KNOWLEDGE ACQUISITION FOR FUZZY EXPERT-SYSTEMS

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Fuzzy Expert Systems

Gwo-Jen Hwang

Computer Center, National Chiao Tung University, Hsinchu, 300, Taiwan, Republic of China

Expert systems have been successfully applied to a wide variety of application domains. To achieve better performance, researchers have tried to employ fuzzy logic to the development of expert systems. However, as fuzzy rules and membership functions are difficult to define, most of the existing tools and environments for expert systems do not support fuzzy representation and reasoning. Thus, it is time-consuming to develop fuzzy expert systems. In this article we propose a new approach to elicit expertise and to generate knowledge bases for fuzzy expert systems. A knowledge acquisition system based upon the approach is also presented, which can help knowledge engineers to create, adjust, debug, and execute fuzzy expert systems. Some control techniques are employed in the knowledge acquisition system so that the concepts of fuzzy logic could be directly applied to conventional expert system shells; moreover, a graphic user interface is provided to facilitate the adjustment of membership functions and the display of outputs. The knowledge acquisition system has been integrated with a popular expert system shell, CLIPS, to offer a complete development environment for knowledge engineers. With the help of this environment, the development of fuzzy expert systems becomes much more convenient and efficient. 0 1995 John Wiley & Sons, Inc.

I. INTRODUCTION

In recent years, expert systems have been applied to a wide variety of application domains, which not only showed the utility of this approach, but also revealed some problems of applying it. Part of the problems in employing conventional expert systems may be due to the use of binary logic to express domain knowledge, whose expressions may not be natural or straightforward and, hence, the expertise is not completely represented. For example, there are only two possible sides (true or false) in binary logic and a clear boundary must be indicated for making choices, while in the real world, it is difficult to judge things to be absolutely true or false. The problem becomes more compli- cated if linguistic hedges (e.g., very, gradually, moderately, more or less, etc.)

are used in expressing expertise.’

A good solution to this problem is to employ the concept of Fuzzy Set and Fuzzy Logic in expert systems; that is, fuzzy expert systems. For example, let E represent the set of “the people who are tall.” In conventional binary logic,

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 10, 541-560 (1995) 0 1995 John Wiley & Sons, Inc. CCC 0884-8 173/Y5/06054 1-20

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we must clearly specify whether an element belongs to E or not. However, in

fuzzy logic, each element belongs to the set with a degree of membership. A person of 160-cm height belongs to E with the degree of membership 0.0;

while the persons of 170-cm, 175-cm, and 180-cm heights may have degrees of membership 0.5, 0.75 and 1 .O, respectively. Moreover, when considering the linguistic hedges (e.g., very, gradually, moderately, inore or less, etc.), all we need to do is to compute the degrees of memberships according to some hedge functions. For example, let the Fu,,(x) = x', where x is degree of memberships without qualifier. If a person is said to be TALL with degree 0.8, according to FveV(x), we conclude that the person is VERY TALL with degree 0.64.

However, the development of a fuzzy expert system is time-consuming. The difficulty may be due to the lack of methodologies and tools to help in eliciting knowledge for constructing fuzzy rules and in defining the membership functions for fuzzy values. Moreover, most existing expert system shells do not support fuzzy reasoning, which increases the cost needed for developing fuzzy expert systems. To cope with these problems, we propose a knowledge acquisition system that not only elicits knowledge from domain experts, but also generates knowledge bases for fuzzy expert systems. We have integrated the environment with a popular expert system shell, CLIPS, to enable fuzzy reasoning. Some experimental results showed that the approach is desirable and is worth further study.

In this article, we propose a knowledge acquisition environment that consists of a knowledge acquisition unit, a graphic membership function developer, a fuzzy interface for expert systems shells, and a set of control rules for fuzzy reasoning. The environment has been integrated with a well-known expert system shell to perform fuzzy reasoning. Finally, some test results of an experi- ment on a practical medical diagnosis problem are shown to evaluate the new approach, and a conclusion is given.

11. KNOWLEDGE ACQUISITION FOR FUZZY EXPERT SYSTEMS One critical bottleneck to building expert systems is the elicitation of knowledge from domain experts. Many knowledge engineering tools (e.g., ETS,? N ~ o E T S , ~ AQUINAS,4 MOLE,' NICOD,' ICONKAT,' KSS0,8 ASK,9 SMORE,'O ALT," RuleCon,'* KITTEN,I3 etc.) and interviewing technique^,'^,'^ have been developed to cope with this problem. In this article, we propose a knowledge acquisition environment, Knowledge Acquisition for Fuzzy Expert Systems (KAFES), which is capable of eliciting expertise from domain experts and generating knowledge bases for fuzzy expert systems. The environment is integrated with a well-known expert system shell, CLIPS, to enable fuzzy reasoning. It consists of four components:

(1) Knowledge acquisition unit: a revised repertory grid mechanismI6 is used to ( 2 ) Graphic membership function developer: a tool to help knowledge engineers

enable the elicitation of fuzzy knowledge. adjust membership functions of fuzzy values.

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Domain Knowledge Engineers

Figure 1. The structure of KAFES.

(3) Fuzzy interface for expert system shells: the interface performs the fuzzification and defuzzification operations, which facilitate fuzzy reasoning on conventional expert system shells. Currently, it is available for CLIPS, a shell for the development and delivery of expert systems developed by the Software Technology Branch of the Information System Directorate at NASA/Johnson Space Center.

