- Email: [email protected]
Approximate knowledge in LEXIT, an expert system for assessing marine lubricant quality and diagnosing engine failures
Computers in Industry 17 (1991) 43-47 Elsevier
43
Forum on Fuzziness
Approximate knowledge in LEXIT, an expert system for assessing marine lubricant quality and diagnosing engine failures Jadranka Jakopovi6 INA Refiner), Rijeka, Product Development Department, Kostrena-Urinj, Croatia, Yugoslavia
Juraj Bo~iEevi6 Department of Measurement and Control, Institute of Chemical Engineering, Faculty of Technology, University of Zagreb, Pierottieva 6, Zagreb, Croatia, Yugoslavia
An approach to dealing with approximate knowledge while developing an expert system for assessing the quality of marine lubricant as well as diagnosing possible engine failures is introduced. The system is implemented by employing the theory of fuzzy sets and an originally developed algorithm. Keywords: Expert systems, Fuzzy relations, Fuzzy expert sys-
tems, Fuzzy logic, Marine engine, Failure diagnosis.
I. Introduction
Today expert systems represent a valuable supporting tool for many domains, and by employing the expert knowledge many problems can be solved quickly and easily [1]. The recently developed expert system LEXIT (Lubricant, EXpert, INA-Refinery Rijeka and Faculty of Technology, University of Zagreb) [2] is introduced with particular attention to its development and the application of the theory of fuzzy sets. The first step in creating an expert system is to apply the expert's knowledge in a specific domain [3]. Although documented and organized knowledge is available in many technical domains, it is
not sufficient to build an expert system. It is also important to recognize the fact that a large part of expertise consists of heuristic knowledge, which relies for a great deal upon subjective judgements and may include incomplete, ambiguous and imprecise information. As a consequence, the application of such uncertain knowledge results in inexact reasoning the expert system has to deal with. There are numerous methods which show how the expert system copes with uncertain knowledge and inexact reasoning [4-8]. Generally it can be said that the theory of probability is employed to solve the problems of plausible reasoning while fuzzy set theory [9] is used to solve the problems of approximate reasoning. Approximate reasoning, as opposed to plausible reasoning, means drawing conclusions by taking into account the linguistic consistency of the facts. In all expert systems based on symbolic manipulation and plausible reasoning, uncertainty resides in the state of our knowledge. In expert systems based on semantic manipulation and approximate reasoning, the emphasis is on fuzziness viewed as an intrinsic property of the natural language [10]. The processing of engineers' experience by linguistic fuzzy models
0166-3615/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved
44
Forumon Fuzziness
Computers in Industry
is already in use [2,11 21] and in our work it served as an useful reference.
experts have their own way of recognizing the correct conclusions, by following the established patterns.
2. Fuzzy model of expert's reasoning
The experts c o m m e n t o n a single analytical result, of course in the context of the p a t t e r n of evidences u n d e r consideration, by m a p p i n g its n u m e r i c a l value into a linguistic form, usually expressed by fuzzy terms like " h i g h " , " n o r m a l " or "low".
(ii) Symbolic representation of numerical values.
The acquisition of knowledge a n d its conceptualization are considered as the first steps in creation of a knowledge base for automatic interpretation laboratory analyses of marine diesel engine l u b r i c a n t a n d for the establishment of a correlation between the c o n d i t i o n of the oil a n d possible failures. In order to follow the characteristics of the expert's reasoning from the s t a n d p o i n t of knowledge engineering, it is necessary to investigate a n d study three i m p o r t a n t areas of expert knowledge: (i) The application of heuristics. The experts skilfully compare the results of an analysis of oil with previous experience and make a quick a n d correct choice a m o n g the evidences. They j u d g e the relevant data, reject r e d u n d a n c i e s and collect new pieces of evidence for final assessment. The
Jadranka Jakopovi6 received her Dip. lng. and MSc in Chemical Engineering from the University of Zagreb. She " is a member of the research staff at the Product Development Department of INA Refinery Rijeka, and her current work includes the application of computers in chemical engineeringand product development. AI and expert systems are her particular interests.
