Proceedings of the 5 Asian Mathematical Conference, Malaysia 2009 th DESIGNING A DISEASE DIAGNOSIS SYSTEM BY USING FUZZY SET THEORY Ahmad Mahir R. , Asaad A. Mahdi and Ali A. Salih School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MALAYSIA E-mail: [email protected] my ; [email protected] com ; [email protected] com Abstract: Many diseases affecting millions of people every day. Information technology could be used to reduce the mortality rate and waiting time to see the specialist.

As clinical decision making inherently requires reasoning under uncertainty, expert systems, fuzzy set theory and fuzzy logic are a highly suitable basis for developing knowledge based systems in medicine for tasks such as diagnosis of diseases, the optimal selection of medical treatments, and for real time monitoring of patient data.

Don't use plagiarized sources. Get Your Custom Essay on

Designing a Disease Diagnosis System by Using Fuzzy Set Theory

Just from $13,9/Page

Our goal is to develop a methodology using fuzzy set theory to assist general practitioner in diagnosing and predicting patients condition from certain “ rules based on experience ”. Medical practitioner other than specialists may not have enough expertise or experience to deal with certain high risk diseases.

With this system the patients with high risk factors or symptoms could be short listed to see the specialists for further treatment. The intuition is based on doctors ability to make initial judgment based on his study and experience . In this paper we designed a questionnaire to collect the data needed. We chose a random sample of 170 patient from clinics and hospitals. The questionnaire depends on three different sets . The first set is the diseases symptoms set, which contain information on symptoms of diseases such as fever, high temperature, headache, rash, vomiting, etc..

The second set is the diseases set ( chicken pox, Hepatitis B, etc. ),and finally the patients set ( a sample of 49 patients), the next step was to form the membership functions for each symptom, and then the membership value was evaluated on the basis of the answers to the questions relative to the particular feature, for the start, only chicken pox and Hepatitis B were considered in the analysis, then the next step will be expanding to include four other diseases such as Dengue, Measles, Flu, and Infectious mononucleosis.

Key Words : Fuzzy sets, fuzzy max-min relations, Membership values, Medical diagnosis, Expert systems. 1. Introduction Medical diagnosing is the art of determining a person’s pathological status from an available set of findings (Steimann & Adlassnig,1997). It is a problem complicated by many factors and its solution involves literally all of a human’s abilities including intuition and the subconscious, patients coming to the doctor showing symptoms and signs and the doctor will conclude which disease these phenomena mean. 2.

Medical Knowledge The history of medical diagnosis is a history of intensive collaboration between physicians and mathematicians respectively (Seising et al. ,1999), In the 1960s and 1970s various approaches to computerized diagnosis arose using Bayes rule, factor analysis, and decision analysis, On the other side artificial intelligence approaches came in to use, e. g. , Dialog(Diagnostic Logic),and Pip(present illness program), which were programs to simulate the physicians reasoning in information gathering and diagnosis using databases in form of networks of symptoms and diagnoses.

We use the term symptom for many information about patients state of health, signs laboratory test results, ultrasonic results, and x- ray findings. Based on this information a physician has to find a list of diagnostic possibilities for the patient, the certain information about relationship that exists between symptoms and symptoms, symptoms and diagnoses, diagnoses and diagnoses and more complex relationships of the combination of symptoms and diagnoses to a symptom or diagnoses, are formalization of what is called medical knowledge.

In recent years , computational intelligence has been used to solve many complex problems by developing intelligent systems, and fuzzy logic has proved to be a powerful tool for decision making systems, such as expert systems. Fuzzy set theory has already been used in some medical expert systems. 2. 1 Fuzziness of medical knowledge It was the result of knowledge explosion in the medical science that there was a highly visible number of symptoms of diseases, and there is no sharp borders between these symptoms (Seising, 2004).

