# An application of fuzzy soft matrix in diabetes

Categories: DiabetesThe Matrix

## ABSTRACT:

In this paper, diabetes related diseases and its symptoms are discussed and the different kinds of type-1 diabetic patients are observed ,analyse which age people are mostly affected by type -1 diabetes using Fuzzy soft matrix.

## INTRODUCTION:

Molodtsov proposed fuzzy set theory in 1999.Zadeh introduced Fuzzy soft set theory in the year 1965.In Fuzzy soft set the matrix was constructed by using Min-Max and Max-min to find the result.Fuzzy soft matrix is used to solve the problem which are not solve by ordinary matrices.

It is best method in decision making .The fuzzy soft matrix used to solve the complicated problems in various field like engineering,medical, etc,.Diabetes type 1 will produces little or no insulin from pancreas under the Chronic condition.The concept of fuzzy soft matrix used here is to find the group of people (based on age) who are affecting from type-1 diabetes.Fuzzy soft matrix is used in many fields like medical diagnosis, Engineering,etc,.

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It is easy to store and manipulate matrices.It is more practical and solve many problems.The Symptoms of type-1 diabetes are increased thirst, frequent urination,Hunger and etc.,It is applied successfully to the problems which contains uncertainities. we use max-min to make final decision.Here we are taking different parameters and symptoms of patients and finally make the best decision to find which age people is affected most.

### 2.1 PRELIMINARIES: [BASIC DEFINITIONS]

SOFT SET:

Let U be an initial universe set and E be the set of parameters. Let P(U) denote the power set of U and let A be a non- empty subset of E.

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A pair ( F,A) is called soft set over U.for each set e in A, the set is called the value set of e in (f,a). The softest over U is parameterized family of subsets of the universe U.

EXAMPLE (A):

Let U={ be a set of four types of mobiles and E=(High quality ( , Medium quality (, Low quality ( be the set of parameters if A = { E . Let = { and = {. Then the soft set ( ={,{ ,,{) over U which describes the models of mobile which model will the respective person will buy.

The soft set can be represent in the form,

U High quality ( Medium quality ( Low quality ( 1 1 0 1 1 0 1 1 0 1 0 0

### 2.1.2 FUZZY SOFT SET:

Let U be a universal set. E is a set of parameters and A? E. Let F(U) denotes the set of all fuzzy subsets of U then a pair (F,A) is called Fuzzy soft set over U, where F is a mapping from A to F(U).

EXAMPLE (B):

We cannot express with only 2 real numbers 0 and 1 and its membership function instead on crisp number 0 and 1, which associate with each element a real number in the interval [0,1]

Then,( , E) = (() = {(,0.6),(,(()}

{(,0.6),(,( is the fuzy soft set representing the “models of the mobile” and which model is choosed by most people.Represent fuzzy soft set in the form : U

• High Quality()
• Medium quality ()
• Low quality()
• o.6
• 0.6
• 0.0
• 0.8
• 0.4
• 0.0
• 0.7
• 0.3
• 0.0
• 0.9
• 0.0
• 0.0

FUZZY MATRIX:

A Fuzzy matrix is defined by A=where is the membership value of the element in A.

FUZZY SOFT MATRIX:

Let (,E ) be a fuzzy soft set over U, then a subset of U ? E is uniquely defined by = {(U,e): e A, U (e)} which is called relation form of (,E ).

The characteristic function of is written by : U ? E ?[0,1],

Where (U,e) [0,1] is the membership value of u U for each e E.

If ( ), we can write the matrix by,

Which is called a m n soft matrix of the soft set (,E ) over U. Therefore we can say that a fuzzy soft set (,E ) is uniquely characterised by the matrix and both concepts are interchargeable. The set of all mxn fuzzy soft matrix as over U will be denoted by .

EXAMPLE(C):

• Let U = { be the universal set and E be parameter set and given by E= {} .
• (E ) = ( = {}
• ( = {}
• ( = {}

The fuzzy soft set in matrix form,

• = (
• ( ( 3 x 3

## COMPLEMENT:

A complement function is said to satisfy

•  the boundary condition if (0)=1 and (1)=0,
•  monotonic condition if x y (x)
•  involute condition if ((x))= x, for all x

## ALGORITHM:

Input the fuzzy soft set (,J) and compute the corresponding matrices and .

Input the fuzzy soft set (,S) and compute ,compute and

Compute = ,Compute MV (), MV (), MV (),and MV () Compute the diagnosis score S() and S() Find = max [S) – S)] .We conclude that the patient is suffering from the disease. If has more than one value, then go to step (1) and repeat the process by reassessing the symptoms for the patient.

APPLICATION OF FUZZY SOFT MATRICES:

Let J={} be three category of age groups like 10-25 , 25-40 , 40 and above

And S= {} are the symptoms .

• =patient suffered from frequent urination.
• =patient suffered from frequent thirst
• =patient suffered from hunger.

