Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products

  • L. J. Kohout
  • W. Bandler
Part of the Applied Optimization book series (APOP, volume 3)

Abstract

Many-valued logic based interval reasoning plays an increasingly important role in fuzzy and other many-valued extensions of two-valued (crisp) logic. It is often overlooked that many-valued logic (MVL) reasoning has a richer inference rule base than the crisp (i.e. classical two-valued) logic. Indeed some rules that are not possible in the crisp logic (which is point-based) do come to existence when we accept intervals as the basic elements of the semantic space ([0, 1] or a more general lattice) into which the logic expressions are valuated [11, 8, 37].

Keywords

Filtration Assure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Anderson, L. J. Kohout, W. Bandler, and C. Trayner, “A knowledge-based clinical decision support system using new techniques”, In: A. H. Levy and B. T. Williams, editors, Proc. of AAMSI Congress 1985, American Association for Medical Systems and Informatics, Washington, DC, May 1985, pp. 187–192.Google Scholar
  2. [2]
    J. P. Aubin and H. Frankowska, Set-valued analysis, Birkhauser, Boston, 1990.MATHGoogle Scholar
  3. [3]
    W. Bandler and L. J. Kohout, “Fuzzy relational products and fuzzy implication operators”, In: International Workshop on Fuzzy Reasoning Theory and Applications, Queen Mary College, University of London, London, September 1978.Google Scholar
  4. [4]
    W. Bandler and L. J. Kohout, “Fuzzy power sets and fuzzy implication operators”, Fuzzy Sets and Systems, 1980, Vol. 4, pp. 13–30. Reprinted in: Readings In Fuzzy Sets for Intelligent Systems, D. Dubois, H. Prade and R. Yager (eds.), Morgan Kaufmann Publishers, San Mateo, Calif., 1993.MathSciNetMATHCrossRefGoogle Scholar
  5. W. Bandler and L. J. Kohout, “Fuzzy power sets and fuzzy implication operators”, Fuzzy Sets and Systems, 1980, Vol. 4, pp. 13–30. Reprinted in: Readings In Fuzzy Sets for Intelligent Systems, D. Dubois, H. Prade and R. Yager (eds.), Morgan Kaufmann Publishers, San Mateo, Calif., 1993.Google Scholar
  6. [5]
    W. Bandler and L. J. Kohout, “Fuzzy relational products as a tool for analysis and synthesis of the behaviour of complex natural and artificial systems”, In: P. P. Wang and S. K. Chang, editors, Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems, Plenum Press, New York and London, 1980, pp. 341–367.Google Scholar
  7. [6]
    W. Bandler and L. J. Kohout, “Semantics of implication operators and fuzzy relational products”, Internat. Journal of Man-Machine Studies, 1980, Vol. 12, pp. 89–116. Reprinted in: E. H. Mamdani and B. R. Gaines, eds., Fuzzy Reasoning and its Applications, Academic Press, London, 1981, pp. 219–246.MathSciNetMATHCrossRefGoogle Scholar
  8. W. Bandler and L. J. Kohout, “Semantics of implication operators and fuzzy relational products”, Internat. Journal of Man-Machine Studies, 1980, Vol. 12, pp. 89-116. Reprinted in: E. H. Mamdani and B. R. Gaines, eds., Fuzzy Reasoning and its Applications, Academic Press, London, 1981, pp. 219–246.MATHGoogle Scholar
  9. [7]
    W. Bandler and L. J. Kohout, “Fast fuzzy relational algorithms”, In: A. Ballester, D. Cardús, and E. Trillas, editors, Proc. of the Second Internat. Conference on Mathematics at the Service of Man, (Las Palmas, Canary Islands, Spain, 28 June-3 July), Universidad Politechnica de las Palmas, Las Palmas, 1982, pp. 123–131.Google Scholar
  10. [8]
    W. Bandler and L. J. Kohout, “The four modes of inference in fuzzy expert systems”, In: R. Trappl, editor, Cybernetics and Systems Research 2, North-Holland, Amsterdam, 1984, pp. 581–586.Google Scholar
  11. [9]
