Fuzzy

logic systems are generally used for system identification, control, and model

recognition problems. To maximize performance, it is often necessary to perform

a project optimization procedure in which the variable parameters of the Fuzzy

systems are tuned to maximize a given performance condition. Some imminent data

are commonly available and produce what is termed a supervised learning

problem. In this regard, we generally want to minimize the sum of error squares

in data approximation.

Fuzzy

logic begins with and builds on a set of human-language rules provided by the

user. The fuzzy system changes these rules to their mathematical equivalents.

This simplifies the work of the system designer and the computer and translates

into a much more accurate representation of how systems behave in the real

world. The additional benefits of fuzzy logic are its simplicity and

flexibility. Fuzzy logic can handle problems with inaccurate and incomplete

data and can model non-linear functions of random complexity. “If you do

not have a good implant model or if the system is changing, then diffusion will

produce a better solution than conventional control techniques,” says Bob

Varley. We can generate a fuzzy system to match any set of input and output

data. Fuzzy Logic Toolbox makes it particularly easy to provide adaptive

techniques such as neuro-diffuse adaptive inference systems (ANFIS) and diffuse

subtractive clustering.

Fuzzy logic models, called fuzzy inference

systems, consist of a series of “if-then” conditional rules. . For

the designer who understands the system, we can easily write these rules and

you can provide all the rules that are essential for correctly explaining the

system (although generally only a moderate number of rules are required). The

rule-based approach and the flexible membership plan not only simplifies the

creation of fuzzy systems, but also simplifies system design and ensures that

the system can be updated and maintained over time. It is recognized that the prepositional

logic is isomorphic to establish the theory under the association between the

components of these two mathematical systems. Furthermore, both systems are

isomorphic to a Boolean algebra, which is a mathematical system defined by

abstract entities and their axiomatic properties.

The isomorphism between Boolean algebra, set

theory and propositional logic ensures that each theorem in one of these

theories has a counterpart in each of the other two theories. These isomorphism

allow us, in effect, to involve all these theories by scaling only one. We will

not spend much time reviewing the clear logic, but at some point we have to

spend, especially in the concept of commitment, to achieve the concept in fuzzy

logic. Fuzzy rules are the cornerstone of fuzzy logic systems. . Rules are a

form of proposition. A proposition is an ordinary statement that implies, for

example, “The ratio of the buffer is low”. Therefore, we can have the

following rule: “If the damping is low, the impulse response of the system

oscillates long before it goes out”. In traditional propositional logic, a

proposition must be meaningful to call it “true” or

“false”, regardless of whether we know which of these terms applies

correctly.

Logical

reasoning is the process of combining the propositions given in other

propositions, and then doing it repeatedly. The proposition can be combined in

many ways, deriving from three fundamental operations: the conjunction

(indicated by p?q),

where the simultaneous truth of two separate sentences peq is said; Disjunction

(p?q), where to affirm the

truth of one or both the different proposals; the implication (p ? q) which

generally takes the form of an IF-THEN rule (also known as the “production

rule”). The implicit IF part is called antecedent, while the THEN part is

called consequential. Generate propositions using union, disjunction or

implication, a new scam The proposition can be obtained from a given prefix of

the clause “is false that …”; This is the negation operation (~ p).

Furthermore, p ? q is the equivalence relation; means that both p and q are

true or false.

Fuzzy

concepts first introduced by Zadeh in the ’60s and’ 70s the focus is basically

a traditional computational logic and set theory concerns:

·

True or False

·

Zero or One

·

In or Out (in terms of set

membership)

·

Black or White (no grey)

·

Not the case with fuzzy logic and fuzzy

sets

Fuzzy logic allows

conclusions to be true or false. However, there are also proposals with

variable answers, such as those that can be found by asking a group of people

to identify a color. In these cases, the truth appears as the result of

reasoning from an inaccurate or partial knowledge in which the sampled answers

are mapped into a spectrum.

Humans and animals

often operate using fuzzy ratings in most situations. The person does not

calculate the exact values ??for weight, density, distance, direction, height

and width of the container and the air resistance of the object to determine

the force and the projection angle of the object. Instead, the person

impulsively applies “fuzzy” calculations quickly, based on previous

experience, to determine which force output values, direction, and vertical

angle will be used to make the tone. Both degrees of truth and probability

range from 0 to 1 and, therefore, may seem the same at the beginning, but fuzzy

logic uses degrees of truth as a mathematical model of ambiguity, while

probability is a mathematical model of ignorance.

The Basic Concepts of

Fuzzy Logic are:

•

Approximation (“granulation”): a color can be accurately described

using RGB values, or it can be roughly

described as “red”, “blue”, etc.

•

Degree (“graduation”): two different colors can be described as

“red”, but one is considered

more red than the other.

•

Fuzzy logic tries to reflect the human way of thinking.

·

Approximation (“granulation”):

a color can be accurately described using RGB values, or it can be roughly described as “red”,

“blue”, etc..

·

Degree (“graduation”): two

different colors can be described as “red”, but one is considered

more red than the other.

·

Fuzzy logic tries to reflect the human

way of thinking.

Implementation of Fuzzy Logic

• Can be implemented in

systems of different sizes and capacities, from small microcontrollers to workstation-based network

control systems.

• It can be implemented

in software, hardware or in a combination of both.