(4) A set of control rules for CLIPS, which enables fuzzy reasoning on CLIPS. The whole structure of the environment is depicted in Figure 1.

A. Knowledge Acquisition Unit

Many existing systems employ the repertory grid test, which was originally invented and widely used by George Kelly in clinical psychology16 when interviewing experts. In a repertory grid, a set of elements is listed across the top of the grid. Various combinations of three elements are then presented to the expert, and the question, “Think of an important trait or characteristic, which makes two of the elements different from the third,” is asked. The trait given by the expert is listed on the left-hand side of the grid, and its opposite is listed on the right-hand side. Each pair of a trait and its opposite is called a construct. After the set of constructs is ready, the expert is asked to fill the grid with ratings. A 1 -+ 5 rating mechanism is often used in filling the grid; i.e., each rating is an integer ranging from 1-5. A 1 is at the left-hand pole, a 5 is at the right-hand pole, while the rest fall between the poles. An example of a repertory

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C

J

1

4

5

1 4 c ;

c 4 1 1 1 5 1 c ;

Figure 2. An example of a repertory grid.

grid with five elements (El, E2, E,, E4, and E,) and four constructs ( C l , C2, C3, and C,) is given in Figure 2.

Each rating expresses the relationship between a construct and an element, which does not provide sufficient information for building fuzzy expert systems. Consider the following repertory grid:

Dangue Measles

. . .

fever Low 5 2

. . .

High . . .

. . .

From the ratings of the grid, we are only aware of the information, “For Dangue Fever, a patient is likely to have a high temperature,” and, “For Measles, a patient’s temperature is usually not high.” It is quite possible that the expert wants to emphasize the expressions by adding some linguistic hedges:

“ F o r Dangue Fever, a patient’s temperature should be VERY high.” “For Measles, a patient’s temperature is usually MORE OR LESS low.”

From the examples, we find it difficult to apply conventional repertory grids to the development of fuzzy expert systems, which is due to the following reasons:

(1) Repertory grids do not explicitly hold information for linguistic hedges. (2) Repertory grids do not hold information for helping the determination of mem-

bership functions.

Thus, it would be more desirable to adapt the grid so that it is appreciate for fuzzy logic instead of using fuzzy logic with repertory grids. To cope with these problems, we propose thefuzzy table to hold the information for generating

fuzzy rules and membership functions. The procedure for constructing a fuzzy table is similar to that of a repertory grid, which consists of three steps shown as follows:

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expert. The elements (e.g., G , , GZ, G,, G4, and G,) provided by the expert are placed across the top of the table:

Step 2: Elicit attributes (fuzzy variables) from the expert. Each time, the expert is asked for an attribute so that three elements can be partially or fully distin- guished. The fuzzy variables are listed on the left-hand side of the table. For each fuzzy variable, three fuzzy values are specified and listed on the right- hand side according to the following procedure:

KAFES: Please select a set of fuzzy values for fuzzy variable V,: 1. LOW/ MIDDLE/HIGH. 2. SHORT/MIDDLE/TALL. 3 . LIGHTINORMALI HEAVY, 4. SMALL/MIDDLE/BIG. 0. Other (user-defined).

EXPERT: 1.

KAFES: Please select a set of fuzzy values for fuzzy variable V,: 1. LOW/

MIDDLEIHIGH. 2. SHORTIMIDDLEITALL. 3 . LIGHT/NORMAL/

HEAVY. 4. SMALL/MIDDLE/BIG. 0. Other (user-defined). EXPERT: 2.

KAFES: Please select a set of fuzzy values for fuzzy variable V,: 1. LOW/ MIDDLE/HIGH. 2. SHORTIMIDDLEITALL. 3 . LIGHT/NORMAL/ HEAVY. 4. SMALL/MIDDLE/BIG. 0. Other (user-defined).

EXPERT: 0.

KAFES: Please indicate the lower bound of the fuzzy values. EXPERT: SLOW.

KAFES: Please indicate the middle of the fuzzy values. EXPERT: NORMAL.

KAFES: Please indicate the upper bound of the fuzzy values. EXPERT: FAST.

An example of a fuzzy table with fuzzy variable and values is given as follows: (3, (3, G3 G4 G.5 Vl v2 v3 v4

LOW ; MIDDLE ; HIGH SHORT ; MIDDLE ; TALL

SLOW ; NORMAL ; FAST LOW ; MIDDLE ; HIGH Step 3: Fill all of the [element, attribute] entries of the grid. Each entry consists of two parts: a rating to indicate the most desirable fuzzy value and the degree of certainty for giving that rating. It is possible that the expert selects the most desirable fuzzy value, but still lacks confidence about his (or her) choice.