    W. Bandler and L. J. Kohout, “Unified theory of multiple-valued logical operators in the light of the checklist paradigm”, In: Proc. of the 1984 IEEE Conference on Systems, Man and Cybernetics, IEEE, New York, 1984, pp. 356–364.Google Scholar
  12. [10]
    W. Bandler and L. J. Kohout, “The interrelations of the principal fuzzy logical operators”, In: M. M. Gupta, A. Kandel, W. Bandler, and J. B. Kiszka, editors, Approximate Reasoning In Expert Systems, North- Holland, Amsterdam, 1985, pp. 767–780.Google Scholar
  13. [11]
    W. Bandler and L. J. Kohout, “Probabilistic vs. fuzzy production rules in expert systems”, Internat. Journal of Man-Machine Studies, 1985, Vol. 22, pp. 347–353.CrossRefGoogle Scholar
  14. [12]
    W. Bandler and L. J. Kohout, “A survey of fuzzy relational products in their applicability to medicine and clinical psychology”, In: L. J. Kohout and W. Bandler, editors, Knowledge Representation In Medicine and Clinical Behavioural Science, an Abacus Book, Gordon and Breach Publ., London and New York, 1986, pp. 107–118.Google Scholar
  15. [13]
    W. Bandler and L. J. Kohout, “The use of checklist paradigm in inference systems”, In: C. V. Negoita and H. Prade, editors, Fuzzy Logic In Knowledge Engineering, Verlag TÜV Rheinland, Köln, 1986, Chapter 7, pp. 95–111.Google Scholar
  16. [14]
    W. Bandler and L. J. Kohout, “Fuzzy implication operators”, In: M. G. Singh, editor, Systems and Control Encyclopedia, Pergamon Press, Oxford, 1987, pp. 1806–1810.Google Scholar
  17. [15]
    W. Bandler and L. J. Kohout, “Relations, mathematical”, In: M. G. Singh, editor, Systems and Control Encyclopedia, Pergamon Press, Oxford, 1987, pp. 4000–4008.Google Scholar
  18. [16]
    W. Bandler and L. J. Kohout, “Special properties, closures and interiors of crisp and fuzzy relations”, Fuzzy Sets and Systems, 1988, Vol. 26, No. 3, pp. 317–332.MathSciNetMATHCrossRefGoogle Scholar
  19. [17]
    J. P. Diognon, M. Monjardet, B. Roubens, and P. Vincke, “Biorders families, valued relations and preference modelling”, J. Math. Psychol., 1986, Vol. 30, pp. 435–480.CrossRefGoogle Scholar
  20. [18]
    D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.MATHGoogle Scholar
  21. [19]
    J. C. Fodor, “Traces of fuzzy binary relations”, Fuzzy Sets and Systems, 1992, Vol. 50, No. 3, pp. 331–341.MathSciNetMATHCrossRefGoogle Scholar
  22. [20]
    M. Higashi and G. J. Klir, “On measures of fuzziness and fuzzy complements”, International Journal of General Systems, 1982, Vol. 8, No. 3, pp. 169–180.MathSciNetMATHCrossRefGoogle Scholar
  23. [21]
    E. Hisdal, Infinite-valued logic based of two-valued logic and probability. Pt. 1.4. The TEE model for grades of membership, ISBN 82-7368-054-1140, University of Oslo, Inst, of Informatics, Box 1080, Blindem Oslo 3, Norway, October 1990.Google Scholar
  24. [22]
    A. Kandel, Fuzzy mathematical techniques with applications, Addison Wesley, Reading, Mass., 1986.MATHGoogle Scholar
  25. [23]
    L. J. Kohout, “Activity structures as a tool for design of technological artifacts”, Systems and Cybernetics: An International Journal, 1987, Vol. 18, No. 1, pp. 27–34.MathSciNetCrossRefGoogle Scholar
  26. [24]
    L. J. Kohout, “Theories of possibility: Meta-axiomatics and semantics”, Fuzzy Sets and Systems, 1988, Vol. 25, pp. 357–367.MathSciNetMATHCrossRefGoogle Scholar
  27. [25]
    L. J. Kohout, A Perspective on Intelligent Systems: A Framework for Analysis and Design, Chapman and Hall and Van Nostrand, London and New York, 1990. In 1991, received an international prize from The International Institute for Advanced Studies In Systems Research: “The best book of the year in the area of AI Systems”.MATHGoogle Scholar
  28. [26]
