules are used for inference of actual speed-control of vehicle.

4. Use Appropriate Defuzzification Method

Defuzzification methods: Centroid Method, Max-Min, Max Principle, Center of Sums, etc. These methods are used to convert fuzzy control signal into crisp control signal which is actual used to control speed of vehicle.

4. How Fuzzy Inference Works? [ Back]

Fuzzy Logic

Figure-3 : Phases of Fuzzy Inference System

Fuzzy Inference System uses inputs, convert them to fuzzy, fires appropriate rules based on input, aggregates results of fired rules, infers final output variable value and converts the fuzzy output value to crisp value. Fuzzy inference system consist of main three phases given below:


Value of input variable is converted to fuzzy value between 0 to 1. Fuzzy inference process uses this fuzzy values.

Fuzzy Inference:

Fuzzy rules are fired based on actual values of input variables. These rules infer actual quantum of speed control signal based on speed and acceleration.


Actual quantum of speed control signal determined from fuzzy inference is fuzzy value between 0 and 1. The fuzzy value is converted to crisp control signal value.

5. Key Applications of Fuzzy Logic [ Back]

Here we list only few applications in control systems and image processing.

Control Systems

  • Automotive Systems: Anti-lock-Brake System, Four-Wheel Steering Control
  • Consumer Electronic Goods: Photocopiers (Cannon), Video Cameras
  • Domestic Goods: Vacuum Cleaners , Microwave Ovens, Refrigerators, Washing Machines
  • Environment Control: Air Conditioners/Dryers/Heaters , Humidifiers
  • Robot Control: manufacturing, humanoid robot, etc.

Image Processing

  • Medical Imaging:
    • Fuzzy image processing
    • Cancer Detection
    • Tumour Detection
  • Detection and Recognition:
    • Face Recognition
    • Object Detection
    • Surveillance
  • Satellite Image Analysis
  • Town Planning
  • Crop Analysis and Estimation

6. Advantages & Limitations of Fuzzy Logic [ Back]

Advantages of Fuzzy Logic

  • Mathematical concepts within fuzzy reasoning are very simple.
  • One can modify a FLS by just adding or deleting rules due to flexibility of fuzzy logic.
  • Fuzzy logic Systems can take imprecise, distorted, noisy input information.
  • Fuzzy logic is a solution to complex problems in all fields of life, including medicine.
  • Fuzzy reasoning resembles human reasoning and decision making.

Limitations of Fuzzy Logic

  • They are suitable for the problems which require 100% precision.
  • Should not use for hard real-time systems
  • Precise problems may result in higher cost of solution.


  1. T. Ross. Fuzzy Logic with Engineering Applications. Wiley, India, 2nd Edition, 2005.
  2. G. Klir and K. Yuan. Fuzzy Sets and Fuzzy Logic. PHI, New Delhi, 2002.
  3. R. Krisnapuram J. C. Bezdek, J. Keller and N. R. Pal. Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Springer, 2005.