A 7-scale rating mechanism is employed in the fuzzy table. The ratings are integers ranging from - 3 to + 3 , which represent the possible combinations

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of linguistic hedges and fuzzy values. Consider the ratings of fuzzy variable V, in the table; 3 means VERY HIGH, 2 means HIGH, 1 means MORE OR LESS HIGH, 0 means MIDDLE, - I means MORE OR LESS LOW, -2 means LOW, and - 3 means VERY LOW. The degree of certainty for each rating is described by “S”or “ N ” , which represent VERYSUREand NOTVERYSURE, respectively. For example:

GI G2 G3 G4 GS

31s OIN -31s 11s 31s LOW ; MIDDLE ; HIGH

21s 1/S 31s 21s O / S SHORT ;MIDDLE ;TALL

v3 21s 21s 31s 1lN 21s SLOW ; NORMAL ; FAST

V, - l l N ‘21s -21s -31s 31s LOW ; MIDDLE ; HIGH

Vl v2

Each column of the fuzzy table will be translated to a fuzzy rule. The truth value for the output of i - th rule is computed by

x 0.8

+

0.2. # of

“S”

TRUTH = ( # of “S,! + # of $“,I)

For example, the first column of the above fuzzy table is translated to the following rule:

IF V, i s V E R Y H I G H , and

V2 i s TALL, and V, i s FAST, and V, is MORE OR LESS LOW

THEN I n s e r t n e w f a c t G , TRUTH= 0 . 9 5 .

Initially, experts are asked to provide numerical information for fuzzy values, and some default functions are employed. Let fuzzy values of afuzzy variable be represented as LS (left side), MS (middle side), and RS (right side). Assuming that the numerical values with membership degrees 1 .O for LS, MS, and RS are a,

p,

and y, respectively, we have the following membership

function^:'^

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,

Low Middle High

V1

250 300 350

Figure 3. Graphic representation of fuzzy values for V , .

For V, in the above table, if the expert gives numerical value 250 for fuzzy value LOW (LS), 300 for MIDDLE (MS), and 350 for HIGH (RS), membership functions given in Figure 3 are derived.

The degrees of memberships of linguistic hedges are computed by the following hedge functions:

1. F(X),Or = 1 - X 2. F(X)vERy = X 2

- xO.5

3. F(X)MORE-OR-LESS - 7

where X is the degree of memberships without considering linguistic hedges.

B. Graphic Membership Function Developer

Graphic membership function developer is used to help knowledge engineers to create and adjust membership functions for input facts. It provides a graphic view, so that knowledge engineers can adjust the shape of membership function curves directly to get the desirable results.

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Defuuificanon

Figure 4. Fuzzy reasoning by applying the fuzzy interface.

C. Fuzzy Interface

The knowledge representation and inference process in a fuzzy expert system is quite different from those in a conventional expert system. However, as there already exist many expert system shells and knowledge engineering tools for conventional expert systems, it would be very convenient if we could build fuzzy expert systems based upon the existing shells or tools. We selected one of the most popular expert system shells, C Language Integrated Production System (CLIPS) to work with the knowledge acquisition system. CLIPS is a tool for the development and delivery of expert systems developed by the Software Technology Branch of the Information System Directorate at NASA/ Johnson Space Center.

The fuzzy interface is capable of accepting input values from users, performing fuzzification operations, invoking the inference of CLIPS, and performing defuzzification operations on the outputs from CLIPS. If the knowledge engineer or the expert is not satisfied with the system output, the graphic developer is helpful in adjusting the membership functions to achieve better performance. The process of fuzzy reasoning by applying the fuzzy interface is shown in Figure 4.

After performing the inference process, all the system outputs are collected by the fuzzy interface to make the final conclusion. The centroid defuzzification is employed to derive a more reasonable result, which will be shown by graphic representation as well as text display to facilitate the modification and debugging of the fuzzy expert systems.

D. Control Rules for Fuzzy Reasoning

A significant difference between fuzzy rules and conventional rules is the use of linguistic hedges, such as

NOT,

VERY,

NOT

VERY, MORE O R LESS, NOT MORE O R LESS, etc. For example, two rules with truth value 1.0 are given as follows:

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( d e f r u l e Domain-Rule, (LEVEL ? gg)

? f f l < - (TEMP I S HIGH ? d d l & : (> ? d d l ?gg) ) ? f f 2 < - (FAN I S NOT FAST ?dd2&: ( > ?dd2 ?gg) )

=>

( a s s e r t (DEL-FACT FAN I S FAST) ) ( b i n d ?dd (min ? d d l ?dd2) )

( p r i n t o u t t 'FAN I S FAST

'

? d d c r l f ) ( a s s e r t (NEW-FACT FAN I S FAST ? d d ) ) ) ( d e f r u l e Domain-Rule,

(LEVEL ?gg)

? f f l < - (TEMP I S VERY HIGH ? d d l & : ( > ? d d l ?gg) ) ? f f 2 < - (FAN I S NOT FAST ?ddZ&: ( > ?dd2 ?gg) )

=>

( a s s e r t (DEL-FACT FAN I S FAST) ) ( b i n d ?dd (min ? d d l ?ddZ) )

( p r i n t o u t t 'FAN I S VERY FAST

'

?dd c r l f ) ( a s s e r t (NEW-FACTFAN ISVERYFAST ? d d ) ) )

For an input value (e.g., 25"C), the fuzzy interface first performs fuzzification operations to produce the corresponding fuzzy fact (e.g., temperature is NORMAL 0.95), and then transfers it to CLIPS for inference. The problem is, how could those fuzzy facts match the premise patterns of rules if linguistic hedges exist. For example, the fact (TEMPERATURE IS HIGH 0.6) should be able to match the patterns (TEMPERATURE IS VERY HIGH) with degree 0.36, (TEMPERATURE IS HIGH) with degree 0.6, (TEMPERATURE IS LOW) with degree 0.4, (TEMPERATURE IS NOT VERY HIGH) with degree 6.4, etc. To cope with this problem, some control rules are used to generate a set of facts with linguistic hedges to replace the original fuzzy fact. One such control rule is shown as follows:

