What is Fuzzy Logic or Fuzzy Set in Soft-Computing & How it works?

Hello friends, In this blog, I have written on the topic of some problem-solving techniques of soft-computing that is What is Fuzzy Logic or Fuzzy Set in Soft-Computing & How it works?. Here, let’s first discuss what is Soft-Computing.

Soft-Computing is the problem-solving technologies which deal with the approximate models with approximate data and give the solution. It is different from hard computing whereas hard computing deals with the precise model with precise (accurate) data. It is an innovative approach for constructing a computationally intelligent system.

Fuzzy Logic

The word Fuzzy means vagueness (not clear) or is not having enough information. It is an organized method for dealing with imprecise data.

* This is an excellent mathematical tour to handle the uncertainty arising due to not having enough information about the particular element of the problem. It is used to try the make computer or machine behaves like human beings.

*It is a mathematical model to describe human-like language.

Fuzzy Set 

 A Fuzzy set is a well define the collection of an object. The collection of the object is may be ambiguous or unambiguous. If the collection is unambiguous. Either some of the objects are a member of a set or it is not. There is no intermediate situation.

                                                     x ∈ A (X belongs to A)   or     x ∉ A (x not belongs to A)

Characteristic  Function,            

                                                    f(x,A)  :  { 1   x ∈ A }

                                                                   { 0   x ∉ A }

                                                    f(x,A) : { 0,1}

Here the Function f contains the elements  x and A. whereas either x element belongs to set A, it appears the value 1 or element x not belongs to set A it appears 0.

The drawback of the conventional set theory is that it does not talk about partial membership. It only talks about the total membership.

In Soft- Computing we want to communicate with the machine in the same manner, the way we communicate with each other(human being). Human beings use the linguistic term like minimum, maximum, less, more, etc.

Problems in Soft-Computing:

The Problems in Soft-Computing is that the machines only understand numbers and mathematics.

Initial Task:

To assign mathematical meaning to linguistic term.

Base Variable or Linguistic Variable:

In a standard fuzzy partition, each fuzzy set corresponds to a linguistic concept, for instance Very Low, Low, Middle, High, Very High. During reasoning, the variables are referred to by the linguistic terms so defined, and the fuzzy sets determine the corresponding with the numerical values.

Semantic: 

Sense being conveyed by the machine.

Syntax:  

Mathematical function that assign meetings to those linguistic terms.

Membership Functions: 

 A fuzzy set is completely characterized by its membership function (MF). A Membership function has a value from 0 to 1. Where 0 indicates the number of belongingness and 1 indicates the total belongingness. The intermediate value indicates partial membership.

For an element  X belonging to the Fuzzy set A, We have two notation for Membership Function.

                                                          A(x)    or     μ_A(x) for value [0,1]

                                                          A(x) : [0,1]  

An increase the Membership value in young with the rise in the age and simultaneously decrease in the membership value for The fuzzy set child shows that we are to capture the gradual change from child to young.

So this is a brief overview of the Fuzzy Logic and Fuzzy Set in Soft-Computing, any further inputs are welcome to be added.