MEDICAL DIAGNOSIS USING NEUTROSOPHIC SOFT MATRICES AND THEIR COMPLIMENTS

: Neutrosophic soft set is a mathematical technique to solve the uncertainties and imprecisions and for decision making problems. In this paper, it is intended to use Neutrosophic soft relations and compliments for medical diagnosis. This paper deals with the symptoms, patients and diseases and then by using compliment algorithm to diagnose the disease


INTRODUCTION
There are many phases oflife in which we face the Uncertainty, Vagueness, complexities and unpredictability.Numerous complexities in engineering, financial, societal disciplines, therapeutic fields and numerous different arenas include provisional information.All such issues, a person comes to confront within life, cannot be illuminated utilizing traditional mathematical techniques.In traditional arithmetic, a numerical model of an entity is created and concept of particular elucidation of this classical paradigm is resolved.Therefore, the numerical model is excessively mind boggling, the particular result can't be found.To resolve these complexities many theories were introduced namely Probability theory, Fuzzy set theory introduced by LotfiZadeh in 1965 [20].Interval valued fuzzy set (IVFS) in 1975 [21], Rough set theory developed by Z.Pawlak in 1982 [10,11],Intuitionistic sets were introduced by KassimirrAtanassov in 1983 [7], Neutrosophic sets were proposed by Smarandachein 1998 [18,19] It is more powerful deals with truthiness, indeterminacy and falseness which exist in the real world.As in uncertain environment decision making is very complex issue so to resolve this issue D. Molodtsov presented Soft set theory in 1999 [8].In 2010, Intuitionistic fuzzy matrices have been derived by Maji.et.al [9] use these terms for decision making.Jafar et al (2019) [2] use soft matrices to disease identification, in this paper we enhance the same work and use Neutrosophic soft matrices relations and their complement for the purpose of medical diagnosis.Neutrosophic sets gives more accurate results then fuzzy or intuitionistic sets.Neutrosophic sets based on Truthiness, Indeterminacy and falseness due to these factors it give more imprecise and accuracy in results.Many researchers [3-6, and 12-17]has work on decision making using soft sets and their relative concepts.

PRELIMINARIES Fuzzy set [2]
If X is a universal setand x 1 X, then a fuzzy set Bdefined as such that

Soft Set [2]
LetŨbe universal set and Ę is the set of attributes.Let Ƥ (Ũ) represents power set of Ũ and Ã ⊆Ę,a pair (ğ, B) is called a soft set overŨ, where ſ is a mapping defined by ſ:B Ƥ(Ũ) The pair (ʌ,έ) is called a FSS over ӳ, where ʌ: έ Ƥ (ӳ) defined a mapping from έ into Ƥ (ӳ).In fuzzy soft set we give fuzzy numbers to each alternative.

Intuitionistic Fuzzy Set [4]
Let Ũ be the universal set and Ę is the set of attributes.IFS (Ũ) are the power set of Ũ. ConsiderB⊆Ę.The pair (ğ, B) is an IFS overŨ where ſ is the mapping defined by ğ: B IFS (Ũ).

Neutrosophic Set [5]
A set B that deals with the order triplet contains the degree of truthiness (T), indeterminacy (I) and falseness (F) value.All Neutrosophic sets of B denoted by F N (B).

Neutrosophic Soft Set [5]
Let Ũ be a universal set andĘ be a set of attributes and B⊆Ę, and then the set (ğ, B) is known as NSS over Û, where ğ is a mapping defined by ğ: B ğ N (B).

Neutrosophic Soft Matrices [4]
Neutrosophic soft matrices deals with the order triplet contains the degree of truthiness (T), indeterminacy (I) and falseness (F) value, in matrices form.

ALGORITHM AND METHODOLOGY
Here, we describe a process used for medical diagnosis by NSS.Suppose that a set of patients is P°, set of symptoms Š and the set of diseases is D ~.

ALGORITHM
i.
The set of diseases related to its symptoms is obtained the symptoms-diseases relation R ˆ1 ii.
The patient symptoms set is obtained the patient symptoms relation Q 1 iii.
Evaluate their corresponding complement matrices R ˆ2 and Q 2 iv. The The complement of R ˆ1 and Q 1 is represented by R ˆ2 and Q 2 respectively.
We have executed the idea of NSS for medical diagnosis.The result Škshows the highest possibility that patient suffer from that disease.It is an approach to evaluate which patient is affected from what disease.By using Neutrosophic fuzzy soft sets we can solve other decision making problems.