Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

Palash Dutta
Copyright: © 2017 |Pages: 21
DOI: 10.4018/IJSDA.2017100104
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The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis has been carried out and exhibits the techniques with a case study under this setting.
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1. Introduction

Real world problems are always tainted with uncertainty; to handle uncertainty in 1965 L. A. Zadeh developed fuzzy set theory. After that various direct/indirect extensions of fuzzy set have been made and successfully applied in most of the problems of real world situation including medical diagnosis. In fuzzy sets to each element of the universe of discourse a degree of membership between 0 and 1 is assigned. However, in some situations it is not always possible for a membership function of the type IJSDA.2017100104.m01 to precisely assign one point from [0,1], so it is more realistic to assign interval value. According to Gehrke et al. (1996), many people believe that assigning an exact number to expert’s opinion is too restrictive and the assignment of an interval valued is more realistic. In such situations interval valued fuzzy set (IVFS) comes into picture. Sambuc (1975) first presented in his doctoral research (thesis) the concept of IVFS names as IJSDA.2017100104.m02fuzzy set.

On the other hand, an important generalization of fuzzy set theory is the theory of intuitionistic fuzzy set (IFS), introduced by Atanassov (1986) ascribing a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one.

1.1. Problem Statement

In medical diagnosis, it is observed that to gauge a set of symptoms, when doctor/physician question a patient regarding patient’s condition, patient is not to be so confident to describe the conditions and it is also seen that they use the linguistic expression to explain their conditions which are more often vague. Doctor/physician needs to evaluate a list of possible symptoms for the respective diseases of the patients based on their vague linguistic expressions. However, the relations between symptoms and their corresponding diseases are not often one-to-one. The exhibition of the same disease may not be identical with different patients and even at different disease stages. Moreover, a particular symptom may signify various diseases and again in some situations in a particular patient may disarray the presumed structure of symptoms. However, knowledge base associating the symptom-disease relationship comprises of imprecision, vagueness and uncertainty in medical diagnosis process. Therefore, FS, IFS and IVFS can be used as the state as well as symptoms of diseases of the patient are only identified by doctors/physician with a very limited degree of accuracy.

1.2. The Motivations behind the Work and Its Context

Generally, a disease is characterized by some directly noticeable symptoms which induce the patient to go to a doctor/physician. A set of clinical examinations are undertaken to identify the occurrence of a disease. In the realm of medical diagnosis, lots of variables are there which influence the decision-making process and consequently, differentiate the opinions of the doctors/physicians. Due to so many factors to analyze for the diagnosis of the disease of a patient makes the doctor’s/physician’s job difficult. In literature, medical diagnosis problems are available on purely fuzzy set, IFSs and IVFSs based methods. However, use of distance measures on IVFSs in medical diagnosis have not been seen in literature though more imprecision frequently involve in medical documents. Also, no connected study between IFS and IVFS are seen in medical diagnosis to cross check the diagnosis results that obtained from IFS. These motivate us more to study distance measures on IVFSs in medical diagnosis.

It is obvious that in the diagnosis of a patient always has to be dependent on the buoyancy level of a doctor/physician which is very limited degree of accuracy. In such situations, IVFS is a more suitable apparatus to embody linguistic opinion of the doctor/physician as it incorporates the complete degree of confidence of doctor’s/physician’s opinion in certain closed region (i.e., interval). From the point of view, in this study, a medical data base is assembled in the form of IVFS. To structure the data base, for patient Bhuyan, Gogoi, Dutta and Borah; five symptoms Temperature, Headache, Stomach pain, Cough and Chest pain and five diseases, Viral Fever, Malaria, Typhoid, Stomach problem and Chest problem are considered.

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