Fuzzy Logic | Introduction

The term fuzzy refers to things that are not clear or are vague. In the real world many times we encounter a situation when we can’t determine whether the state is true or false, their fuzzy logic provides very valuable flexibility for reasoning. In this way, we can consider the inaccuracies and uncertainties of any situation. 

Fuzzy Logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, instead of just the traditional values of true or false. It is used to deal with imprecise or uncertain information and is a mathematical method for representing vagueness and uncertainty in decision-making.

Fuzzy Logic is based on the idea that in many cases, the concept of true or false is too restrictive, and that there are many shades of gray in between. It allows for partial truths, where a statement can be partially true or false, rather than fully true or false.

Fuzzy Logic is used in a wide range of applications, such as control systems, image processing, natural language processing, medical diagnosis, and artificial intelligence.

The fundamental concept of Fuzzy Logic is the membership function, which defines the degree of membership of an input value to a certain set or category. The membership function is a mapping from an input value to a membership degree between 0 and 1, where 0 represents non-membership and 1 represents full membership.

Fuzzy Logic is implemented using Fuzzy Rules, which are if-then statements that express the relationship between input variables and output variables in a fuzzy way. The output of a Fuzzy Logic system is a fuzzy set, which is a set of membership degrees for each possible output value.

In summary, Fuzzy Logic is a mathematical method for representing vagueness and uncertainty in decision-making, it allows for partial truths, and it is used in a wide range of applications. It is based on the concept of membership function and the implementation is done using Fuzzy rules.

In the boolean system truth value, 1.0 represents the absolute truth value and 0.0 represents the absolute false value. But in the fuzzy system, there is no logic for the absolute truth and absolute false value. But in fuzzy logic, there is an intermediate value too present which is partially true and partially false. 

ARCHITECTURE 

Its Architecture contains four parts :

• RULE BASE: It contains the set of rules and the IF-THEN conditions provided by the experts to govern the decision-making system, on the basis of linguistic information. Recent developments in fuzzy theory offer several effective methods for the design and tuning of fuzzy controllers. Most of these developments reduce the number of fuzzy rules.
• FUZZIFICATION: It is used to convert inputs i.e. crisp numbers into fuzzy sets. Crisp inputs are basically the exact inputs measured by sensors and passed into the control system for processing, such as temperature, pressure, rpm’s, etc.
• INFERENCE ENGINE: It determines the matching degree of the current fuzzy input with respect to each rule and decides which rules are to be fired according to the input field. Next, the fired rules are combined to form the control actions.
• DEFUZZIFICATION: It is used to convert the fuzzy sets obtained by the inference engine into a crisp value. There are several defuzzification methods available and the best-suited one is used with a specific expert system to reduce the error.

Membership function

Definition: A graph that defines how each point in the input space is mapped to membership value between 0 and 1. Input space is often referred to as the universe of discourse or universal set (u), which contains all the possible elements of concern in each particular application. 

There are largely three types of fuzzifiers:  

• Singleton fuzzifier
• Gaussian fuzzifier
• Trapezoidal or triangular fuzzifier

What is Fuzzy Control? 

• It is a technique to embody human-like thinkings into a control system.
• It may not be designed to give accurate reasoning but it is designed to give acceptable reasoning.
• It can emulate human deductive thinking, that is, the process people use to infer conclusions from what they know.
• Any uncertainties can be easily dealt with the help of fuzzy logic.

Advantages of Fuzzy Logic System 

• This system can work with any type of inputs whether it is imprecise, distorted or noisy input information.
• The construction of Fuzzy Logic Systems is easy and understandable.
• Fuzzy logic comes with mathematical concepts of set theory and the reasoning of that is quite simple.
• It provides a very efficient solution to complex problems in all fields of life as it resembles human reasoning and decision-making.
• The algorithms can be described with little data, so little memory is required.

Disadvantages of Fuzzy Logic Systems 

• Many researchers proposed different ways to solve a given problem through fuzzy logic which leads to ambiguity. There is no systematic approach to solve a given problem through fuzzy logic.
• Proof of its characteristics is difficult or impossible in most cases because every time we do not get a mathematical description of our approach.
• As fuzzy logic works on precise as well as imprecise data so most of the time accuracy is compromised.

Application 

• It is used in the aerospace field for altitude control of spacecraft and satellites.
• It has been used in the automotive system for speed control, traffic control.
• It is used for decision-making support systems and personal evaluation in the large company business.
• It has application in the chemical industry for controlling the pH, drying, chemical distillation process.
• Fuzzy logic is used in Natural language processing and various intensive applications in Artificial Intelligence.
• Fuzzy logic is extensively used in modern control systems such as expert systems.
• Fuzzy Logic is used with Neural Networks as it mimics how a person would make decisions, only much faster. It is done by Aggregation of data and changing it into more meaningful data by forming partial truths as Fuzzy sets.

Fuzzy Logic | Set 2 (Classical and Fuzzy Sets)