Smooth transitions in the space of diseases feed from one symptom to another symptoms and very small variations could be the reason that the physician diagnoses a patient with x instead of y. It is understood that physicians count on their experience and intuition and not on strong and rational rules to deduce from the patients data to a disease . 256 Ludwig fleck was an opponent of the view that medical diagnoses are the result of strong logical reasoning . He thought that the elements of medical knowledge , symptoms and diseases, are essentially fuzzy. . Fuzzy sets In 1965 Lotfi Zadeh, professor and head of electrical engineering department at the University of California at Berkley , published his famous paper “Fuzzy Set” in fact , Zadeh rediscovered fuzziness, identified and explored it , and promoted and fought for it. Zadeh extended the work on possibility theory a formal system of mathematical logic , and even more importantly , he introduced a new concept for applying natural language term . This new logic for representing and manipulating Fuzzy terms was called Fuzzy Logic.

Fuzzy logic is just a small part of the fuzzy set theory, fuzzy logic is determined as a set of mathematical principles for knowledge representation based on degree of membership rather than on crisp membership of classed binary logic. Unlike two valued Boolean logic, fuzzy logic is multi -valued where it deals with degrees of membership and degree of truth . Fuzzy logic uses the continuous of logical values between 0 (Completely false) and 1 (completely true) . Instead of just black and white , it employs the spectrum of colours accepting that things can be partly true and partly false at the same time , as can be seen below.

Figure 1. Range of logical values in Boolean and fuzzy logic values: (a) Boolean logic (b) multi-valued logic Fuzzy logic adds a range of logical values to Boolean logic. Classical binary logic now can be considered as a special case of multi – valued fuzzy logic. Fuzzy logic is a logic that describes fuzziness. As fuzzy logic attempts to model humans sense of words, decision making and common sense, it is leading to more human intelligent machines. A fuzzy set is a set with fuzzy boundaries , such as short , average or tall for men’s height.

To represent a fuzzy set in a computer we express it as a function and then map the elements of the set to their degree of membership. Typical membership functions used in fuzzy expert systems are triangle and trapezoids. The basic ideas of the fuzzy set theory is that an element belongs to a fuzzy set with a certain degree of membership, thus a proposition is not either true or false, but may be partly true (or partly false), to any degree this degree is usually taken as a real number in the interval [0,1]. 4. Application of Fuzzy set Theory 4. Collecting data: At first we chose certain diseases which have nearly the same symptoms, we will collect the data from hospitals and clinics in order to build a system to distinguish between those diseases with the help of the patient and the doctors. The questionnaire we designed has two types of questions, the first consists of questions concerning the background of the patient the second part consists of the questions concerning the patient symptoms, after collecting these data we will build the membership functions needed.