( d e f r u l e G e n e r a t e - L i n g u i s t i c - H e d g e - F a c t s ( d e c l a r e ( s a l i e n c e 9 9 7 ) ) ? f f < - (NEW-FACT ? O O I S $?CCl ? C C ~ ?dd) => ( r e t r a c t ? f f ) ( i f (member NOT $ ? c c l ) t h e n ( b i n d ? d d ( - 1 ? d d ) ) ) ( i f (member VERY $ ? c c l ) t h e n ( b i n d ? d d ( * * ? d d O . 5 ) ) ) ( i f (member MORE-OR-LESS $?ccl) t h e n ( b i n d ? d d ( * * ?dd 2 ) ) ) (assert (?oo IS?ccZ?dd)

( ? o o I S N O T ? c c 2 = ( - l ? d d ) ) (?ooISVERY?cc2 = ( * * ? d d Z ) )

( ? O O I S NOTVERY ? C C Z = ( - 1 ( * * ?dd 2 ) ) ) (?OOISMORE-OR-LESS?CCZ=(** ?ddO. 5 ) )

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For example, let the input fact be (temperature is 18"C), the following fuzzy facts will be produced by fuzzification operations:

(temperature is HIGH 0.5) (temperature is MIDDLE 0.8) (temperature is LOW 0.0)

The fact (temperature is LOW 0.0) is not removed immediately, since some of its corresponding facts with linguistic hedges will have nonzero degrees. To enable fuzzy inference with linguistic hedges, the following fuzzy facts are generated by the control rules to replace the three original facts:

(temperature is HIGH 0.5) (temperature is NOT HIGH 0.5) (temperature is VERY HIGH 0.25) (temperature is NOT VERY HIGH 0.75) (temperature is MORE-OR-LESS HIGH 0.707) (temperature is NOT MORE-OR-LESS HIGH 0.293) (temperature is MIDDLE 0.8)

(temperature is NOT MIDDLE 0.2) (temperature is VERY MIDDLE 0.64) (temperature is NOT VERY MIDDLE 0.36) (temperature is MORE-OR-LESS MIDDLE 0.894) (temperature is NOT MORE-OR-LESS MIDDLE 0.106) (temperature is LOW 0.0)

(temperature is NOT LOW 1.0) (temperature is VERY LOW 0.0) (temperature is NOT VERY LOW 1 .O) (temperature is MORE-OR-LESS-LOW 0.0) (temperature is NOT MORE-OR-LESS LOW 1 .O)

111. EVALUATION OF THE NEW APPROACH

Some experiments concerning the diagnosis of Acute Exanthema were made to evaluate the new approach. The earlier knowledge base was constructed by applying the EMCUD method," and 47 rules are generated for 14 diseases. In Appendix A, it can be seen that there are lots of redundant rules although the test results (in Table I) seem to be desirable. With the new approach, 14 fuzzy rules are generated (as given in Appendix B) with the same test results.

IV. CONCLUSIONS

In this article, we propose a knowledge acquisition system, KAFES, for constructing fuzzy expert systems. We have applied KAFES to a medical application. According to our experience, it can be seen that the use of fuzzy concepts to represent expertise significantly reduces the redundant rules in the knowledge bases while achieving a promising performance. Moreover, it seems

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Table I. Test results of the knowledge base with redundant rules.a

Case number 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

Physician 12 3 3 1 2 1 1 4 2 6 5 5 3 1

Without redundant rules 12 X X X X X 14 X 6 X X 3 1

With redundant rules 12 3 3 1 2 1 1 4 2 6 5 5 3 1

Case number 14 15 16 17 18 19 20 21 22 23 24 25

Physician 6 6 1 2 5 8 9 1 4 1 3 4 1 2 1 4

Without redundant rules X X 12 5 X 9 14 13 4 1 2 14

With redundant rules 6 6 1 2 5 8 9 1 4 1 3 4 1 2 1 4

aThe codes of diseases and their translations are: I-Measles, 2-German measles, 3-Chickenpox, 4-Smallpox, 5-Scarlet fever, 6-Exanthem subitum, 7-Fifth disease, 8-Meningococcemia, 9-Rocky MI. spotted fever, 10-Typhus fevers, I I-Infectious mononucleosis, 12-Enterovirus infections, 13-Drug eruptions, and 14-Eczema herpeticum.

to be more natural and straightforward to represent knowledge of experts by fuzzy rules. Currently, we are trying to enhance the system by applying multimedia techniques. Some related studies, including the learning algorithm for the adjustment of membership functions, the improvement of inference methodologies, and the representation of multimedia knowledge bases, are in progress.

