key: cord-1009019-rhrw5s4v
authors: Antonysamy, V.; Lellis Thivagar, M.; Jafari, S.; Abdullah Hamad, Abdulsattar
title: Neutrosophic Sets in Determining Corona Virus
date: 2021-09-03
journal: Mater Today Proc
DOI: 10.1016/j.matpr.2021.08.290
sha: 11ee76cd07bba1f18a66c98e6699634d25e688da
doc_id: 1009019
cord_uid: rhrw5s4v

An attempt that is made here is to apply neutrosophic sets to a medical data. By means of extended Hausdorff minimum distance we find out the core symptoms of the patients. From the minimum distance or the core symptoms we can get a clue for the type of disease affecting the patient.

Zadeh [1] in 1965 introduced fuzzy set to study uncertainty or vagueness and partial truth by assigning percentage to the truth value of the data. Atanassov [2, 3] in 1986 proposed intuitionistic fuzzy set which is one step further than fuzzy set to studyimprecisive data since it gives percentage not only to membership value but also to non-membership value. Neutrosophic sets, which are defined by Smarandache [4] is an advanced system to intuitionistic fuzzy set. In neutrosophic set all three parameters, namely membership value, non-membership value and indeterminacy value, are given importance by assigning its due percentage. Hence it is found to be more effective than fuzzy and intuitionistic sets. In 2012, Salama, Alblowi [5] induced the concept of neutrosophic topological space. Lellis Thivagar et al. [6] , [7] [8] [9] [10] [11] [12] produced neutrosophic nano topology reducing theentire universe under five open sets. In this paper, we try to find out the normalised hamming minimum distance to neutrosophic sets data by applying Hausdorff minimum distance. The minimum distance is nothing but narrowing down the given medical data to a desirable result. In other words the minimum number gives us an indication for the kind of sickness affecting a sick person. By this method we can easily find out the decease of a sick person and enable the doctors to start the treatment at once. So that the life of a patient is saved without prolonging his suffering.

To apply neutrosophic sets to a medical data we recall here a few related concepts and definitions that will enable us to apply the theory efficiently. Definition 1 [1] Let . A fuzzy set  is an object having the form={(,  ()):} , where 0  ()1 represents the degree of membership of each  to the set .

, where   () and   () represent the degree of membership and non-membership function respectively of each  to the set  and 0  ()+  ()1 for all

Definition 3 [4] let  be a non-empty set. A neutrosophic set  having the form={(,  (),  (),  ()):} , where   (),  () and   () represent the degree of membership function (namely  ()), the degree of indeterminacy (namely  ()) and

the degree of non-membership (namely  ()) respectively of each  to the set . Also  0  ()+  ()+  ()3 + for all . 

Based on Neutrosophic Hamming distance we develop an application to find the core attribute of the disease. By the core attribute one can conclude whether the patient is affected by Viral fever or Malaria or Typhoid or Chicken gunya or Corona virus.

for every  i  representing membership, indeterminacy, and non-membership values respectively.

The distance between two neutrosophic sets, say  and , is defined as follows:

denotes the extended Hausdorff distance between two neutrosophic sets (NS)  and .

Definition 2 Let L, M and N be three neutrosophic sets. Then the distance between L and M is denoted

Similarly the distance between L and N can be written as:

between M and N is written as:

be two neutrosophic sets of the universe of discourse={ 1 , 2 , 3 ,..., n } . Then the neutrosophic Hamming distance defined as:

The neutrosophic normalized Hamming distance is given as: l NNH (1,2)= 1

When a person is affected by a particular disease that person will have more than one symptoms such as Temperature, Cough, Throat infection, Headache, Sneezing etc. Also each viral disease will have more than one symptoms. For example Malaria, Typhoid, Chicken gunya will have various symptoms, like temperature, body pain, cough etc. A person who is affected by corona virus also will have the symptoms of temperature, cough, sneezing, body pain etc. Now to find out the core symptom of corona virus we will use neutrosophic normalized Hamming distance method. By Neutrosophic Normalised Hamming distance we can find the lowest/minimum distance or core symptom by which we can conclude the kind of sickness affecting the person or the patient suffering from. Let us take eight patients for our case study, i.e., P={P 1 ,P 2 ,P 3 ,P 4 ,P 5 ,P 6 ,P 7 ,P 8 }. Each patient is experiencing more than one symptoms say, S={Temperature, Headache, body pain, Cough, Sneezing}. Now using the neutrosophic data we want to find out the kind of disease affecting the person from the common prevalent diseases say, d={Viral fever, Malaria, Typhoid, Chicken gunya, Corona virus}. For this purpose we need two kinds of observations: (i) In each patient the multiple symptoms found.

