Representing and Managing Unbalanced Multi-sets

  • Nouha Chaoued
  • Amel Borgi
  • Anne Laurent
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 631)


In Knowledge-Based Systems, experts should model human knowledge as faithful as possible to reality. In this way, it is essential to consider knowledge imperfection. Several approaches have dealt with this kind of data. The most known are fuzzy logic and multi-valued logic. These latter propose a linguistic modeling using linguistic terms that are uniformly distributed on a scale. However, in some cases, we need to assess qualitative aspects by means of variables using linguistic term sets which are not uniformly distributed. We have noticed, in the literature, that in the context of fuzzy logic many researchers have dealt with these term sets. However, it is not the case for multi-valued logic. Thereby, in our work, we aim to establish a methodology to represent and manage this kind of data in the context of multi-valued logic. Two aspects are treated. The first one concerns the representation of terms within an unbalanced multi-set. The second deals with the use of symbolic modifiers within such kind of imperfect knowledge.


Imperfect knowledge Multi-valued logic Unbalanced terms Symbolic modifiers 


  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    De Glas, M.: Knowledge representation in a fuzzy setting. Rapp. Interne 89, 48 (1989)Google Scholar
  3. 3.
    Akdag, H., De Glas, M., Pacholczyk, D.: A qualitative theory of uncertainty. Fundamenta Informaticae 17, 333–362 (1992)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Inf. Sci. 8, 199–249 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Herrera, F., Martínez, L.: A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 31, 227–234 (2001)CrossRefGoogle Scholar
  6. 6.
    Herrera, F., Enrique, H., Martínez, L.: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans. Fuzzy Syst. 16, 354–370 (2008)CrossRefGoogle Scholar
  7. 7.
    Abchir, M.A.: Towards fuzzy semantics for geolocation applications. Ph.D. Thesis, University of Paris VIII Vincennes-Saint Denis (2013)Google Scholar
  8. 8.
    Chaoued, N., Borgi, A., Laurent, A.: Representation of unbalanced terms in multi-valued logic. In: 12th IEEE International Multi-conference on Systems, Signals and Devices (2015)Google Scholar
  9. 9.
    Herrera-Viedma, E., López-Herrera, A.G.: A model of an information retrieval system with unbalanced fuzzy linguistic information. Int. J. Intell. Syst. 22, 1197–1214 (2007)CrossRefzbMATHGoogle Scholar
  10. 10.
    Martínez, L., Herrera, F.: An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf. Sci. 207, 1–18 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Xu, Z.: An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis. Negot. 18, 119–145 (2009)CrossRefGoogle Scholar
  12. 12.
    Wang, B., Liang, J., Qian, Y., Dang, C.: A normalized numerical scaling method for the unbalanced multi-granular linguistic sets. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 23, 221–243 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Marin, L., Valls, A., Isern, D., Moreno, A., Merigó, J.M.: Induced unbalanced linguistic ordered weighted average and its application in multiperson decision making. Sci. World J. 2014, 19 p. (2014). Article ID 642165, doi: 10.1155/2014/642165
  14. 14.
    Bartczuk, Ł., Dziwiński, P., Starczewski, J.T.: A new method for dealing with unbalanced linguistic term set. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012. LNCS (LNAI), vol. 7267, pp. 207–212. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29347-4_24 CrossRefGoogle Scholar
  15. 15.
    Jiang, L., Liu, H., Cai, J.: The power average operator for unbalanced linguistic term sets. Inf. Fusion 22, 85–94 (2015)CrossRefGoogle Scholar
  16. 16.
    Akdag, H., Pacholczyk, D.: Incertitude et logique multivalente, première partie: Etude théorique. BUSEFAL 38, 122–139 (1989)zbMATHGoogle Scholar
  17. 17.
    Adkag, H.: Une approche logique du raisonnement incertain. Ph.D. Thesis, University of Paris, 6 (1992)Google Scholar
  18. 18.
    Zadeh, L.A.: A fuzzy-set-theoretic interpretation of linguistic hedges. J. Cybern. 2, 4–34 (1972)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Akdag, H., Mellouli, N., Borgi, A.: A symbolic approach of linguistic modifiers. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, pp. 1713–1719 (2000)Google Scholar
  20. 20.
    Akdag, H., Truck, I., Borgi, A., Mellouli, N.: Linguistic modifiers in a symbolic framework. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 9, 49–61 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Truck, I.: Approches symbolique et floue des modificateurs linguistiques et leur lien avec l’agrégation: application: le logiciel flous. Ph.D. Thesis, University of Reims Champagne-Ardenne (2002)Google Scholar
  22. 22.
    Truck, I., Borgi, A., Akdag, H.: Generalized modifiers as an interval scale: towards adaptive colorimetric alterations. In: Garijo, F.J., Riquelme, J.C., Toro, M. (eds.) IBERAMIA 2002. LNCS (LNAI), vol. 2527, pp. 111–120. Springer, Heidelberg (2002). doi: 10.1007/3-540-36131-6_12 CrossRefGoogle Scholar
  23. 23.
    Espinilla, M., Liu, J., Martínez, L.: An extended hierarchical linguistic model for decision-making problems. Comput. Intell. 27, 489–512 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kacem, S.B.H., Borgi, A., Tagina, M.: Extended symbolic approximate reasoning based on linguistic modifiers. Knowl. Inf. Syst. 42, 633–661 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Université de Tunis El Manar, LIPAHTunisTunisia
  2. 2.Université de Montpellier, LIRMMMontpellierFrance

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