APPENDIX A: THE REPERTORY GRID FOR ACUTE EXANTHEMA D , - Measles D2 - German measles D3 - Chickenpox D4 - Smallpox D , - Scarlet D6 - Exanthem subitum D , - Fifth disease D8 - Meningococcemia D9 - Rocky Mt. spotted fever D l 0 - Typhus fevers D,, - Infectious mononucleosis D , , - Enterovirus infections D , , - Drug eruptions D , , - Eczema herpeticum Koplik’s spots 3-4 days of fever 1-2 days of fever Headache Flushed cheeks Vomiting Lymphadenopathy Red Maculopapular Deep lesion Centripetal Circumoral pallor Petechiae Splenomegaly Chills Sore throat Desauamation D l D 2 D 3 D4 D , D6 Ol 1 3 3 3 3 3 3 N o Koplik’s spots 1 5 3 3 4 1 5 Not 3-4days 3 5 4 4 2 3 5 Not 1-2days 3 3 1 1 3 3 3 No headache 3 3 3 3 3 3 1 No flushedcheeks 5 5 5 5 1 5 5 Novomiting 3 1 3 3 3 3 3 No Lymphadenopathy 1 2 2 2 1 2 1 Notred 3 3 5 1 3 3 3 Superficial 3 3 1 5 3 3 3 Centrifugal 5 5 5 5 1 5 1 No circumoral pallor 5 5 5 3 5 5 5 No petechiae 3 3 3 3 3 3 3 No Splenomegaly 3 5 3 1 3 3 5 No chills 3 3 3 1 3 3 3 No sore throat 1 5 3 3 1 3 3 No desauamation

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DS D9 D I O D I l D 1 2 D 1 3 D14 Koplik's spots 3 3 3 3 3 3 3 3-4days of fever 4 I 1 4 4 4 5 1-2 days of fever 2 4 2 2 1 2 5 Headache 3 1 1 3 3 3 3 Flushed cheeks 3 3 3 3 3 3 3 Vomiting 1 5 5 5 5 5 5 Lymphadenopathy 3 3 3 3 3 3 3 Red Maculopapular 2 2 2 2 2 2 2 Deep lesion 3 3 3 3 3 3 3 Centripetal 3 5 1 3 3 3 3 Circum. pallor 5 5 5 5 5 5 5 Petechiae 1 1 1 3 5 5 3 Splenomegal y 3 3 3 1 3 3 3 Chills 3 1 1 3 3 3 5 Sore throat 3 3 3 1 3 3 5 Desquamation 3 3 3 3 3 3 3 No Koplik's spots Not 3-4 days Not 1-2 days No headache No flushed cheeks No vomiting No Lymphadenopathy Not red Superficial Centrifugal No circumoral pallor No petechiae No Splenomegaly No chills No sore throat No desquamation

Rules generated from the Repertory Grids by EMCUD:

RULE,: I F THEN RULE,, ,: I F THEN RULE,,,: I F THEN RULE,,,: I F THEN RULE,: I F (Koplik'sspots = T) A (daysoffever 5 4 ) A (daysoffever 2 3 ) A (vomiting = Fj A (Maculopapularcolor = brickred) A (circumoralpallor = Fj A (petechiae = F ) A (desquamation = T ) Disease = Measles CF = 1 . 0 (Koplik'sspots = Tj ((daysoffever > 4 ) V (daysoffever < 3 ) ) A (vomiting = Fj A (Maculopapularcolor = brickredj A (circumoralpallor = Fj A (petechiae = Fj A (desquamation = T ) Disease = Measles CF = 0 . 8 (Koplik'sspots = T ) A (daysoffever 5 4 ) A (daysoffever 2 3 ) A (vomiting = F ) A (Maculopularcolor = brickred) A (circumoralpallor = F ) A (petechiae = T ) A (desquamation = T ) Disease = Measles CF = 0 . 9 (Koplik'sspots = T) A (daysoffever 5 4 ) A (daysoffever 2 3 ) A (vomiting = F ) A (Macu1opapularcolor = bri ckred) A (circumoralpallor = F) A (petechiae = F) A (desquamation = F ) Disease = Measles CF = 0 . 8 (daysoffever = 0 ) A

(vomi ting = F ) A (Lymphadenopathy = T ) A (Maculopapularcofor = pink) A (circumoralpal- l o r = F ) A

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THEN RULE2,1: IF THEN RULE2,2: IF THEN RULE,,,: IF THEN RULE,,,: IF THEN RULE,: IF THEN RULE,,,: IF THEN RULE,.,: IF THEN

(petechiae = F ) A (chills = F ) A (desquamation = F )

Disease = German Measles CF = 1.0

(daysoffever > 0 ) A (vomiting = F ) A (Lymphade- nopathy = T ) A

(Maculopapularcolor = p i n k ) A (circumoralpal- lor = F ) A

(petechiae = F ) A (chills = F ) A (desquama- tion = F )

Disease = German Measles CF = 0 . 8

(daysoffever = 0) A (vomiting = F ) A (Lymphade- nopathy = T ) A

(Maculopapularcolor = pink) A (circumoralpal- lor = F ) A

(petechiae = T ) A (chills = F ) A (desquama- tion = F )

Disease = German Measles CF = 0.9

(daysoffever = 0) A (vomiting = F ) A (Lymphade- nopathy = T ) A

(petechiae = F ) A (chills = T ) A (desquama- tion = F )

(daysoffever = 0 ) A (vomiting = F ) A (Lymphade- nopathy = T ) A

(Maculopapularcofor = pink) A (circumoralpal- l o r = F ) A

(petechiae = T ) A (chills = F ) A (desquama- tion = T )

(daysoffever 5 1) A (daysoffever > 0) A (head- ache = T ) A

(vomiting = F ) A (Maculopapufarcolor E {pink, red}) A

(lesiondegree = superficial) A (distribution = centripetal) A (circumoralpallor = F ) A (petechiae = F ) Disease = Chickenpox CF = 1 . 0 ((daysoffever > 1)

v

(daysoffever = 0 ) ) A (headache = T ) A (vomiting = F ) A (Maculopapularcolor E {pink, red}) A