The diseases we chose were, Chicken pox and hepatitis B. From the questionnaire we can see that we have three sets of questions such as shown below: 1- Symptoms set: S= { S1, S2, S3, S4, ………….. , S20} The symptoms are: 1-Fever 3-Headache 2-HighTemperature 4-Pain behind the eyes 257 5-Nausea 7-Rash 9-Muscle pain 11-Lethargic 13-Diarrhea 15-Chest pain 17-Sorethoat 19-Abdominal pain 2- Diseases set: D= { d1, d2} where d1= Chicken pox 6-Vomiting 8-Joint Pain 10-Bleeding 12-Loss of appetite 14-Cough 16-Chills 18-Itchyness 20- Runny Nose d2= Hepatitis B – Patient set : P= { p1, p2, p3, p4, …………,p49}, depends on sample size 4. 2 membership functions For each symptoms above we generate the following membership function: 1 if if ? S ( x1 ) = 1 1= 1 2 for answers yes 0 where 1 1= ? S ( x1 ) is the membership function for S1 (fever), with two values 1and 0 0 if if if if if if if if if if if if if if if if 3=1 3=2 3=3 4= 2? 38 and no respectively. ? S ( x2 ) = 2 ( 2-38)/ (40 – 38) if 1 38; 2 ; 40 2? 40 ? S ( x3 ) = 3 1 0. 3 0 1 1 2 1 ? S ( x4 ) = 4 0 1 4= 5= ? S ( x5 ) = 5 0 1 5=2 6= 1 2 ? S ( x6 ) = 6 0 1 0. 8 0. 6 0. 2 0 = 7=1 7=2 7=3 7= 4 7=5 ? S ( x7 ) = 7 258 1 if if if if if if ? S ( xi ) = i i=1 for i=8,9 0 1 i= 2 ? S ( x10 ) = 10 10=1 0 1 10=2 i= 1, i= 2 for i= 11,……. ,20 ? S ( x10 ) = 10 0 4. 3Fuzzy relations A relation, is a mathematical description of a situation where certain elements of sets are related to one another in some way (Nguyen et al. ,2003). To describe medical knowledge as the relationship between symptoms Si and disease Dj Adlassing found two fuzzy relationships, namely Occurrence- how often does Si occur with Dj? And Conformability –how strongly does Si confirm Dj? (Seising, 2004), these functions could be determined by Linguistic documentation by medical experts and Medical database evaluation by statistical means or a combination of both. We will determine the fuzzy Occurrence and Conformability relations from expert medical documentation. Since this documentation usually takes the form of statements such as symptom s seldom occurs in disease d or symptom s always indicates disease d, we assign membership grades of 1, 0. 75, 0. 5, 0. 25, 0 in fuzzy set Rc for the linguistic terms always , frequently , don’t know, rarely, and never respectively.

In 1973, Zadeh, introduced the combination rule of a max-min-composition , that is if we have three sets A, B, and C, to compose fuzzy relations Q ? L(A x B) and R ? L(B x C) to get another fuzzy relation T ? L(A x C), (Vig, 2004). then T = Q ° R is defined by the following membership function , ?T (x,y) = maxy B min { ? Q (x,y); ? R (y,z)}, x? A y? B z? C Let Rs= PxS, this indicates the degree to which the symptoms (s) is present in patient (p),calculated from the membership functions. Let Ro= SxD, (Schuerz,1998), this indicates the frequency of occurrence of symptoms (s) with disease (d) .

Table 1. Frequency of occurrence of symptoms (S) with disease (d) Ro= SxD No. 1 2 3 4 5 6 7 8 9 10 11 12 Symptoms Fever Temperature Headache Pain behind the eyes Nausea Vomiting Rash Joint pain Muscle pain Bleeding Lethargic Loss of appetite Chicken pox 0. 59 0. 59 0. 40 0. 03 0. 18 0. 28 0. 81 0. 34 0. 46 0. 03 0. 09 0. 25 Hepatitis B 0. 29 0. 29 0. 53 0. 00 0. 47 0. 52 0. 29 0. 64 0. 64 0. 17 0. 05 0. 29 259 13 14 15 16 17 18 19 20 Diarrhea Cough Chest pain Chills Sore throat Itchiness Abdominal pain Runny nose 0. 06 0. 37 0. 06 0. 46 0. 34 0. 31 0. 15 0. 15 0. 23 0. 11 0. 05 0. 7 0. 05 0. 00 0. 58 0. 00 Let Rc= SxD, this indicates the degree to which symptoms s confirms the presence of disease d . Table 2. The degree to which symptoms (S) confirms the presence of disease (d). Rc =SXD No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Symptoms Fever Temperature Headache Pain behind the eyes Nausea Vomiting Rash Joint pain Muscle pain Bleeding Lethargic Loss of appetite Diarrhea Cough Chest pain Chills Sore throat Itchiness Abdominal pain Runny nose Chicken pox 1. 00 1. 00 0. 75 0. 25 0. 25 0. 25 1. 00 0. 75 0. 75 0. 00 0. 75 0. 75 0. 25 0. 25 0. 00 0. 5 0. 25 0. 75 0. 25 0. 25 Hepatitis B 0. 75 0. 75 0. 25 0. 00 0. 75 0. 75 0. 25 0. 75 0. 75 0. 25 0. 75 0. 75 0. 25 0. 25 0. 00 0. 75 0. 25 0. 00 1. 00 0. 00 Using relations Rs, Ro, Rc “Sanchez approach”, we can now calculate four different indication relations defined on the set PxD of patient and diseases (Radha & Rajagopalan, 2007). The first occurrence indication R1, defined by R1 = Rs ° Ro The conformability indication R2 defined by R2= Rs ° Rc. The non-occurrence indication R3 defined by R3= Rs ° (1 – Ro) Finally the non symptoms indication R4 defined by R4=(1-Rs) ° Ro.

