# An Overview Of Fuzzy Logic

## A Brief History of Fuzzy Logic

The issues of uncertainty, imprecision and vagueness have been on the discussion for many years. These issues form the primary topics in philosophical circles bringing many debates specifically in regard to the nature of vagueness and ability of the Boolean logic coping with perceptions and concepts that seem vague or inaccurate. Fuzzy logic is considered as bypass-valued logics. It has a close similarity with Fuzzy set theory and it’s applied in the fuzzy systems. The origin of fuzzy logics dates back to the Greek philosophers precisely in the era of Plato (428-347 B.C). Fuzzy logic seems plausible to trace its origin in India and china. It is because the Indians and Chinese were the first people to understand that all things are needed to be of a specific type or quit, however, the perception faced a stopover. The two groups are the pioneers of the notion that there are variations in the degree of truth or false. Recent theorems indicate that fuzzy systems can be used in modelling any continuous system which is based on artificial intelligence, physics, economics, or any other science. The researchers have found that fuzzy commonsense models are important and also they are accurate than the standard mathematical models.

## Overview of Fuzzy Logic Theory

Fuzzy set theory was discovered by Prof. Lofti Zadeh in 1965. The theory denotes that there are set rules and regulations which give a definition of boundaries. These rules give a guide to successful problem-solving. Fuzzy logic is built on a set of user-supplied rules of human language. Fuzzy systems basically translate these rules to the mathematical equivalents. The conversion generally simplifies the work of the system designer, the computer and the outcome becomes more precise in regard to the way the system behaves in the real world. Fuzzy logic is usually simple and flexible, therefore, it can be used to handle problems with imprecise and data that is not complete. Fuzzy logic can make nonlinear functions of arbitrary complexity. Fuzzy logic indicates that the truth of any statement is a matter of degree. Fuzzy inference systems rely on membership functions when giving commands to the computer on how to find the correct value between 0 & 1. The degree of precision of a statement is doted by numbers between 0 and 1. According to fuzzy set operations, the membership function of the union of two fuzzy sets A &B which have the membership functions and is maximum of two respective membership functions.

## Applications of Fuzzy Logic in Control Systems

Control systems are common in our everyday life. The systems that are controllable basically have three key features: inputs, outputs and control parameters which are used in perturbing the system into a desirable state. The system undergoes monitoring in some fashion and it’s then left at the desired mode or else it is perturbed with control actions that ensure the desired state is achieved. A control system has an arrangement of hardware components that are designed in a way that it can alter, regulate, and command through a control action another system so that it can give the desired behaviour. The control systems are basically classified into two categories; open loop control system and closed loop control system. The open-loop control system includes the toaster, where the amount of heat needed is set by the operator and automatic washing machine which controls the temperature of the water and the spinning cycle. These attributes are also set by the machine user. Examples of closed loop control system include room temperature thermostat which uses the room temperature to set itself and activates a cooling or heating unit when a specific threshold is reached.

Another example of application is autopilot mechanism which gives an automatic course correction to the aircraft when there is an altitude deviation from the preset values. Anti-lock braking systems An antilock braking system is a safety system which protects the wheels of a vehicle from locking up. ABS basically minimizes the break distance while the ability of steer is restrained even during hard braking. The absence of Fuzzy in ABS would cause wheels to block within a very short period of driving. The result is unstable characteristics, the vehicle cannot be steered anymore and the distance of stopping increase. The primary objective of ABS is the reduction of braking distance while steerability is retained regardless of the nature of braking. The coefficient of friction is considered as a function of the wheel slip. At the start of uncontrolled full braking, the point begins at s=0 and then it increases to a point s=s (max). After this point, the wheels lock within a few milliseconds due to the declining characteristics coefficient which is the positive feedback. At this time the force of the wheel is constant at the low level of sliding friction. A fast and precise control system is needed to keep the vehicle wheels within the coefficient of friction (shaded area). Sensors and Actuators are the components of the antilock braking system that use Fuzzy logic in the implementation of ABS. Fuzzy ABS controller activated ensures that the steer has the ability not only on restrained breaking manoeuvre but also during slowing down length is shortened.

## Discussion on the Future of Fuzzy Logic

The article written by Charles Elkan indicates that the foundation of fuzzy logic is the perception of partial truth and the degree of truth in the sense that the proposition that state about the real world object. Generally, the propositions may be uncertain, ambiguous or sometimes incomplete. The propositions are goal oriented, intentional or sometimes they can be subjective to the observer perpetual ability, mental constructs and the meaning of the system. Fuzzy logic is a theory of human understanding and cognition. The subjectivity of fuzzy modelling is a blessing today. The variables used in fuzzy theory have the meaning as represented in each corresponding membership functions which are compatible and consistent to the rules that bring the required objective. Fuzzy logic has brought mechanism that gives room for sharing, communicating and transfer of wealth of individual technical expertise into the computer. Fuzzy logic with the assistance of probability theory will give other powerful tool/gadgets for coping with the complexity and nonlinearity in the systems of the new world. Fuzzy logic will also furnish the answers that are never precise and certain, but acceptable within a given constraint of real-time, energy resources and memory.

09 March 2021

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