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What Is Fuzzy Logic?

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1
Introduction

Electric cars are becoming quite popular nowadays with the continuous increase on fuel prices. These cars not only economical, they are also better for environment, they do not emit carbon dioxide. It is an accepted worldwide fact that in our near future, we will be seeing a lot more of these cars. 1.1 What Is Fuzzy Logic?

Fuzzy Logic: | a form of mathematical logic in which truth can assume a continuum of values between 0 and 1. | | Princeton Web Dictionary

Fuzzy logic is a form of logic with more than two values. Formally it can be called as probabilistic logic and it simply deals with approximated values rather than exact ones; as in daily language, it includes grays along with black and white. It is also accepted as a problem solving control system methodology.
Fuzzy logic is a type of logic that recognizes more than only true and false values. With fuzzy logic, variables can be represented with degrees of truthfulness and falsehood. As an example ‘today is sunny’ statement can be used; this statement, might be 100% true if there are absolutely no clouds, 80% true if there are a few clouds, 50% true if it's partly cloudy and 0% true if it rains all day.
Advantages of fuzzy logic can be listed as: * Fuzzy logic is easy to understand. * Fuzzy logic is flexible. * Fuzzy logic is based on natural language. * Fuzzy logic can model nonlinear functions of arbitrary complexity.
Advantages of fuzzy logic continued: * Fuzzy logic is tolerant of imprecise data. * Fuzzy logic can be blended with conventional control techniques. * Fuzzy logic can be built on top of the experience of experts. * Fuzzy logic does not solve new problems. It uses new methods to solve everyday problems. * Mathematical concepts within fuzzy reasoning are very simple.

1.2 What Is A Membership Function?

Membership Function : | The characteristic function of a fuzzy set, which assigns to each element in a universal set a value between 0 and 1. | | McGraw-Hill Science & Technology Dictionary

“A fuzzy set A in X is characterized by a membership function fA(x) which associates with each point in X a real number in the interval [0,1], with the values of fA(x) at x representing the "grade of membership" of x in A. Thus, the nearer the value of fA(x) to unity, the higher the grade of membership of x in A.” From Fuzzy Sets, by Lofti A. Zadeh
A membership function is the representation of the trueness level of a statement in fuzzy logic. Or by another definition, membership function is a generalized form of the values in a fuzzy set as a function.
Some commonly used membership functions are listed as: * S-shaped built-in membership function * Triangular-shaped built-in membership function * Trapezoidal-shaped built-in membership function * Built-in membership function composed of difference between two sigmoidal membership functions
Some commonly used membership functions continued: * Z-shaped built-in membership function * Generalized bell-shaped built-in membership function * Π-shaped built-in membership function * Built-in membership function composed of product of two sigmoidally shaped membership functions * Gaussian curve built-in membership function * Gaussian combination membership function * Sigmoidally shaped built-in membership function

Fuzzy Inference System: | The overall name for a system that uses fuzzy reasoning to map an input space to an output space | | Mathworks.com
1.3 What Is Fuzzy Inference System?

Fuzzy inference system is a method for mapping input and output variables and rules that shape them. These rules are formed by membership functions, logical operations and if-then rules. Fuzzy inference systems are used for data classification, expert systems and decision analysis. Membership function is a generalized form of the values in a fuzzy set as a function. Logical operations are two or more statements connected with a logical operator in order to get a new statement. This new statement is shaped by the initial statements. If-then rules are conditional statements with two parts. In order to complete the second part (then), first part (if) must be satisfied.

Figure 1: Fuzzy Inference System Block Diagram

1.4 General View
With the main concepts of fuzzy logic is being introduced, now it is relevant to mention about the aim and objectives of this project.
With the increasing demand on electric cars, new stations to satisfy their need for electricity will be built after a while just like gas stations were built when cars became widespread.
Today every driver knows by heart that when the gas station will be busy and when not. With the idea that the same observations will be valid for the electric stations, I am going to create a fuzzy inference system. This fuzzy inference system will be about hybrid car charging stations and their busyness levels.
The aim of the project is creating a fuzzy inference system about electric stations. Learning fuzzy inference systems and using fuzzy logic toolbox on Matlab can be listed as objectives.

2
Literature Review

Fuzzy logic is not an old concept like algebra; it is newly developed as a concept. This does not mean that we were not using fuzzy logic. Fuzzy logic was in our daily lives for a very long time; we were using it even when we wanted to describe someone. For example when you describe someone as fat, there is a satisfactory degree for the person for the statement. The person may be obese or only have a few pounds more. Fuzzy logic is introduced here, describing the fatness level or the trueness level of the statement by a degree.
2.1 Introducing Fuzzy Logic
Lotfi A. Zadeh, a well-known mathematician, electrical engineer, computer scientist, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley. Fuzzy logic was first introduced by Zadeh in his paper "Fuzzy Sets" in 1965.
While Zadeh and other mathematicians were continuing to develop fuzzy logic; the idea of fuzzy sets and fuzzy logic were not accepted well within academic circles because some of the underlying mathematics had not yet been explored.
The applications of fuzzy logic were slow to develop because of this, except in the east. In Japan specifically fuzzy logic was fully accepted and implemented in products simply because fuzzy logic worked, regardless of whether mathematicians agreed or not. The success of many fuzzy logic based products in Japan in the early 80s led to a revival in fuzzy logic in the US in the late 80s. Since that time America has been playing catch up with the east in the area of fuzzy logic. Some of the objections that faced fuzzy logic in its early days are shown below. Note that Professor William Kahan is Lofti Zadeh colleague at UC Berkely. Most objections to fuzzy logic have since faded due to the success of fuzzy applications.
Zadeh, in his theory of fuzzy sets, proposed using a membership function (with a range covering the interval [0,1]) operating on the domain of all possible values. He proposed new operations for the calculus of logic and showed that fuzzy logic was a generalisation of classical and Boolean logic. He also proposed fuzzy numbers as a special case of fuzzy sets, as well as the corresponding rules for consistent mathematical operations (fuzzy arithmetic).[11]

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