(iii) Consideration of time-varying component. Every conclusion that has been reached is p u t into the context of the overall analytical a n d perform a n c e history of the oil u n d e r exploitation. In other words, the experts have to deal with timevarying data.
3. Knowledge base and fuzzy inference The elicited knowledge, which allows interpretation and diagnostics, is organized in the knowledge base as a set of fuzzy c o n d i t i o n a l statements that relate test results to conclusions a b o u t oil c o n d i t i o n or possible failures. The natural, logical way of reasoning a n d data reduction is applied. At the first level, a statement which estimates the possible situation based on the analytical i n p u t data is selected. Then, at the second level, adequate additional i n p u t data are collected a n d the situation is specified more closely. The fuzzy conditional statements are of the form: If A1, I a n d A1,2 a n d ... and A~, N then B~ or If Az, I and A2. 2 a n d ... a n d A2. N then B 2 or
Juraj Bo~ii~evi~received his Dipl. Ing. and Dr. Tech. Sci. degrees at the University of Zagreb. He is Professor and Head of the Department of Measurement and Control at the Faculty of Technology, University of Zagreb. He has been acting as UNESCO expert at the Philippines, where he founded the First Philippines National Institute for Instrumentation and Control. He has been visiting professor, fellow, lecturer etc., in the Netherlands, Norway, UK, USA, France etc., UNIDO expert, and UNESCO expert. Since 1967 he has founded and chaired graduate and postgraduate studies and has educated numerous engineers and scientists pushing permanently his coworkers to follow the frontiers of science. As the Chairman of IMEKO TC II for Developing Countries he has founded the International IMEKO School of Measurement "Measurement Training for Transfer of Practical Experience" in 1980 and since then he has been transferring knowledge and engineering skills to engineers in developing countries. Dr. Bo~.i~evi6has published extensively,and he is author of numerous scientific and professional papers and books, editor of proceedings, vocabularies etc. His current research interests, are intelligent measurements and AI.
If AM. 1 a n d AM. 2 and ... AM. N then BM,
(1)
where A,,/ is a linguistic variable. A linguistic variable is a variable whose value can be presented by a linguistic term used by experts such as " h i g h " , " n o r m a l " or "low". Its value can be presented by a fuzzy set [9] which permits the d e f i n i t i o n of a m e m b e r s h i p f u n c t i o n /~, reflecting the degree to which an element belongs to the set. The m e m b e r ship function for elicited expert knowledge a b o u t the fuzzy test limits can be represented b y a piecewise linear function [13,21-24]. Such a function is presented in Fig. 1. The four values a, b, c, a n d d are numerical values stated by the experts in the process of knowledge acquisition [22-24]. B i is a possible conclusion.
Computers in Industry
J. Jakopovid, J. Bo#i?evid
03
E
b
c
d
Vorioble
Fig. 1. Representation of the fuzzyfunction. Since the value Ai, I is represented by a fuzzy set, it is possible to associate it with the grade of membership of conclusion by means of rules of fuzzy logic, even in cases where the input value A~ is not equal to that in the implication part of the rule, as contrary to the " m o d u s ponens" of traditional logic [6,9,10]: A*
input value
A ---, B
fuzzy statement
A*o( A --, B) = B*
fuzzy conclusion.
(2)
The truthfulness designated as a grade of membership for this simple implication is evaluated through the operation called composition and provided by the m i n - m a x operator:
r n s . ( y ) = max(min(mA. ( x ) , mAxB(X, Y))).
(3) Another way of writing eqn. (3) is:
-,..(y) = min(m,(y), max(min(mA(x),
mA.(X)))).