(lesiondegree = superficial) A (distribution = centripetal) A

(circumoralpallor = F ) A (petechiae = F )

Disease = chickenpox CF = 0.8

(daysoffever 5 1) A (daysoffever > 0) A (head- ache = F ) A

(vomiting = F ) A (Maculopapularcolor E {pink, red}) A

(circumoralpallor = F ) A (petechiae = F )

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RULE,,,: IF THEN RULE,: IF THEN RULE,,,: I F THEN RULE,,,: IF THEN RULE,,,: IF THEN RULE,: IF THEN RULE,,,: IF

(daysoffever I 1) A (daysoffever > 0) A (head- ache = T ) A

(vomiting = F) (Maculopapularcolor E {pink, red}) A

(circumoralpallor = F ) r\ *petechiae = T) Disease = Chickenpox CF = 0 . 9

(daysoffever < 4 ) A (daysoffever 2 3 )

A

(head- ache = T ) A

(vomiting = F )

A

(Maculopapularcolor E {pink, red}) A

(lesiondegree = deepseated) A (distribution = centrifugal) A

(circumoralapplor = F ) A (chills = T ) A (sore- throat = T ) Disease = Smallpox CF = 1.0 ( (daysoffever 2 4 )

v

(daysoffever < 3 ) ) A (headache = T ) A (vomiting = F ) A (Maculopapularcolor E {pink, red}) A

(lesiondegree = deepseated) A (distribution = centrifugal)

A

(circumoralpallor = F ) A (chills = T ) A (sore- throat = T )

Disease = Smallpox CF = 0 . 8

(daysoffever < 4 ) A (daysoffever 2 3 ) A (head- ache = F ) A

(vomiting = F ) A Maculopapularcolor E {pink, red}) A

(lesiondegree = deepseated) A (distribution = centrifugal) A

(circumoralpallor = F ) A (chills = T ) A (sore- throat = T )

Disease = Smallpox CF = 0 . 8

(daysoffever < 4 ) A (daysoffever 2 3 ) A (head- ache = T ) A

(lesiondegree = deepseated) A (distribution = centrifugal A

(circumoralpallor = F ) (chills = T ) A (sore- throat = F )

Disease = Smallpox CF = 0 . 9

(daysoffever 5 2 ) A (daysoffever > 0 . 5 ) A (vom- iting = T ) A

(Maculopapularcolor = red) A (circumoralpallor = T ) A

(petechiae = F ) A (desquamation = T )

Disease = Scarlet fever CF = 1.0

((daysoffever > 2 )

v

(daysoffever 5 0 . 5 ) )

A

(vomiting = T ) A

(Maculopapularcolor = red) A (circumoralpall or = T ) A

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RULE,, 2 : RULE, : RULE,, : RULE,, 2 : RULE, : RULE,, : RULE, : RULE,, : RULE, : THEN IF THEN IF THEN IF THEN IF THEN IF THEN IF THEN IF THEN IF THEN IF

Disease = Scarlet fever CF = 0 . 8

(daysoffever 5 2 ) A (daysoffever > 0 . 5 ) A (vom- iting = T ) A

(Maculopapularcolor = red) A (circumoralpallor = T ) A

(petechiae = T ) A (desquamation = T )

Disease = Scarlet fever CF = 0 . 9

(daysoffever c: 4) A (daysoffever 2 3 ) A (vomit- ing = F ) A

(petechiae = F )

Disease = Exanthem subitum CF = 1. 0

( (daysoffever > 4)

v

(daysoffever < 3 ) ) A (vom- iting = F ) A

(Maculopapularcolor = pink) A (circumoralpal- l o r = F ) A

Disease = Exanthem subitum CF = 0.8

(daysoffever 5 4) A (daysoffever 2 3 ) A (vomit- ing = F ) A

(petechiae = T )

Disease = Exanthem subitum CF = 0 . 9

(daysoffever = 0 ) A (flushedcheeks = T ) A (vom- iting = F ) A

(Macul opapul arcol or = red) A (circumoralpall or = T ) A

(petechiae = F) A (chills = F) Disease = Fifth disease CF = 1. 0

(daysoffever = 0 ) A (flushedcheeks = T ) A (vom- iting = F ) A

(Macul opapul arcol or = red) A (circumoralpall or = T ) A

(petechiae = T ) A (chills = F ) Disease = Fifth disease CF = 0 . 8

(daysoffever < 1) A (daysoffever > 0 ) A (vomit- ing = F ) A

(Maculopapularcolor E {pink, red}) A (circumoral- pallor = F ) A

Disease = Meningococcemia CF = 1.0

( (daysoffever > 1)

v

(daysoffever = 0 ) ) A (vom- iting = T ) A

Disease = Meningococcemia CF = 0 . 8

(daysoffever 5 4) A (daysoffever 2 3) A (head- ache = T ) A

(vomiting = Fj A (Maculopapularcolor E {pink, red} j A

(distribution = centrifugal) A (circumoralpal- lor = F j A

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THEN RULE,, ,: IF THEN RULE,,: IF THEN RULE,,,,: IF THEN RULE,,: IF THEN RULE,,,,: IF THEN RULE,,,,: IF THEN RULE,,,,: IF THEN RULE,,: IF (petechiae = T) A (chills = T)

Disease = Rocky Mt. spots fever CF = 1 . 0 (daysoffever 5 4 ) A (daysoffever 2 3) A (head- ache = F ) A