( , J) over T . is the mapping : J ? (s)

Symptoms and the age group. Let,

• () = { (,0.3,0),(,0.4,0),(,0.6,0)}
• ( = () = { (,0.9,0),(,0.7,0),(,0.5,0)}
• () = {(,0.1,0),(,0.8,0),(,0.1,0)}
• 0.3,0 0.9,0 0.1,0
• = 0.7,0 0.8,0
• 0.6,0 0.5,0 0.1,0
• 1,0.7 1,0.9 0.1,0
• = 6 1,0.7 1,0.8
• 1,0.6 1,0.5 1,0.1
• ) = { (,0.8,0),(,0.7,0),(,0.2,0)}
• ( R ) = () = { (,0.9,0),(,0.3,0),(,0.6,0)}
• () = { (,0.1,0),(,0.5,0),(,0.4,0)}
• 0.8,0 0.9,0 0.1,0
• = 0.3,0 0.5,0
• 0.2,0 0.6,0 0.4,0
• 1,0.8 1,0.9 1,0.1
• = 1,0.3 1,0.5
• 1,0.2 1,0.6 1,0.4

=

• 0.8,0 0.9,0 0.1,0 0.3,0 0.9,0 0.1,0
• 0.3,0 0.5,0 0.4,0 0.7,0 0.8,0
• 0.2,0 0.6,0 0.4,0 0.6,0 0.5,0 0.1,0
• = 0.4,0 0.7,0 0.3,0
• 0.7,0 0.3,0
• 0.4,0 0.6,0 0.6,0

=

• 0.8,0 0.9,0 0.1,0 1,0.3 1,0.9 1,0.1
• 0.3,0 0.5,0 1,0.4 1,0.7 1,0.8
• 0.2,0 0.6,0 0.4,0 1,0.6 1,0.5 1,0.1
• 0.9,0.3 0.9,0.5 0.9,0.1

=

• .3 0.7,0.5 0.7,0.1
• 0.6,0.3 0.6,0.5 0.6,0.1

The matrix membership value is MV () and MV ()

• MV () = 0.4 0.7 0.3
• 0.7 0.3
• 0.4 0.6 0.6
• 0.7 0.4 0.8
• 0.2 0.6
• 0.3 0.1 0.5

Similarly,

• = (0.6,0.1) (0.9,0.1) (0.8,0.1)
• .3) (0.9,0.3) (0.8,0.3)
• (0.6,0.2) (0.9,0.2) (0.8, 0.2)
• = (1,0.6) (1,0.5) (1,0.1)
• ) (1,0.5) (1,0.5)
• (1,0.3) (1,0.5) (1,0.2)
• MV () = 0.5 0.8 0.7
• 0.6 0.5
• 0.4 0.7 0.6
• 0.4 0.5 0.9
• MV () = 0.5 0.5
• 0.7 0.5 0.8

The score of diagnosis S and S

• S = 0.4,0 0.7,0 0.3,0 0.6,0.1 0.9,0.1 0.8,0.0
• 0.7,0 0.3,0 – 0.6,0.3 0.9,0.3 0.8,0.3
• 0.4,0 0.6,0 0.6,0 0.6,0.2 0.9,0.2 0.8,0.2
• S =
• = ( – (
• 0.1 0.1 0.5
• 0.1 0.2
• 0.0 -0.1 0.0

Similarly,

• S = =( – (
• S = 0.9,0.3 0.9,0.5 0.9,0.1 1,0.6 1,0.5 1,0.1
• 0.7,0.5 0.7,0.1 – 1,0.4 1,0.5 1,0.5
• 0.6,0.3 0.6,0.5 0.6,0.1 1,0.3 1,0.5 1,0.2
• -0.2 -0.1 -0.1
• S = -0.2 -0.3 -0.1
• -0.4 -0.4 -0.3

Finding the difference:-

S – S

Maximum value

• 0.3
• 0.2
• 0.6
• 0.6
• 0.4
• 0.4
• 0.3
• 0.4
• 0.4
• 0.3
• 0.4
• 0.4

## CONCLUSION:

Thus from the difference we can find the maximum value of the patients age group who are affecting the most from type 1 diabetes.From the above table we can say has the maximum value as 0.5.

(ie) the patients from age group 10-25 is mostly affected by the type-1 diabetes.

## REFERENCE:

• An analysis of Diabetes Using Fuzzy Soft Matrix, Dr.N.Sarala, I. Jannathulfirthouse,international journal of innovative research in science and technology, vol 6, issue 3, march 2017.
• soft computing diagnostic system for diabetes,P.Srinivastava,NSharma ,R Singh,International journal of computer application.
• Fuzzy soft setsm The journal of fuzzy mathematics,P.K.Maji, R.Biswas And A.R.Roy(2001), volume 9, N0.3,pp :589-602.
• Fuzzy sets, Information and control,L.A.Zadeh(1965), 8 pp.338  353. 