(4) The practical solution of eqn. (3) suggested by us, for rn 8 = 1 as in our case, is shown in Fig. 2. The explanation is as follows:
o, ~ = ~ )
/J /'
45
As the fuzzy set A is defined by four values a, b, c, d and by their membership degrees, the two lines of different slope and known equation describing this set are y( + ) and y ( - ). Similarly, as the set A* is also fuzzy, taking into account the measuring errors that may occur, it is described by the lines y * ( + ) and y * ( - ) . The maximum ordinate of the intersection (z) between these two sets can be found by means of the following three rules:
o~ 03 1D
o
/ A p p r o x i m a t e knowledge in expert systems
(1) If 2(1,2 ) ~ 1 then rnB.(y (2) If zo,2) > 1 then rnB.(y (3) If zd,2~ > 1 then rnB.(y
and Z(2d) > 1
) = z <~ 1. and z~2,1) > 1
) = 1. and z~2,1) ~ 1 ) = O.
The quantitative analysis of the possibility of a certain situation in the system described by the rules (1) is made through the evaluation of its grade of membership according to the equation: mB.(y)=
max ( m i n ( m , , ( y ) ,
l <~i <~rn
min ( m a x ( m i n ( m ~ t ( x j ) ,
1 <~j~
rn,,/(xj)))))),
(5) taking into account the solution for the intersections mentioned above. Since each Bi (i = 1, 2 . . . . . n) in the rules (1) can be considered as a fuzzy singleton over a domain consisting of certain situations y, the starting value for roB, while evaluating m o . ( y ) at the first level is 1, and at the second level the evaluated m B.(y ) becomes the starting value. The uncertainty of the knowledge in the knowledge base is taken into consideration by giving different weight factors to fuzzy conditional statements. The choice of weight factors is rather subjective.
'x
/' ..............
T
mB
/
A
",
i
a = r ~ z, and z, = o,b,c,d =
b
i ..........
~-r
c
4. Implementation and verification of the expert system
A*
z~ =
~
d
~+r
~
(~)
x
measured value r e p a t i b i l i t y of m e a s u r e m e n t i n t e r s e c t i o n of two lines y ond y* p r e d e t e r m i n e d v a l u e s f o r d e f i n i t i o n o f f u z z y sets
Fig. 2. Determination of the maximum ordinate of intersection between A and A*.
LEXIT is based on the Pascal programming language and has a friendly menu-driven user interface. The main characteristics of the system performance are: - automatic interpretation of relations among the test results and possible situations pointing out the condition of oil and engine failures;
46
Forum on Fuzziness
- detailed explanation of how the particular conclusion has been reached; indication of the possible causes of failures; - description of the possible consequences; - recommendation for engine maintenance and repair under new circumstances; - recommendation regarding maintenance of proper oil quality. It is also possible to monitor the overall analytical and diagnostic history of the particular oil-engine system owing to a connection with a database containing all relevant information on samples of the oils under exploitation. Furthermore LEXlT allows monitoring and interpreting the time trends of selected analytical properties such as the metal content of oil, which is an important indication of possible engine wear. The system has been tested and evaluated very carefully in numerous practical situations which have been interpreted by independent experts. A high degree of agreement of the expert system's advice and the expert's advice has been obtained, but it is still possible that the long-term tests will lead to additional improvements.
5. Conclusion An evident advantage of applying a fuzzy set theory approach in the expert system LEXIT is the possibility of representing numeric and linguistic variables in a uniform way and of using a sound formalism to handle them. The tests have shown that LEXIT performs excellently and that the use of the fuzzy model is justified. LEXIT has confirmed the advantage of generalizing the conventional set theory. Because of this generalization, the fuzzy set theory has wider scope of application than the conventional one when solving problems which involve, to some degree subjective evaluation.
Acknowledgement The research reported here was supported in part by the Croatian Science Foundation through grant 2-99-027.
