What is Fuzzy Logic? What are its features and applications?

By | October 25, 2021
What is Fuzzy Logic

Generally, we refer to the term ‘fuzzy’ as not clear or vague. Humans are more intelligent than computers and can make use of reasoning to tackle vague situations. For example, consider that the weather is neither too cold nor less cold, and is something between them both. Therefore, humans can tell what exactly the weather is, like too cold, a little cold, cannot determine, or less cold.

But for this situation, computers with a conventional logic block can either generate too cold or less cold as their output. They do not know intermediate possibilities, and to overcome this limitation, fuzzy logic comes into play. Fuzzy Logic offers flexibility for reasoning. More precisely, it is a reasoning approach that resembles human reasoning.

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This article will help you understand what fuzzy logic is, its key characteristics, and why you need to use fuzzy logic. Later, we will make you aware of the architecture of fuzzy logic, membership function, and the difference between a classical and a fuzzy set. Finally, this article will throw light on the applications and the pros and cons of fuzzy logic. So, without further ado, let us get started.

What is Fuzzy Logic?

Fuzzy logic is a reasoning approach that works similarly to the way humans think and make decisions. It is a computing technique that considers all possible intermediate values between Yes and No, like Certainly Yes, Possibly Yes, Cannot Determine, Possibly No, and Certainly No.

Unlike the boolean logic that only works on only two inputs, Fuzzy logic considers multiple input values, ranging between two boolean values, 0 and 1, and produces a definite and acceptable output. In boolean logic, 1 denotes absolute true, whereas 0 denotes absolute false.

Lofti Zadeh, in 1965, introduced Fuzzy logic based on the Fuzzy Set Theory. He found that conventional computer logic was not able to handle data that represents subjective human ideas. Therefore, he introduced fuzzy logic, enabling computers or systems that can take such human ideas.

To understand more about Fuzzy logic, let us look at a simple example. Consider that a system has to produce an output for a sentence ‘Is it hot water?’.

The boolean logic involves only two inputs: Yes/1 or No/0. On the other hand, fuzzy logic involves three input values: Very Much/0.9, Little/0.25, and Very Less/0.1.

Therefore, fuzzy logic considers all available data before coming to a conclusion for any problem and makes the best possible decision. The implementation of fuzzy logic is supported in large network-based systems, microcontrollers, and workstation-based systems. Moreover, you can implement fuzzy logic in hardware, software, or a combination of both.

Features of Fuzzy Logic

Here are some significant features of fuzzy logic that you should know:

  1. Fuzzy logic helps imitate the human thinking process to generate the best possible output from the available input values.
  2. It is the most suitable approach to determine a solution to issues that involve contradictory and uncertain conditions.
  3. Fuzzy logic is easy to comprehend and implement.
  4. It supports developing non-linear functions of arbitrary complexities.
  5. Data Analysts use Fuzzy Logic to improve an algorithm’s execution.

Why use Fuzzy Logic?

Below are the three reasons why fuzzy logic is used in commercial applications:

  1. Fuzzy logic assists us in dealing with the uncertain and contradictory conditions in engineering.
  2. Though it does not provide accurate reasoning, it offers acceptable and relevant reasoning.
  3. Fuzzy logic controls machines and consumer products.

The Fuzzy Logic System Architecture

There are four components in the fuzzy logic system, as explained below:

1. Rule Base

Experts define rules and if-then conditions to implement fuzzy logic in systems. Rule base stores all these rules and if-then conditions.

2. Fuzzification Module

This component transforms system inputs, i.e., crisp numbers, into fuzzy sets. The Fuzzification Module divides an input signal into five different states, as listed below:

  • LP: X is a Large Positive.
  • MP: X is a Medium Positive.
  • S: X is Small.
  • MN: X is a Medium Negative.
  • LN: X is a Large Negative.

3. Inference Engine

The inference engine is responsible for determining the degree of match between rules defined by experts and the current Fuzzy input. Depending upon the matching degree, the system determines the rule to be implemented according to the given Fuzzy input value. Later, it develops control actions, which is a combination of all the implemented or applied rules.

4. Defuzzification

Finally, the defuzzification process transforms fuzzy sets into crisp numbers, which are acceptable by users. Numerous techniques for converting fuzzy sets into crisp numbers are available. Therefore, it is important to choose the best suitable technique.

Membership Function in Fuzzy Logic

The membership function enables us to represent fuzzy sets in terms of a graph. It is also referred to as an indicator or characteristic function. For every element present in the fuzzy set, its value is mapped to the value ranging between 0 and 1.

For the fuzzy set A, the membership function for X is given as:

μA: X → [0,1].

Every element of set X is mapped to a value between 0 and 1. It is known as membership value or a degree of membership.

Classical Set vs Fuzzy Set Theory

The below table shows some major differences between a classical set or crisp set and a fuzzy set.

Classical Set Fuzzy Set
A set consisting of distinct objects is called a classical set. For example, a set of days in a week. A set consisting of degrees of membership between 0 and 1 is called a fuzzy set. For example, a set of young people.
Classical sets have precise and certain boundaries. Fuzzy sets have vague or ambiguous boundaries.
An individual entity in a classical set is referred to as an element or a member of that set. Any element is either a member of a set or not, and it does not support partial membership. When a member of one fuzzy set is also the part of another fuzzy set, the partial membership exists.
Classical sets are based on bi-valued logic. Fuzzy sets are based on infinite-valued logic.
It is used extensively in designing digital systems. It is used in fuzzy controllers.

Applications of Fuzzy Logic

Below are some crucial applications of Fuzzy logic:

  • The aerospace industry uses fuzzy logic to control the altitude of satellites and spacecraft.
  • In automotive systems, fuzzy logic helps in controlling speed and traffic.
  • Large organizations use fuzzy logic for personal evaluation and decision-making support systems.
  • In chemical industries, fuzzy logic helps in managing the distillation process and controlling the ph.
  • It is widely used in artificial intelligence applications and natural language processing (NLP).
  • Smart air conditioners, humidifiers, and heaters also make use of Fuzzy logic.
  • In the finance sector, fuzzy logic is used to predict the stock market and manage the funds.

Pros and Cons of Fuzzy Logic

Pros

  • Algorithms in fuzzy logic can be described using fewer data, which does not require large memory.
  • The structure of fuzzy logic is so simple that anyone can understand it quickly.
  • Numerous sectors of life use fuzzy logic to provide effective solutions to complex problems.
  • The fuzzy logic system supports noisy, distorted, and imprecise input data.
  • Anyone can add or delete rules defined in fuzzy logic. Hence, it is more flexible.
  • Though it does not require precise inputs, it produces acceptable and definite results.

Cons

  • Fuzzy logic is ideal for only those problems that do not require accurate results.
  • It cannot identify neural network types and machine learning patterns.
  • The fuzzy logic system takes a long time to generate outputs.
  • Fuzzy logic systems are entirely dependent on human expertise and knowledge.
  • The challenging task in fuzzy logic is setting precise membership functions and fuzzy rules.
  • Verification and validation of fuzzy logic systems require a lot of testing.

Conclusion

Fuzzy logic helps systems or machines to think similarly to humans and make decisions accordingly. It has wide applications in numerous industries, and it is also one of the easiest machine learning techniques. However, designing a fuzzy logic system requires guidance from experts a solid understanding of how fuzzy logic works.

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