This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Knowledge Representation Using Fuzzy Petri Nets
September 1990 (vol. 2 no. 3)
pp. 311-319

A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy production rule describes the fuzzy relation between two propositions. Based on the fuzzy Petri net model, an efficient algorithm is proposed to perform fuzzy reasoning automatically. It can determine whether an antecedent-consequence relationship exists from proposition d/sub s/ to proposition d/sub j/, where d/sub s/ not=d/sub j/. If the degree of truth of proposition d/sub s/ is given, then the degrees of truth of proposition d/sub j/ can be evaluated. The formal description of the model and the fuzzy reasoning algorithm are shown in detail. The upper bound of the time complexity of the fuzzy reasoning algorithm is O(nm), where n is the number of places and m is the number of transitions. Its execution time is proportional to the number of nodes in a sprouting tree generated by the algorithm only generates necessary reasoning paths from a starting place to a goal place, it can be executed very efficiently.

[1] K. P. Adlassning, "Fuzzy set theory in medical diagnosis,"IEEE Trans. Syst., Man, Cybern., vol. SMC-16, no. 2, pp. 270-276, Mar./Apr. 1986.
[2] P. L. Bogler, "Shafer-Dempster reasoning with applications to multisensor target identification systems,"IEEE Trans. Syst., Man, Cybern., vol. SMC-17, no. 6, pp. 968-977, Nov./Dec. 1987.
[3] B. G. Buchanan and E. H. Shortliffe,Rule-Based Expert Systems: The MYCIN Experiments of The Standford Heuristic Programming Projects. Reading, MA: Addison-Wesley, 1984.
[4] C. L. Chang,Introduction to Artificial Intelligence Techniques. Austin, TX: JMA Press, 1985.
[5] S. M. Chen, "A new approach to handling fuzzy decision-making problems,"IEEE Trans. Syst., Man, Cybern., vol. SMC-18, no. 6, pp. 1012-1016, Nov./Dec. 1988.
[6] S. M. Chen, J. S. Ke, and J. F. Chang, "Techniques for handling multicriteria fuzzy decision-making problems," inProc. 4th Int. Symp. Comput. Inform. Sci., Turkey, vol. 2, 1989, pp. 919-925.
[7] S. M. Chen, J. S. Ke, and J. F. Chang, "An efficient algorithm to handle medical diagnostic problems,"Cybern. Syst.: An International Journal, vol. 21, no. 4, 1990.
[8] P. N. Creasy, "An information systems view of conceptual graphs," inProc. Int. Comput. Symp., Taiwan, vol. 2, 1988, pp. 833-838.
[9] H. Farreny and H. Prade, "Default and inexact reasoning with possibility degrees,"IEEE Trans. Syst., Man, Cybern., vol. SMC-16, no. 2, pp. 270-276, Mar./Apr. 1986.
[10] B. R. Gaines and M. L. Shaw, "From fuzzy logic to expert systems,"Inform. Sci., vol. 36, pp. 5-15, 1985.
[11] A. Giordana and L. Saitta, "Modeling production rules by means of predicate transition networks,"Inform. Sci., vol. 35, pp. 1-41, 1985.
[12] K. S. Leung and W. Lam, "Fuzzy concepts in expert systems,"IEEE Comput. Mag., vol. 21, no. 9, pp. 43-56, 1988.
[13] C. G. Looney and A. R. Alfize, "Logical controls via Boolean rule matrix transformations,"IEEE Trans. Syst., Man, Cybern., vol. SMC-17, no. 6, pp. 1077-1082, Nov./Dec. 1987.
[14] C. G. Looney, "Fuzzy Petri nets for rule-based decisionmaking,"IEEE Trans. Syst., Man, Cybern., vol. SMC-18, no. 1, pp. 178-183, Jan./Feb. 1988.
[15] M. Mizumoto, "Fuzzy controls under various fuzzy reasoning methods,"Inform. Sci., vol. 45, pp. 129-151, 1988.
[16] C.V. Negoita,Expert Systems and Fuzzy Systems, Benjamin/Cummings, Menlo Park, Calif., 1985.
[17] Y. Peng and J. A. Reggia, "A probilistic casual model for diagnostic problem solving, Part II: diagnostic strategy,"IEEE Trans. Syst., Man, Cybern., vol. SMC-17, no. 3, pp. 395-406, May/June 1987.
[18] J. L. Peterson,Petri Net Theory and the Modeling of Systems. Englewood Cliffs, NJ: Prentice-Hall, 1981.
[19] A. Rage and A. M. Agogino, "Topological framework for representing and solving probablistic inference problems in expert systems,"IEEE Trans. Syst., Man, Cybern., vol. SMC-18, no. 3, pp. 402-414, May/June 1988.
[20] S. Ribaric, "Knowledge representation scheme based on Petri net theory,"Int. Pattern Recognition Artif. Intell., vol. 2, pp. 691-700, 1988.
[21] R. C. Schank and R. P. Abelson, "Scripts, plans, and knowledge," inProc. 4th Int. Joint Conf. Artif. Intell., 1975, pp. 151-157.
[22] J. F. Sowa, "Conceptual graph for a database interface,"IBM J. Res. Develop., vol. 20, pp. 336-357, 1976.
[23] Sowa, J.F.,Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, Reading, Mass., 1984. (Conceptual Graphs)
[24] D. Tabak, "Petri net representation of decision models,"IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 6, pp. 812-818, Nov./Dec. 1985.
[25] J. Warfield, "Binary matrices in system modeling,"IEEE Trans. Syst., Man, Cybern., vol. SMC-3, no. 5, pp. 441-449, 1973.
[26] R. R. Yager, "Approximate reasoning as a basis for rule-based expert systems,"IEEE Trans. Syst., Man, Cybern., vol. SMC-14, no. 4, pp. 636-643, July/Aug. 1984.
[27] L. A. Zadeh, "Fuzzy sets,"Inform. Contr., vol. 8, pp. 338-353, 1965.
[28] L. A. Zadeh, "A theory of commonsense knowledge," inAspects of Vagueness, H. J. Skala, S. Termini, and E. Trillas, Eds. Dortrecht: Reidel, 1984, pp. 257-295.
[29] L. A. Zadeh, "Fuzzy logic,"IEEE Comput. Mag., vol. 21, no. 4, pp. 83- 93, 1988.

Index Terms:
fuzzy Petri nets; fuzzy production rule; rule-based system; fuzzy relation; fuzzy reasoning; formal description; upper bound; time complexity; execution time; sprouting tree; computational complexity; knowledge representation; Petri nets
Citation:
S.-M. Chen, J.-S. Ke, J.-F. Chang, "Knowledge Representation Using Fuzzy Petri Nets," IEEE Transactions on Knowledge and Data Engineering, vol. 2, no. 3, pp. 311-319, Sept. 1990, doi:10.1109/69.60794
Usage of this product signifies your acceptance of the Terms of Use.