Computers in lndusto"
References [1] D.A. Waterman, A Guide to Expert Systems, AddisonWesley, Reading, MA, 1986. [2] M. Dohnal. "Fuzzy simulation of industrial problems"+ Computers in Industt:v, Vol. 4, No. 4, 1983, pp. 347 352. [31 A. Hart, Knowledge Acquisition for Expert Systems, McGraw-Hill, New York, 1986. [4] P.P. Bonissone and R.M. Tong, "'Reasoning with uncertainty in expert systems", Int. J. Man Mach. Stud., Vol. 22+ 1985, pp. 241 250. [5] A. Durra, "Reasoning with imprecise knowledge in expert systems", Inf. Sci., Vol. 37, 1985, pp. 3-24. [6] N.S. Lee, Y.L. Grize and K. Dehnald, "'Quantitative models for reasoning under uncertainty in knowledgebased expert systems", Int. J. lntell. Syst., Vol. 2, 1987+ pp. 15 38. [7] H. Prade, "A computation approach to approximate and plausible reasoning with applications to expert systems", IEEE Trans. Pattern Anal. Mach. lntell., Vol. PAMI-7. 1985, pp. 260 283. [8] H.E. Stephanou and A.P. Sage, "'Perspectives on imperfect information processing", IEEE Trans. 5~vst. Man (~vbern.. Vol. SMC-17, 1987, pp. 780-798. [9] L.A. Zadeh, "'Fuzzy sets", Inf. Control, Vol. 8. 1965, pp. 338 353. [10] C.V. Negoita, Expert S~vstems and Fuzzy Systems, Benj a m i n / C u m m i n g s , London, 1985. [11] T.E. Ayral, "On-line expert systems for process control", Hvdroearbon Process., Vol. 68+ No. 6, 1989+ pp. 33 61. [12] M. Dohnal, '+Linguistic and fuzzy models", Computers in lndusto'+ Vol. 4, No. 4+ pp. 341 345. [13] M. Dohnal, "A versatile expert system SENECA in chemical system engineering", Coll. C=ech. Chem. Commun., Vol. 51, No. 5, 1986, pp. 1027-1039. [14] L.T. Fan, M.M. Gharpuray and Y.W. Huang, "'Sequencing a separation via fuzzy heuristics", Chem. Eng. J., Vol. 94, No. 3, 1987, pp. 57-59. [15] P.M. Larsen, "Industrial applications of fuzzy logic control", in: E.M. Mamdani and B.R. Gaines (eds.), Fuz:v Reasoning and Its Applieattons, Academic Press, New York, 1981, pp. 335--342. [16] E.M. Mamdani and S. Assilian, " A n experiment in linguistic synthesis with a fuzzy logic controller", in: E.M. Mamdani and B.R. Gaines (eds.), Fuzzy Reasoning and Its Applications, Academic Press, New York, 1981, pp. 311 323. [17] E.H. Mamdani, "Advances in the linguistic synthesis of fuzzy controllers", in: E + M . M a m d a n i and B.R. Gaines (eds.), Fuzzy Reasoning and Its Applications, Academic Press, New York, 1981, pp. 325-333. [18] N. Togai and H. Watanabe, "A VLSI implementation of fuzzy interference engine: Toward an expert system on a chip", in: C.R. Weisbin (ed.), Artificial Intelligence Applications. The Engineering of Knowledge-Based Systems (Proc. 2nd Conf., Miami Beach. FL, December 1985). IEEE Computer Society Press/North-Holland, Amsterdam, 1985. [19] R.M. Tong, +'Fuzzy control systems: A retrospective". American Control Conf., San Francisco, June 1983, pp. 1224
- 1229.
Computers in Industry
J. Jakopovi(, J. Bo~i?evi( / Approximate knowledge in expert systems
[20] I. Turunen, T. Nyberg, J. Jaervelainen, Y.Y. Linko, P. Linko and M. Dohnal, "Fuzzy modelling in biotechnology: Sucrose inversion", Chem. Eng. J., Vol. 30, 1985, pp. B51- B60. [21] P. Vaija, J. Jaervelainen and M. Dohnal, "Multilevel failure detection system", Computers in Industry, Vol. 6, No. 4, 1985, pp. 253-263. [22] J. Bo~.i~evi6 and J. Jakopovi6, "A project on knowledgebased technical diagnostics of ship engines", Internal Note, Department of Measurement and Control, Institute of Chemical Engineering, University of Zagreb, Yugoslavia, 1988.
