An Algebraic Tool for Classification in Fuzzy Environments

  • Antonio Gisolfi
  • Luigi Di Lascio
  • Enrico Fischetti
Part of the Advances in Soft Computing book series (AINSC, volume 11)


This paper illustrates the behavior of a commutative l-monoid, endowed with a suitable operation of composition, as regards the problem of classification with fuzzy attributes. The concepts of relevance and similarity are introduced, then a mechanism for weighing the attributes is shown. Finally, a case study concerning graphology is illustrated in


Fuzzy Number Linguistic Variable Fuzzy Triangular Number Fuzzy Environment Real User 
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.
    Baldwin J. F., (1994) “FRIL-Fuzzy and Evidential Reasoning” in AI, Research Studies Press.Google Scholar
  2. 2.
    Bellman R. E. and Zadeh L. A., (1970) “Decision-making in a fuzzy environment”,Management Sci., 17(4) 141–164.Google Scholar
  3. 3.
    Biswas R., (1995) “An application of fuzzy sets in students’ evaluation”, Fuzzy Sets and Systems 74, 187–195.Google Scholar
  4. 4.
    Bloom B.S. etal., (1984) “Taxonomy of educational objectives: Handbook 1-2”, Addison Wesley.Google Scholar
  5. 5.
    Brusilovsky P., (1996) “Methods and techniques of adaptive hypermedia”,User Modeling and User-Adapted Interaction, 6, (2–3), 87–129.Google Scholar
  6. 6.
    Comi G., Galardi G., Amadio S., Bianchi E., Secchi A., Martinenghi S., Caldara R., Pozza G., Canal N., (1991) “Neurophysiological study of the effect of combined kidney and pancreas transplantation ondiabetic neuropathy: a 2-year follow-up evaluation”, Diabetologia 1991;34 Suppl 1: S103–7.Google Scholar
  7. 7.
    Di Lascio L., Fischetti E., Gisolfi A., (1999)“ A Fuzzy-Based Approach To Stereotype Selection In Hypermedia”, User Modeling and User-Adapted Interaction, 9:285–320.Google Scholar
  8. 8.
    Di Lascio L., Fischetti E., Gisolfi A., (2000) “ Learning Evaluation= Computing with Words”, Techical Report, DMI-0043, 2000.Google Scholar
  9. 9.
    Di Lascio L., Fischetti E., Gisolfi A., (2001) “Fuzzy modeling and evaluation of an ITM user”,Computacion and Systemas, in press.Google Scholar
  10. 10.
    Di Lascio L., Fischetti E., Gisolfi A., (2000) “Molto attento x abbastanza buono = pig the discreto”, Atti DIDAMATICA-AICA, Cesena, Italy, 2000.Google Scholar
  11. 11.
    Di Lascio L., Gisolfi A., (1998) “Averaging linguistic truth values in fuzzy approximate reasoning”, International Journal of Intelligent Systems, 13, 301–318.Google Scholar
  12. 12.
    Di Lascio L., Gisolfi A., Albunia A., Galardi G., Meschi F., (2000) “A fuzzy-based methodology for the analyis of diabetic neuropathy”,submittedGoogle Scholar
  13. 13.
    Di Lascio L., Gisolfi A., (2000) “Decision Making and Fuzzy Screeneng: a new computational approach”, Techical Report, DMI-0045, 2000.Google Scholar
  14. 14.
    Di Lascio L., Gisolfi A., Loia V., (1998) “Uncertainty processing in user-modeling activity”, Information Sciences, 106, 25–47.Google Scholar
  15. 15.
    Di Lascio L., Gisolfi A., Rosa G., (2000) “A commutative 1-monoid for classification with fuzzy attributes”, to appear in Int. J. Of Approx. Reasoning.Google Scholar
  16. 16.
    Di Nola A., Gisolfi A., Loia V., Sessa S., “Emerging Behaviors in Fuzzy Evolutionary Agents ”, Proceedings of 7th European Congress on Intelligent Techniques and Soft, Aachen, Germany, Sept. 13–16, 1999.Google Scholar
  17. 17.
    Gisolfi A., (1992) “An Algebraic Fuzzy Structure For The Approximate Reasoning”,Fuzzy Sets And Systems 45, 37–43.Google Scholar
  18. 18.
    Gisolfi A., (1995), “Classifying Through An Algebraic Fuzzy Structure: The Relevance Of The Attributes”,International Journal Of Intelligent Systems, Vol. 10, pp. 715–734.Google Scholar
  19. 19.
    Gisolfi A., Cicalese F., (1996) “Classifying through a fuzzy algebraic structure”, Fuzzy Sets and systems 78, 317–331.Google Scholar
  20. 20.
    Gisolfi A., Loia V., (1995) “A Complete, Flexible Fuzzy-Based Approach To The Classification Problem”, International Journal Of Approximate Reasoning, 13, 151–183.Google Scholar
  21. 21.
    Gisolfi A., Nunez G., (1993) “An Algebraic Approximation to the Classification with Fuzzy Attributes”, International Journal of Approximate Reasoning, 9, 75–95.Google Scholar
  22. 22.
    Klir G. J., Yuan B., (1995) “Fuzzy sets and fuzzy logic: theory and applications”, Prentice - Hall, London.MATHGoogle Scholar
  23. 23.
    Martinenghi S., Comi G., Galardi G., Di Carlo V., Pozza G., Secchi A., (1997) “Amelioration of nerve conduction velocity following simultaneous kidney/pancreas transplantation is due to the glycaemic control provided by the pancreas”, Diabetologia 1997; 40 (9): 1110–2.CrossRefGoogle Scholar
  24. 24.
    Ribeiro R. A., (1996) “Fuzzy multiple attribute decision making: A review and new preference elicitation techniques”, Fuzzy Set and Systems, 78, 155–181.Google Scholar
  25. 25.
    Sato. M, Sato Y., Jain L.C., (1997) “Fuzzy Clustering Models and Applications”, Studies in Fuzzyness and Soft Computing n. 9, Physica-Verlag, New York.Google Scholar
  26. 26.
    Yager R. R., (1977) “Multiple objective decision-making using fuzzy sets”, Int. J. Man-Machine Studies 9, 375–382.Google Scholar
  27. 27.
    Yager R. R., (1987) “Fuzzy decision making including unequal objectives”,Fuzzy Set and Systems, 87–95.Google Scholar
  28. 28.
    Zadeh L. A., (1975) “The concept of a Linguistic Variable and Its Application to Approximate Reasoning”,I, II, III, Information Sciences, 1975 (8) 199–249, (8) 301–357, (9) 43–89.Google Scholar
  29. 29.
    Zadeh L. A., (1996) “Fuzzy Logic = Computing with Words”“, IEEE Transactions on Fuzzy Systems, (4): 2, 103–111.Google Scholar
  30. 30.
    Zadeh, L. A., (1965) “Fuzzy sets”, Information and Control, (8): 3, 338–353.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Antonio Gisolfi
    • 1
  • Luigi Di Lascio
    • 1
  • Enrico Fischetti
    • 1
  1. 1.Dip. Matematica e InformaticaUniversitá di SalernoBaronisiItaly

Personalised recommendations