Table 3. R1, R2, R3, R4 for both diseases (d1, d2) Patient R1 R2 R3 R4 R1 R2 R3 R4 R1 R2 R3 R4 . . . . d1 0. 81 1. 00 0. 75 0. 59 0. 8 0. 8 0. 69 0. 59 0. 59 1. 00 0. 94 0. 81 . . . . 0. 46 d2 0. 64 0. 75 0. 95 0. 58 0. 64 0. 75 1. 00 0. 58 0. 52 0. 75 1. 00 0. 64 . . . . 0. 64 Doctors Diagnosi s d1 System Diagnosis d1 P1 P2 d1 d2 P3 d1 d1 . . . . . . . . . . . . R1 260 P47 P48 P49 R2 R3 R4 R1 R2 R3 R4 R1 R2 R3 R4 0. 75 0. 94 0. 81 0. 46 0. 75 0. 85 0. 81 0. 59 1. 00 0. 85 0. 81 0. 75 0. 95 0. 58 0. 64 1. 00 0. 71 0. 53 0. 64 1. 00 0. 71 0. 52 d2 d2 d2 d2 d2 d2

From these four indications relation( Binary relations), we may draw different types of diagnostic conclusions concerning the diagnosis of the 49 patients diseases (Klir and folger, 1988). Conclusion From table 3, we can see that the diagnosis system was correct with twenty seven Chicken pox cases out of thirty two, that means the system was successful in 84% of the cases, while for Hepatitis B the system was correct in thirteen cases out of seventeen cases that means the system was successful in 76% of the cases. For the whole sample of forty nine patients the system was correct in 81% of the cases, with both Chicken pox and Hepatitis B.

Based on the results above, we think that fuzzy set theory has the potential to be used in diagnosis of diseases. References 1. 2. 3. 4. Klir,G,J. and Folger ,T. A. , (1988), fuzzy sets, uncertainty and information , Prentice Hall, New Jersey, p71-74. Nguyen, H. T. , Prasad,N. R. ,Walker,C. L. ,Walker,E. A (2003), A first course in fuzzy and neural control, Chapman& Hall, p 117-119. Radha, R. , and Rajagopalan,S. P. , (2007), Fuzzy logic Approach for Diagnosis of Diabetics, information technology journal 6(1):96-102. Schuerz, M. , Adlassnig, K-P, Lagor, C. , Scheide, B. and Grabner, G. 1998), Definition of fuzzy sets representing medical concepts and acquisition of fuzzy relationships between them by semi-automatic procedures, medical information system. Seising,R. , Schuh,C. , and Adlassnig, K-P, (1999), Medical knowledge , fuzzy sets, and Expert systems. Seising , R,(2004), A history of medical diagnosis using fuzzy relation (draft paper, fuzziness in finland 04(fif04)) Unpublished paper. Steiman, F. ,and Adlassnig, K-P, fuzzy medical diagnosis. Vig, R. , Handa, N. M. , Bali,H. K. , Sridher, (2004), Fuzzy Diagnostic systems for Coronary Artery Disease. Vol 85 5. 6. 7. 8. 261