47
[23] J. Jakopovi6 and J. Bo~i~evi6, "Fuzzy modelling approach in the decision support knowledge-based system for condition-based maintenance of ship engines", in: Conf. Proc. on Modelling, Identification and Control, IASTED, Innsbruck, Austria, 1990. [24] J. Jakopovic, "Expert system supported condition-based diagnostics of ship engines", MSc Thesis, Faculty of Technology, University of Zagreb, Yugoslavia, May 1990 (in Croatian).
43
Forum on Fuzziness
Approximate knowledge in LEXIT, an expert system for assessing marine lubricant quality and diagnosing engine failures Jadranka Jakopovi6 INA Refiner), Rijeka, Product Development Department, Kostrena-Urinj, Croatia, Yugoslavia
Juraj Bo~iEevi6 Department of Measurement and Control, Institute of Chemical Engineering, Faculty of Technology, University of Zagreb, Pierottieva 6, Zagreb, Croatia, Yugoslavia
An approach to dealing with approximate knowledge while developing an expert system for assessing the quality of marine lubricant as well as diagnosing possible engine failures is introduced. The system is implemented by employing the theory of fuzzy sets and an originally developed algorithm. Keywords: Expert systems, Fuzzy relations, Fuzzy expert sys-
tems, Fuzzy logic, Marine engine, Failure diagnosis.
I. Introduction
Today expert systems represent a valuable supporting tool for many domains, and by employing the expert knowledge many problems can be solved quickly and easily [1]. The recently developed expert system LEXIT (Lubricant, EXpert, INA-Refinery Rijeka and Faculty of Technology, University of Zagreb) [2] is introduced with particular attention to its development and the application of the theory of fuzzy sets. The first step in creating an expert system is to apply the expert's knowledge in a specific domain [3]. Although documented and organized knowledge is available in many technical domains, it is
not sufficient to build an expert system. It is also important to recognize the fact that a large part of expertise consists of heuristic knowledge, which relies for a great deal upon subjective judgements and may include incomplete, ambiguous and imprecise information. As a consequence, the application of such uncertain knowledge results in inexact reasoning the expert system has to deal with. There are numerous methods which show how the expert system copes with uncertain knowledge and inexact reasoning [4-8]. Generally it can be said that the theory of probability is employed to solve the problems of plausible reasoning while fuzzy set theory [9] is used to solve the problems of approximate reasoning. Approximate reasoning, as opposed to plausible reasoning, means drawing conclusions by taking into account the linguistic consistency of the facts. In all expert systems based on symbolic manipulation and plausible reasoning, uncertainty resides in the state of our knowledge. In expert systems based on semantic manipulation and approximate reasoning, the emphasis is on fuzziness viewed as an intrinsic property of the natural language [10]. The processing of engineers' experience by linguistic fuzzy models
0166-3615/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved
44
Forumon Fuzziness
Computers in Industry
is already in use [2,11 21] and in our work it served as an useful reference.
experts have their own way of recognizing the correct conclusions, by following the established patterns.
2. Fuzzy model of expert's reasoning
The experts c o m m e n t o n a single analytical result, of course in the context of the p a t t e r n of evidences u n d e r consideration, by m a p p i n g its n u m e r i c a l value into a linguistic form, usually expressed by fuzzy terms like " h i g h " , " n o r m a l " or "low".
(ii) Symbolic representation of numerical values.
The acquisition of knowledge a n d its conceptualization are considered as the first steps in creation of a knowledge base for automatic interpretation laboratory analyses of marine diesel engine l u b r i c a n t a n d for the establishment of a correlation between the c o n d i t i o n of the oil a n d possible failures. In order to follow the characteristics of the expert's reasoning from the s t a n d p o i n t of knowledge engineering, it is necessary to investigate a n d study three i m p o r t a n t areas of expert knowledge: (i) The application of heuristics. The experts skilfully compare the results of an analysis of oil with previous experience and make a quick a n d correct choice a m o n g the evidences. They j u d g e the relevant data, reject r e d u n d a n c i e s and collect new pieces of evidence for final assessment. The
Jadranka Jakopovi6 received her Dip. lng. and MSc in Chemical Engineering from the University of Zagreb. She " is a member of the research staff at the Product Development Department of INA Refinery Rijeka, and her current work includes the application of computers in chemical engineeringand product development. AI and expert systems are her particular interests.