    L. J. Kohout, “Paraconsistency in activity structures”, In: G. E. Lasker, editor, 3rd Internatinal Symposium on Systems Research, Informatics and Cybernetics, Germany, August 12–18, 1991.Google Scholar
  29. [27]
    L. J. Kohout, “Activity Structures: A methodology for design of multi-environment and multi-context knowledge-based systems”, In: L. J. Kohout, J. Anderson, and W. Bandler, editors, Knowledge-Based Systems for Multiple Environments, Ashgate Publ. ( Gower ), Aldershot, U.K., 1992, Chapter 5.Google Scholar
  30. [28]
    L. J. Kohout, J. Anderson, and W. Bandler, Knowledge-Based Systems for Multiple Environments. Ashgate Publ. (Gower), Aldershot, U.K., 1992. Awarded “Outstanding Scholarly Contribution Award” by the Systems Research Foundation In 1993.Google Scholar
  31. [29]
    L. J. Kohout, J. Anderson, W. Bandler, A. Behrooz, S. Gao, and C. Trayner, “Activity structures based architectures for knowledge-based systems, part I: Dynamics of localised fuzzy inference and its interaction with planning”, Fuzzy Sets and Systems, 1991, Vol. 44, No. 4, pp. 405–420.CrossRefGoogle Scholar
  32. [30]
    L. J. Kohout, J. Anderson, W. Bandler, S. Gao, and C. Trayner, “CLI-NAID: A knowledge-based system for support of decisions in the conditions of risk and uncertainty”, In: L. J. Kohout, J. Anderson, and W. Bandler, editors, Knowledge-Based Systems for Multiple Environments, Ashgate Publ. ( Gower ), Aldershot, U.K., 1992, Chapter 10.Google Scholar
  33. [31]
    L. J. Kohout and W. Bandler, Checklist paradigm and group transformations, Technical Note EES-MMS-ckl91. 2, Dept. of Electrical Engineering, University of Essex. U.K, 1979.Google Scholar
  34. [32]
    L. J. Kohout and W. Bandler, “Relational-product architectures for information processing”, Information Science, 1985, Vol. 37, pp. 25–37.CrossRefGoogle Scholar
  35. [33]
    L. J. Kohout and W. Bandler, “Knowledge representation, clinical action and expert systems”, In: L. J. Kohout and W. Bandler, editors, Knowledge Representation In: Medicine and Clinical Behavioural Science, an Abacus Book, Gordon and Breach Publ., London and New York, 1986, pp. 1–8.Google Scholar
  36. [34]
    L. J. Kohout and W. Bandler, “Fuzzy relational products in knowledge engineering,” In: V. Novák et al., editor, Fuzzy Approach to Reasoning and Decision Making, Academia and Kluwer, Prague and Dordrecht, 1992, pp. 51–66.CrossRefGoogle Scholar
  37. [35]
    L. J. Kohout and W. Bandler. “How the checklist paradigm elucidates the semantics of fuzzy inference,” In: Proc. of the IEEE Internat. Conference on Fuzzy Systems 1992, IEEE, New York, 1992, pp. 571–578.CrossRefGoogle Scholar
  38. [36]
    L. J. Kohout and W. Bandler, “Use of fuzzy relations in knowledge representation, acquisition and processing”, In: L.A. Zadeh and J. Kacprzyk, editors, Fuzzy Logic for the Management of Uncertainty, John Wiley, New York, 1992, pp. 415–435.Google Scholar
  39. [37]
    L. J. Kohout and W. Bandler, “Interval-valued systems for approximate reasoning based on the checklist paradigm”, In: P. Wang, Paul, editor, Advances In Fuzzy Theory and Technology, Vol 1, Bookwrights Press, Durham, N.C., 1993, pp. 167–193.Google Scholar
  40. [38]
    L. J. Kohout and W. Bandler, “Modes of interval-based plausible reasoning vieved via the checklist paradigm”, In: B. Bouchon-Meunier, L. Valverde, and R. R. Yager, editors, IPMU’92 Advanced Methods In Artificial Intel¬ligence (Lecture Notes in Computer Science Vol 682), Springer, Berlin, 1993, pp. 256–264.Google Scholar
  41. [39]
    L. J. Kohout, W. Bandler, J. Anderson, and C. Trayner, “Knowledge- based decision support system for use in medicine”, In: G. Mitra, editor, Computer Models for Decision Making, North-Holland, Amsterdam, 1985, pp. 133–146.Google Scholar