(vomiting = F ) A (Maculopapularcolor E {pink, red}) A

(distribution = centrifugal) A (circumoralpal- lor = F ) A

(petechiae = T) A (chills = T )

Disease = Rocky Mt. spots fever CF = 0.8 (daysoffever 5 4) A (daysoffever 2 3 ) A (head- ache = T ) A

(vomiting = F )

A

(Maculopapularcolor E {pink, red}) A

(distribution = centripetal) A (circumoralpal- lor = F ) A

(petechiae = T ) A (chills = T) Disease = Typhus fevers CF = 1.0

(daysoffever 5 4) A (daysoffever 2 3 ) A (head- ache = F ) A

(distribution = centripetal) A (circumoralpal- l o r = F ) A

(petechiae = T ) A (chills = T)

Disease = Typhus fevers CF = 0 . 8

(daysoffever I 1) A (daysoffever > 0 )

A

(vomit- ing = F ) A

(Maculopapularcolor E {pink, red}) (circumoral- pallor = F ) A

(Splenomegaly = T ) A (sorethroat = T ) Disease = Infectious mononucleosis CF = 1.0

((daysoffever > 1)

v

(daysoffever = 0 ) ) A (vom- iting = F ) A

(Splenomegaly = T ) A (sorethroat = T )

Disease = Infectious mononucleosis CF = 0 . 8

(daysoffever 5 1) A (daysoffever > 0) A (vomit- ing = F ) A

(Maculopapularcolor E {pink, red}) A (circumoral- pallor = T ) A

(Splenomegaly = T ) A (sorethroat = T ) Disease = Infectious mononucleosis CF = 0 . 8

(daysoffever 5 1) A (daysoffever > 0 ) A (vomit- ing = F ) A

(Splenomegaly = T) A (sorethroat = F )

Disease = Infectious mononucleosis CF = 0 . 9 (daysoffever 5 2 ) A (daysoffever 2 1)

A

(vomit- ing = F ) A

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THEN RULE,,,,: I F RULE,, : RULE,, , 1 RULE,, : RULE,, , : RULE, : RULE, : RULE, : RULE, : RULE, : RULE, : RULE, : RULE, : THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F THEN I F

Disease = Enterovirus infections CF = 0 . 8 (daysoffever 5 2) A (daysoffever 2 1 ) A (vomit- ing = F ) A

(Macul opapul arcol or = pink) A (circumoralpal- l o r = F ) A

(petechiae = T )

Disease = Enterovirus infections CF = 0 . 6

(daysoffever 5 1) A (daysoffever > 0 ) A (vomit- ing = F ) A

(Maculopapularcolor = pink) (circumoralpall or =

F ) A

Disease = Drug eruptions CF = 0.8

(daysoffever 5 1) A (daysoffever > 0 ) A (vomit- ing = F ) A

(Maculopapularcol or = pink) (circumoralpall or =

F ) A

(petechiae = T )

Disease = Drug eruptions CF = 0 . 6 (daysoffever = 0) A (vomiting = F ) A

(chills = F ) A (sorethroat = F ) Disease = Eczema herpeticum CF = 0 . 8

(daysoffever = 0) A (vomiting = F ) A

(chills = F ) A (sorethroat = T ) Disease = Eczema herpeticum CF = 0.6

(WBC f low)

Disease = Measles CF = 0.2 (WBC # low)

Disease = Exanthem subitum CF = 0.2 ( WBC # low) A ( WBC f normal )

Disease = German measles CF = 0 . 2 ( Whil eBallCel lamount i5000)

WBC = low CF = 1 . 0

( Whi 1 eBal1 Cell amount 2 5000) A (WhileBallCellamount 5 10000)

WBC = normal CF = 1.0

(WhileBallCellamount > 10000) WC = highCF = 1.0

APPENDIX B: FUZZY RULES

(Koplik’s spots is definite) A (fever is seri- ous) A (vomiting is not apparent)A

(Maculopapular color is brick red) A (circu- moral pallor is not apparent) A

(petechiae is not apparent) A (desquamation is apparen t 1

Disease = Measles CF = 1.0

(fever is none) A (petechiae is not apparent)A (vomiting is not apparent) A (Lymphadenopathy is definite) A

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THEN RULE,: I F THEN RULE,: I F THEN RULE,: I F THEN RULE,: I F THEN RULE,: I F THEN RULE,: I F THEN RULE,: I F THEN ( M a c u l o p a p u l a r c o l o r i s p i n k ) A ( c i r c u m o r a l p a l - l o r i s n o t a p p a r e n t ) A ( c h i l l s i s n o t a p p a r e n t ) A ( d e s q u m a t i o n i s n o t a p p a r e n t ) D i s e a s e = German M e a s l e s CF = 1 . 0 ( f e v e r i s l i g h t ) A ( h e a d a c h e i s a p p a r e n t ) A ( v o m i t i n g i s n o t a p p a r e n t ) A ( M a c u l o p a p u l a r c o l o r i s more or l e s s r e d ) A ( l e s i o n d e g r e e i s s u p e r f i c i a l ) A ( d i s t r i b u t i o n i s c e n t r i p e t a l ) A ( c i r c u m o r a l p a l l o r i s not a p p a r e n t ) A ( p e t e - c h i a e i s n o t a p p a r e n t ) D i s e a s e = C h i c k e n p o x CF = 1 . 0 ( f e v e r i s s e r i o u s ) A ( h e a d a c h e i s a p p a r e n t ) A ( s o r e t h r o a t i s a p p a r e n t ) ( v o m i t i n g i s not a p p a r e n t ) A ( M a c u l o p a p u l a r c o l o r i s p i n k o r r e d ) A ( l e s i o n d e g r e e i s d e e p s e a t e d ) A [ d i s t r i b u t i o n i s c e n t r i f u g a l ) A ( c i r c u m o r a l p a l l o r i s not a p p a r e n t ) A ( c h i l l s i s a p p a r e n t ) A D i s e a s e = S m a l l p o x CF = 1. 0 ( f e v e r i s more o r l e s s s e r i o u s ) A (vomiting i s a p p a r e n t ) A ( M a c u l o p a p u l a r c o l o r i s r e d ) A ( c i r c u m o r a l p a l