(iii) Consideration of time-varying component. Every conclusion that has been reached is p u t into the context of the overall analytical a n d perform a n c e history of the oil u n d e r exploitation. In other words, the experts have to deal with timevarying data.
3. Knowledge base and fuzzy inference The elicited knowledge, which allows interpretation and diagnostics, is organized in the knowledge base as a set of fuzzy c o n d i t i o n a l statements that relate test results to conclusions a b o u t oil c o n d i t i o n or possible failures. The natural, logical way of reasoning a n d data reduction is applied. At the first level, a statement which estimates the possible situation based on the analytical i n p u t data is selected. Then, at the second level, adequate additional i n p u t data are collected a n d the situation is specified more closely. The fuzzy conditional statements are of the form: If A1, I a n d A1,2 a n d ... and A~, N then B~ or If Az, I and A2. 2 a n d ... a n d A2. N then B 2 or
Juraj Bo~ii~evi~received his Dipl. Ing. and Dr. Tech. Sci. degrees at the University of Zagreb. He is Professor and Head of the Department of Measurement and Control at the Faculty of Technology, University of Zagreb. He has been acting as UNESCO expert at the Philippines, where he founded the First Philippines National Institute for Instrumentation and Control. He has been visiting professor, fellow, lecturer etc., in the Netherlands, Norway, UK, USA, France etc., UNIDO expert, and UNESCO expert. Since 1967 he has founded and chaired graduate and postgraduate studies and has educated numerous engineers and scientists pushing permanently his coworkers to follow the frontiers of science. As the Chairman of IMEKO TC II for Developing Countries he has founded the International IMEKO School of Measurement "Measurement Training for Transfer of Practical Experience" in 1980 and since then he has been transferring knowledge and engineering skills to engineers in developing countries. Dr. Bo~.i~evi6has published extensively,and he is author of numerous scientific and professional papers and books, editor of proceedings, vocabularies etc. His current research interests, are intelligent measurements and AI.
If AM. 1 a n d AM. 2 and ... AM. N then BM,
(1)
where A,,/ is a linguistic variable. A linguistic variable is a variable whose value can be presented by a linguistic term used by experts such as " h i g h " , " n o r m a l " or "low". Its value can be presented by a fuzzy set [9] which permits the d e f i n i t i o n of a m e m b e r s h i p f u n c t i o n /~, reflecting the degree to which an element belongs to the set. The m e m b e r ship function for elicited expert knowledge a b o u t the fuzzy test limits can be represented b y a piecewise linear function [13,21-24]. Such a function is presented in Fig. 1. The four values a, b, c, a n d d are numerical values stated by the experts in the process of knowledge acquisition [22-24]. B i is a possible conclusion.
Computers in Industry
J. Jakopovid, J. Bo#i?evid
03
E
b
c
d
Vorioble
Fig. 1. Representation of the fuzzyfunction. Since the value Ai, I is represented by a fuzzy set, it is possible to associate it with the grade of membership of conclusion by means of rules of fuzzy logic, even in cases where the input value A~ is not equal to that in the implication part of the rule, as contrary to the " m o d u s ponens" of traditional logic [6,9,10]: A*
input value
A ---, B
fuzzy statement
A*o( A --, B) = B*
fuzzy conclusion.
(2)
The truthfulness designated as a grade of membership for this simple implication is evaluated through the operation called composition and provided by the m i n - m a x operator:
r n s . ( y ) = max(min(mA. ( x ) , mAxB(X, Y))).
(3) Another way of writing eqn. (3) is:
-,..(y) = min(m,(y), max(min(mA(x),
mA.(X)))).