  42. [40]
    L. J. Kohout, A. Behrooz, J. Anderson, S. Gao, C. Trayner, and W. Bandler, “Dynamics of localised inference and its embedding in activity structures based IKBS architectures”, In: Proc. of Second IFSA Congress, International Fuzzy Systems Association, July 1987, pp. 740–743.Google Scholar
  43. [41]
    L. J. Kohout and S. M. A. Mohamad, “Development of support tools and methodology for design and validation of multi-environmental computer architectures”, In: L. J. Kohout, J. Anderson, and W. Bandler, editors, Knowledge-Based Systems for Multiple Environments, Ashgate Publ. ( Gower ), Aldershot, U.K., 1992, Chapter 17.Google Scholar
  44. [42]
    L. J. Kohout, S. M. A. Mohamad, and W. Bandler, “A support tool for evaluation of knowledge enginnering structures” In: FLAIRS - 89 Proceedings, The Florida Artificial Intelligence Research Society, 1989, pp. 113–117.Google Scholar
  45. [43]
    L. J. Kohout and I. Stabile, “Interval-valued inference in medical knowledge-based system Clinaid”, Interval Computations, 1993, No. 3, pp. 88–115.MathSciNetGoogle Scholar
  46. [44]
    L. J. Kohout and I. Stabile, “Interval-valued information retrieval and inference in medical knowledge-based system Clinaid,” In: Conf. on Numerical Analysis with Automatic Result Verification, Lafayette, Louisiana, February 25–March 1, 1993.Google Scholar
  47. [45]
    L. J. Kohout, I. Stabile, W. Bandler, and J. Anderson, “CLINAID: Medical knowledge-based system based on fuzzy relational structures”, In: M. Cohen and D. Hudson, editors, Comparative Approaches in Medical Reasoning, World Scientific, 1995, (in press).Google Scholar
  48. [46]
    V. Novák. On the position of fuzzy sets in modelling of vague phenomena. In: R. Lowen and M. Roubens, editors, IFSA’91 Brussels, vol. Artificial Intelligence, International Fuzzy Systems Association, 1991, pp. 165–167.Google Scholar
  49. [47]
    V. Pinkava, Introduction to Logic for System Modelling, Gordon and Breach, London and New York, 1988.Google Scholar
  50. [48]
    G. Priest, R. Routley, and J. Norman, (eds.), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, München, Wien, 1989.MATHGoogle Scholar
  51. [49]
    G. Resconi, G. J. Klir, and U. St.Clair, “Hierarchical uncetrainty metatheory based upon modal logic”, Internat. J. of General Systems, 1992.Google Scholar
  52. [50]
    J. Riguet, “Relations binaires, fermetures, correspondences de Galois”, Bull. Soc. Math. France, 1948, Vol. 76, pp. 114–155.MathSciNetMATHGoogle Scholar
  53. [51]
    B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.MATHGoogle Scholar
  54. [52]
    E. Stiller, S. Løvstad, W. Bandler, and V. a Mancini. “Representing the social dimension: Design and methodology for an urban planning system”, In: M. B. Fishman, editor, Proceedings of 2nd Florida Artificial Intelligence Research Symposium, The Florida AI Research Symposium, P. O. Box 12560, St Petersburgh, Florida 33733, 1989, pp. 216–220.Google Scholar
  55. [53]
    I.B. Turksen. “Containment and Klein groups of fuzzy propositions”, Working Paper 79-010, Dept. of Industrial Eng., University of Toronto, Canada, 1979.Google Scholar
  56. [53]
    I.B. Turksen. “Containment and Klein groups of fuzzy propositions”, Working Paper 79-010, Dept. of Industrial Eng., University of Toronto, Canada, 1979.Google Scholar
  57. [55]
    R. Yager, “On the measure of fuzziness and negation. Part I: Membership in the unit interval”, International Journal of General Systems, 1979, Vol. 5, No. 4, pp. 221–229.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • L. J. Kohout
    • 1
  • W. Bandler
    • 1
  1. 1.Department of Computer ScienceFlorida State UniversityTallahasseeUSA

Personalised recommendations