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A Framework of Fuzzy Diagnosis
December 2004 (vol. 16 no. 12)
pp. 1571-1582
Fault diagnosis has become an important component in intelligent systems, such as intelligent control systems and intelligent eLearning systems. Reiter's diagnosis theory, described by first-order sentences, has been attracting much attention in this field. However, descriptions and observations of most real-world situations are related to fuzziness because of the incompleteness and the uncertainty of knowledge, e.g., the fault diagnosis of student behaviors in the eLearning processes. In this paper, an extension of Reiter's consistency-based diagnosis methodology, Fuzzy Diagnosis, has been proposed, which is able to deal with incomplete or fuzzy knowledge. A number of important properties of the Fuzzy diagnoses schemes have also been established. The computing of fuzzy diagnoses is mapped to solving a system of inequalities. Some special cases, abstracted from real-world situations, have been discussed. In particular, the fuzzy diagnosis problem, in which fuzzy observations are represented by clause-style fuzzy theories, has been presented and its solving method has also been given. A student fault diagnostic problem abstracted from a simplified real-world eLearning case is described to demonstrate the application of our diagnostic framework.

[1] R. Reiter, “A Theory of Diagnosis from First Principle,” Artificial Intelligence, vol. 32, no. 1, pp. 57-95, 1987.
[2] J. de Kleer and B.C. Williams, “Diagnosing Multiple Faults,” Artificial Intelligence, vol. 32, no. 1, pp. 97-130, 1987.
[3] J. de Kleer et al., “Characterizing Diagnoses and Systems,” Artificial Intelligence, vol. 56, pp. 192-222, 1992.
[4] P.M. Frank and B. Koppen-Seliger, “New Developments Using AI in Fault Diagnosis,” Eng. Applications of Artificial Intelligence, vol. 10, no. 1, pp. 3-14, 1997.
[5] P.M. Frank and B. Koppen-Seliger, “Fuzzy Logic and Neural Network Applications to Fault Diagnosis,” Int'l J. Approximate Reasoning, vol. 16, pp. 67-88, 1996.
[6] Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, B.G. Buchanan and E.H. Shortliffe, eds., Reading, Mass.: Addison-Wesley, 1984.
[7] D.L. Poole et al., “Theorist: A Logic Reasoning System for Defaults and Diagnosis,” The Knowledge Frontier: Essays in the Representation of Knowledge, N. Cercone and G. McCalla, eds., pp. 331-352, Springer Verlag, 1987.
[8] D. Poole, “Representing Knowledge for Logic-Based Diagnosis,” Proc. Int'l Conf. Fifth Generation Computing Systems, pp. 1282-1290, 1988.
[9] D. Poole, “Explanation and Predication: An Architecture for Default and Abductive Reasoning,” Technical Report 89-4, Computer Science U.B.C., 1989.
[10] B. El Ayeb et al., “A New Diagnosis Approach by Deduction and Abduction,” Proc. Int'l Workshop Expert Systems in Eng., 1990.
[11] C. Boutillier, “Abduction to Plausible Causes: An Event Based Model of Belief Update,” Artificial Intelligence, vol. 83, pp. 143-166, 1996.
[12] C. Boutillier and V. Becher, “Abduction as Belief Revision,” Artificial Intelligence, vol. 77, pp. 43-94, 1995.
[13] R. Reggia, “Diagnostic Expert System Based on a Set Covering Model,” Int'l J. Man Machine Studies, vol. 19, no. 5, pp. 437-460, 1983.
[14] T. Eiter et al., “Semantics and Complexity of Abduction from Default Theories,” Artificial Intelligence, vol. 90, pp. 177-223, 1990.
[15] D. Poole, “Normality and Faults in Logic-Based Diagnosis,” Proc. 11th Int'l Joint Conf. Artificial Intelligence (IJCAI-89), pp. 1304-1310, 1989.
[16] L. Console et al., “A Theory of Diagnosis for Incomplete Causal Models,” Proc. 11th Int'l Joint Conf. Artificial Intelligence (IJCAI-89), pp. 1311-1317, 1989.
[17] P. Struss and O. Dressler, “Physical Negation— Integrating Fault Models into General Diagnostic Engine,” Proc. Int'l Joint Conf. Artificial Intelligence (IJCAI-89), pp. 1318-1323, 1989.
[18] E. Naito et al., “A Proposal of a Fuzzy Connective with Learning Function,” Fuzziness Database Management Systems, P. Bosc and J. Kaczprizk, eds., pp. 345-364, 1995.
[19] L.A. Zadeh, “Fuzzy Sets,” Inform. and Control, vol. 8, pp. 338-353, 1965.
[20] L.I. Kuncheva and F. Steimann, “Fuzzy Diagnosis,” Artificial Intelligence in Medicine, vol. 16, pp. 121-128, 1999.
[21] K. Yamada and M. Mukaidono, “Fuzzy Abduction Based on Lukasiewicz Infinite-Valued Logic,” Proc. Fuzzy-IEEE/IFES'95, pp. 343-350, 1995.
[22] N. Sano and R. Takahashi, “Natural Language Input for Fuzzy Diagnosis,” Advances in Soft Computing— Fuzzy Control: Theory and Practice, R. Hampel et al., eds., pp. 265-273, 2000.
[23] N. Sano and R. Takahashi, “Solution on Fuzzy Diagnosis by Inverse Process,” Proc. Sixth Zittau Fuzzy-Colloquium, pp. 7-12, 1998.
[24] U.M. Isermann, “Design of a Fuzzy-Logic Based Diagnostic Model for Technical Processes,” Fuzzy Sets and Systems, vol. 58, no. 3, pp. 249-271, 1993.
[25] P. Vojtas, “Fuzzy Logic Programming,” Fuzzy Sets and Systems, vol. 124, pp. 361-370, 2001.
[26] G. Gottlob and Z. Ming, “Cumulative Default Logic: Characterization, Algorithms, and Complexity,” Artificial Intelligence, vol. 69, pp. 329-345, 1994.
[27] J.W. Lloyd, Foundation of Logic Programming. Springer, 1987.
[28] P. Hajek, Metamathematics of Fuzzy Logic. Kluwer, 1998.
[29] D. Xu et al., “Intelligent Student Profiling with Fuzzy Models,” Proc. 35th Hawaii Int'l Conf. System Science (HICSS '35), 2002. (CD-ROM.)

Index Terms:
Knowledge representation, fuzzy diagnosis, fault diagnosis, uncertainty reasoning, fuzzy truth function logic, clause-style fuzzy theories.
Huaiqing Wang, Mingyi Zhang, Dongming Xu, Dan Zhang, "A Framework of Fuzzy Diagnosis," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 12, pp. 1571-1582, Dec. 2004, doi:10.1109/TKDE.2004.80
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