(4) The practical solution of eqn. (3) suggested by us, for rn 8 = 1 as in our case, is shown in Fig. 2. The explanation is as follows:
o, ~ = ~ )
/J /'
45
As the fuzzy set A is defined by four values a, b, c, d and by their membership degrees, the two lines of different slope and known equation describing this set are y( + ) and y ( - ). Similarly, as the set A* is also fuzzy, taking into account the measuring errors that may occur, it is described by the lines y * ( + ) and y * ( - ) . The maximum ordinate of the intersection (z) between these two sets can be found by means of the following three rules:
o~ 03 1D
o
/ A p p r o x i m a t e knowledge in expert systems
(1) If 2(1,2 ) ~ 1 then rnB.(y (2) If zo,2) > 1 then rnB.(y (3) If zd,2~ > 1 then rnB.(y
and Z(2d) > 1
) = z <~ 1. and z~2,1) > 1
) = 1. and z~2,1) ~ 1 ) = O.
The quantitative analysis of the possibility of a certain situation in the system described by the rules (1) is made through the evaluation of its grade of membership according to the equation: mB.(y)=
max ( m i n ( m , , ( y ) ,
l <~i <~rn
min ( m a x ( m i n ( m ~ t ( x j ) ,
1 <~j~
rn,,/(xj)))))),
(5) taking into account the solution for the intersections mentioned above. Since each Bi (i = 1, 2 . . . . . n) in the rules (1) can be considered as a fuzzy singleton over a domain consisting of certain situations y, the starting value for roB, while evaluating m o . ( y ) at the first level is 1, and at the second level the evaluated m B.(y ) becomes the starting value. The uncertainty of the knowledge in the knowledge base is taken into consideration by giving different weight factors to fuzzy conditional statements. The choice of weight factors is rather subjective.
'x
/' ..............
T
mB
/
A
",
i
a = r ~ z, and z, = o,b,c,d =
b
i ..........
~-r
c
4. Implementation and verification of the expert system
A*
z~ =
~
d
~+r
~
(~)
x
measured value r e p a t i b i l i t y of m e a s u r e m e n t i n t e r s e c t i o n of two lines y ond y* p r e d e t e r m i n e d v a l u e s f o r d e f i n i t i o n o f f u z z y sets
Fig. 2. Determination of the maximum ordinate of intersection between A and A*.
LEXIT is based on the Pascal programming language and has a friendly menu-driven user interface. The main characteristics of the system performance are: - automatic interpretation of relations among the test results and possible situations pointing out the condition of oil and engine failures;
46
Forum on Fuzziness
- detailed explanation of how the particular conclusion has been reached; indication of the possible causes of failures; - description of the possible consequences; - recommendation for engine maintenance and repair under new circumstances; - recommendation regarding maintenance of proper oil quality. It is also possible to monitor the overall analytical and diagnostic history of the particular oil-engine system owing to a connection with a database containing all relevant information on samples of the oils under exploitation. Furthermore LEXlT allows monitoring and interpreting the time trends of selected analytical properties such as the metal content of oil, which is an important indication of possible engine wear. The system has been tested and evaluated very carefully in numerous practical situations which have been interpreted by independent experts. A high degree of agreement of the expert system's advice and the expert's advice has been obtained, but it is still possible that the long-term tests will lead to additional improvements.
5. Conclusion An evident advantage of applying a fuzzy set theory approach in the expert system LEXIT is the possibility of representing numeric and linguistic variables in a uniform way and of using a sound formalism to handle them. The tests have shown that LEXIT performs excellently and that the use of the fuzzy model is justified. LEXIT has confirmed the advantage of generalizing the conventional set theory. Because of this generalization, the fuzzy set theory has wider scope of application than the conventional one when solving problems which involve, to some degree subjective evaluation.
Acknowledgement The research reported here was supported in part by the Croatian Science Foundation through grant 2-99-027.
Computers in lndusto"
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Computers in Industry
J. Jakopovi(, J. Bo~i?evi( / Approximate knowledge in expert systems
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