(ii) For each disease, in a normal given circumcisions, the kind of symptoms found. Both these observations are recorded in a neutrosophic set form, namely describing the percentage of membership function , percentage of indeterminacy function  and percentage of nonmembership function  etc. To find the core attribute by utilising neutrosophic normalised Hamming distance formula for every symptoms of i th patient from k th diagnosis is:

Step 1: The characteristic symptoms observed in every patient (Table 1) .

Step 2: For each disease the type of symptoms usually found so that we can obtain symptomdisease relation ( Table 2) .

Step 3:

The computed values are tabulated for each person as per diseases (Table 3) .

Step 4: Finally, the minimum value for each person is identified from table 3 to find the kind of sickness from which the patient is suffering from.

The required inputs are P i i.e. the number of patients i=1,2,3,4,5,6,7,8.

S j Denotes the symptoms where j=1, 2,3,4,5. d k Denotes the kind of diagnosis i.e. k=1, 2,3,4,5 and Tables 1 and 2 are the required observations. Computing the algorithm as per the given input i.e.

l NNH (S(P 1 ),d 1 )= 1 5 [ max {| 1 (p 1 ) 1 (d 1 )|,| 1 (p 1 ) 1 (d 1 )|,| 1 (p 1 ) 1 (d 1 )|} +max {| 2 (p 1 ) 2 (d 1 )|,| 2 (p 1 ) 2 (d 1 )|,| 2 (p 1 ) 2 (d 1 )|} + max {| 3 (p 1 ) 3 (d 1 )|,| 3 (p 1 ) 3 (d 1 )|,| 3 (p 1 ) 3 (d 1 )|} + max{| 4 (p 1 ) 4 (d 1 )|,| 4 (p 1 ) 4 (d 1 )|,| 4 (p 1 ) 4 (d 1 )|} + max{| 5 (p 1 ) 5 (d 1 )|,| 5 (p 1 ) 5 (d 1 )|,| 5 (p 1 ) 5 (d 1 )|}] . From the above calculation we get the output for the patient P 1 with respect to diagnosis k=1.

Similarly computing for k=2,3,4 and 5 we get the entire output for P 1 from which the required minimum distance or the core attribute is obtained. The core attribute or the minimum distance is the desired diagnosis of the patient. Continuing the process for P 2 ,P 3 ,...,P 8 we complete Table  3 . Table 1 : Symptoms characteristic for the patients considered The above sample data as well as symptoms sample for our study are collected from Fatima Medical College Kadapa run by a private trust, which is also one of the corona quarantine centre for Kadapa district in Andhra Pradesh, India. Kadapa district had number of suspected cases but fortunately many after quarantine treatment have come out successfully and tested negative results for corona.

The following sample code of EXCEL programme, for finding the possible minimum number or the core symptom, is used to simplify our calculation work. The output is tabulated in Table 3 .

The above Excel programme is designed to find the Hausdorff minimum distance that indicates the core number of the patient In the above table with bold letters are the minimum distance or core attribute acquired by using Hausdorff Hamming distance as per the given neutrosophic data.

The above histogram indicates the minimum distance or the core attribute of the particular patient in a graph.

As a result by executing the neutrosophic extended Hausdorff normalised Hamming distance programme for each patient we observer that patients P 1 ,P 3 and P 7 have got their minimum number under the column Viral fever. Hence, by this minimum number (distance) method, we conclude that in all likelyhood they will be suffering from viral fever. Following this pattern we can say that patients P 2 and P 5 will have Typhoid, patient P 4 will have Malaria, patient P 6 will have Chicken Gunya and patient P 8 will be affected by Corona virus. Further we hope that this application can open up a lot of scope for future study which may be very useful for the common people.

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

We are authors, submitting the manuscript for publication in your journal. This is our research manuscript and has not been published or considered for publication by any other journal or elsewhere. Kindly consider the manuscript for publication in your journal.

Warms Regards, V. Antonysamy, M. Lellis Thivagar, S. Jafari and Abdulsattar Abdullah Hamad

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Writing-Original draft preparation, Software M. Lellis Thivagar : Editing Conceptualization S. Jafari : idation, Writing-Reviewing Abdulsattar Abdullah Hamad : Methodology,. Visualization, Investigation. Supervision

Acknowledgements: The authors would like to thank the referees for providing very useful comments and suggestions that helped in improving the quality of the paper.