Inference Algorithms in Knowledge-Based Systems

  • Antonio di Nola
  • Salvatore Sessa
  • Witold Pedrycz
  • Elie Sanchez
Part of the Theory and Decision Library book series (TDLD, volume 3)


This Ch. summarizes some common techniques of inference utilized for fuzzy data. Special attention has been paid to the implementation of modus ponens (which realizes a data-driven mode of reasoning) and modus tollens (corresponding to a goal-driven mode of reasoning). The detachment principle (corresponding to a means of expressing a similarity between fuzzy statements) is also investigated. We discuss how different forms of fuzzy relation equations are used to handle each of these modes of inference. Also the question of a direct link between the relevancy of the KB and the length of the inference chain leading to meaningful conclusions is considered. This is of primordial importance; it has to be analyzed to interpret the results of inference and, in particular, to visualize precision. A proper reformulation of the problem in terms of fuzzy equations makes it possible to consider this knowledge transformation in a greater detail.


Membership Function Composition Operator Fuzzy Logic Controller Fuzzy Relation Inference Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Buchanan and E.M. Shortliffe, Rule-Based Expert Systems, Addison-Wesley, Reading, Mass., 1984.Google Scholar
  2. [2]
    E. Czogala and W. Pedrycz, Some problems concerning the construction of algorithms of decision-making in fuzzy systems, Internat. J. Man-Machine Studies 15 (1981), 201–211.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    A. Di Nola, W. Pedrycz and S. Sessa, Towards handling fuzziness in intelligent systems, in Fuzzy Computing ( M.M. Gupta and T. Yamakawa, Eds.), Elsevier Science Publishers B.V. (North-Holland), Amsterdam (1988), pp. 365–374.Google Scholar
  4. [4]
    D. Dubois and H. Prade, The principle of minimum specificity as a basis for evidential reasoning, in: Uncertainty in Knowledge-Based Systems (B. Bouchon and R.R. Yager, Ed.) Lecture Notes in Computer Science, Vol. 286, Springer-Verlag, Berlin (1987), pp. 75–84.Google Scholar
  5. [5]
    S. Fukami, M. Mizumoto and S. Tanaka, Some considerations on fuzzy conditional inferences, Fuzzy Sets and Systems 4 (1980), 243–273.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    F. Hayes-Roth, Rule-Based Systems, Communications of ACM 28 (1985), 921932.Google Scholar
  7. [7]
    W.J.M. Kickert and E.M. Mamdani, Analysis of a fuzzy logic controller, Fuzzy Sets and Systems 1 (1978), 29–44.zbMATHCrossRefGoogle Scholar
  8. [8]
    R. Kowalski, Logic for Problem Solving, North-Holland, New York, 1979.zbMATHGoogle Scholar
  9. [9]
    E.M. Mamdani, Advances in the linguistic synthesis of fuzzy controllers, Internat. J. Man-Machine Studies 8 (1976), 669–678.zbMATHCrossRefGoogle Scholar
  10. [10]
    E.M. Mamdani and S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, Internat. J. Man-Machine Studies 7 (1978), 1–13.CrossRefGoogle Scholar
  11. [11]
    M. Mizumoto and M J Zimmermann, Comparison of fuzzy reasoning methods, Fuzzy Sets and Systems 8 (1982), 253–283.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    W. Pedrycz, Fuzzy Control and Fuzzy Systems, J. Wiley (Research Studies Press), 1988, to appear.Google Scholar
  13. [13]
    H. Prade, A computational approach to approximate and plausible reasoning with applications to expert systems, IEEE Trans. on Pattern Analysis and Machine Intelligence, 7 (1985), 260–283.zbMATHCrossRefGoogle Scholar
  14. [14]
    E. Sanchez, On truth-qualification in natural languages, Proc. Internat. Conf. Cybernetics and Society, Tokyo-Kyoto (Japan), 3–7 Nov. 1978, Vo1. II, 1233–1236.Google Scholar
  15. [15]
    M. Togai and H. Watanabe, Expert-Systems on a chip: An engine for real-time approximate reasoning, IEEE Expert 1, no. 3, (1986), 55–62.CrossRefGoogle Scholar
  16. [16]
    Y. Tsukamoto, Fuzzy logic based on Lukasiewicz logic and its application to diagnosis and control, Ph. D. Thesis, Tokyo Inst. of Technology, Tokyo, 1979.Google Scholar
  17. [17]
    Y. Tsukamoto, T. Takagi and M. Sugeno, Fuzzification of Aleph-1 and its application to control, Proc. Internat. Conf. Cybernetics and Society, Tokyo-Kyoto (Japan), 3–7 Nov. 1978, Vol. II, 1217–1221.Google Scholar
  18. [18]
    S. Weiss and C.A. Kulikowski, A Practical Guide to Designing Expert Systems, Rowman & Allanheld, Philadelphia, 1984.Google Scholar
  19. [19]
    D. Willaeys and N. Malvache, The use of fuzzy sets for the treatment of fuzzy information by computer, Fuzzy Sets and Systems 3 (1981), 323–328.CrossRefGoogle Scholar
  20. [20]
    L.A. Zadeh, Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions, IEEE Trans. Syst. Man. Cybern. SMC-15 (1985), 754763.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1989

Authors and Affiliations

  • Antonio di Nola
    • 1
  • Salvatore Sessa
    • 1
  • Witold Pedrycz
    • 2
  • Elie Sanchez
    • 3
  1. 1.Facoltà di ArchitetturaUniversità di NapoliNapoliItaly
  2. 2.Department of Electrical EngineeringWinnipegCanada
  3. 3.Faculté de MédecineUniversité Aix-Marseille IIMarseilleFrance

Personalised recommendations