-

l o r i s a p p a r e n t ) A ( p e t e c h i a e i s n o t a p p a r e n t ) A ( d e s q u a m a t i o n i s a p p a r e n t ) D i s e a s e = S c a r l e t f e v e r CF = 1 . 0 ( f e v e r i s s e r i o u s ) A (vomiting i s not a p p a r e n t ) A (Maculopapular color is p i n k ) ( c i r c u m o r a l p a l l o r i s n o t a p p a r e n t ) A ( p e t e - c h i a e i s not a p p a r e n t ) D i s e a s e = Exanthem subitum C F = 1 . 0 ( f e v e r i s n o n e ) A ( f l u s h e d cheeks i s a p p a r e n t ) A ( v o m i t i n g i s not a p p a r e n t ) A [ M a c u l o p a p u l a r color i s r e d ) A ( c i r c u m o r a l p a l - l o r i s a p p a r e n t ) A ( p e t e c h i a e i s n o t a p p a r e n t ) A [ c h i l l s i s not a p - p a r e n t ) D i s e a s e = F i f t h d i s e a s e C F = 1 . 0 ( f e v e r i s l i g h t ) A ( v o m i t i n g i s a p p a r e n t ) A ( p e t e c h i a e i s a p p a r e n t ) ( M a c u l o p a p u l a r c o l o r i s p i n k o r r e d ) A ( c i r c u - moral p a l l o r i s not a p p a r e n t ) A D i s e a s e = Meningococcemia C F = 1. 0 ( f e v e r i s s e r i o u s ) A ( h e a d a c h e i s a p p a r e n t ) A ( v o m i t i n g i s not a p p a r e n t ) A ( M a c u l o p a p u l a r c o l o r i s p i n k o r r e d ) A ( d i s t r i b u t i o n i s c e n t r i f u g a l ) A ( c i r c u m o r a l p a l - l o r i s not a p p a r e n t ) A ( p e t e c h i a e i s a p p a r e n t ) A ( c h i l l s i s a p p a r e n t ) D i s e a s e = R o c k y Mt. s p o t s f e v e r CF = 1 . 0

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RULE,,: RULE,, : RULE,, : RULE,,: RULE,, : I F THEN I F THEN I F THEN I F THEN IF THEN ( f e v e r i s s e r i o u s ) A ( h e a d a h c e i s a p p a r e n t ) A ( v o m i t i n g i s n o t a p p a r e n t ) A ( M a c u l o p a p u l a r c o l o r i s p i n k o r r e d ) A ( d i s t r i b u t i o n i s c e n t r i p e t a l ) A ( c i r c u m o r a l p a l - l o r i s n o t a p p a r e n t ) A ( p e t e c h i a e i s a p p a r e n t ) A ( c h i l l s i s a p p a r e n t ) D i s e a s e = T y p h u s f e v e r s CF = 1 . 0 ( f e v e r i s l i g h t ) A ( v o m i t i n g i s n o t a p p a r e n t ) A (Maculopapular c o l o r i s p i n k o r r e d ) A ( c i r - cumoral p a l l o r i s not a p p a r e n t ) A ( S p l e n o m e g a l y i s a p p a r e n t ) A ( s o r e t h r o a t i s ap- p a r e n t ) D i s e a s e = I n f e c t i o u s m o n o n u c l e o s i s CF = 1 . 0 ( f e v e r i s more o r l e s s s e r i o u s ) A (vomiting i s not a p p a r e n t ) A

(Maculopapular color is more or l e s s p i n k ) A ( c i r c u m o r a l p a l l o r i s n o t a p p a r e n t ) ( p e t e c h i a e i s not a p p a r e n t ) D i s e a s e = Enterovirus i n f e c t i o n s C f = 0 . 8 ( f e v e r i s l i g h t ) A ( v o m i t i n g i s n o t a p p a r e n t ) A ( p e t e c h i a e i s not a p p a r e n t ) ( M a c u l o p a p u l a r color i s more or l e s s p i n k ) ( c i r - cumoral p a l l o r i s not a p p a r e n t ) / D i s e a s e = Drug e r u p t i o n s CF = 0 . 8

[fever i s none) A ( v o m i t i n g i s not a p p a r e n t ) A (Maculopapular c o l o r i s more or l e s s p i n k ) A ( c i r c u m o r a l p a l l o r i s not a p p a r e n t )

( c h i l l s i s not a p p a r e n t ) A ( s o r e t h r o a t i s not a p p a r e n t )

D i s e a s e = Eczema h e r p e t i c u m CF = 0 . 8

This study was supported by the National Science Council, Republic of China, under the contract number: NSC82-0408-E-009-049.

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