Paired Structures, Imprecision Types and Two-Level Knowledge Representation by Means of Opposites

  • J. Tinguaro RodríguezEmail author
  • Camilo Franco
  • Daniel Gómez
  • Javier Montero
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


Opposition-based models are a current hot-topic in knowledge representation. The point of this paper is to suggest that opposition can be in fact introduced at two different levels, those of the predicates of interest being represented (as short/tall) and of the logical references (true/false) used to evaluate the verification of the former. We study this issue by means of the consideration of different paired structures at each level. We also pay attention at how different types of fuzziness may be introduced in these paired structures to model imprecision and lack of knowledge. As a consequence, we obtain a unifying framework for studying the relationships between different knowledge representation models and different kinds of uncertainty.


Intuitionistic fuzzy sets Bipolar fuzzy sets Paired fuzzy sets 



This paper has been partially supported by grants TIN2012-32482 of the Government of Spain and S2013/ICCE-2845 of the Government of Madrid.


  1. 1.
    Amo, A., Gómez, D., Montero, J., Biging, G.: Relevance and redundancy in fuzzy classification systems. Mathw. Soft Comput. 8, 203–216 (2001)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Amo, A., Montero, J., Biging, G., Cutello, V.: Fuzzy classification systems. Eur. J. Oper. Res. 156, 495–507 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, K.T.: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s paper “Terminological difficulties in fuzzy set theory—the case of “Intuitionistic fuzzy sets”. Fuzzy Sets Syst. 156, 496–499 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Anal. 72, 1488–1499 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cacioppo, J.T., Berntson, G.G.: The affect system, architecture and operating characteristics—current directions. Psychol. Sci. 8, 133–137 (1999)Google Scholar
  7. 7.
    Cacioppo, J.T., Gardner, W.L., Berntson, C.G.: Beyond bipolar conceptualizations and measures—the case of attitudes and evaluative space. Pers. Soc. Psychol. Rev. 1, 3–25 (1997)CrossRefGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23, 866–877 (2008)CrossRefzbMATHGoogle Scholar
  9. 9.
    Dubois, D., Prade, H.: An overview of the asymmetric bipolar representation of positive and negative information in possibility theory. Fuzzy Sets Syst. 160, 1355–1366 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Dubois, D., Prade, H.: Gradualness, uncertainty and bipolarity—making sense of fuzzy sets. Fuzzy Sets Syst. 192, 3–24 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic, Dordrecht, Boston (1994)CrossRefzbMATHGoogle Scholar
  12. 12.
    Franco, C., Rodríguez, J.T., Montero, J.: Building the meaning of preference from logical paired structures. Knowl.-Based Syst. 83, 32–41 (2015)CrossRefGoogle Scholar
  13. 13.
    Kaplan, K.: On the ambivalence-indifference problem in attitude theory and measurement—a suggested modification of the semantic differential technique. Psychol. Bull. 77, 361–372 (1972)CrossRefGoogle Scholar
  14. 14.
    Likert, R.: A technique for the measurement of attitudes. Arch. Psychol. 140, 1–55 (1932)Google Scholar
  15. 15.
    Montero, J.: Comprehensive fuzziness. Fuzzy Sets Syst. 20, 79–86 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Montero, J.: Extensive fuzziness. Fuzzy Sets Syst. 21, 201–209 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Syst. 158, 2429–2442 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Montero, J., Bustince, H., Franco, C., Rodríguez, J.T., Gómez, D., Pagola, M., Fernandez, J., Barrenechea, E.: Paired structures and bipolar knowledge representation, Working paperGoogle Scholar
  19. 19.
    Osgood, C.E., Suci, G.J., Tannenbaum, P.H.: The Measurement of Meaning. University of Illinois Press, Urbana (1957)Google Scholar
  20. 20.
    Rodríguez, J.T., Franco, C., Gómez, D., Montero, J.: Paired structures and other opposites-based models. Proc. of IFSA-EUSFLAT 1375–1381, 2015 (2015)Google Scholar
  21. 21.
    Rodríguez, J.T., Franco, C., Montero, J.: On the semantics of bipolarity and fuzziness. Proc. Eurofuse 193–205, 2011 (2011)Google Scholar
  22. 22.
    Rodríguez, J.T., Franco, C., Montero, J., Lu, J.: Paired structures in logical and semiotic models of natural language. Inf. Process. Manage. Uncertainty Knowl.-Based Syst. Part II, 566–575 (2014)Google Scholar
  23. 23.
    Rodríguez, J.T., Turunen, E., Ruan, D., Montero, J.: Another paraconsistent algebraic semantics for Lukasiewicz-Pavelka logic. Fuzzy Sets Syst. 242, 132–147 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ruspini, E.H.: A new approach to clus8tering. Inf. Control 15, 22–32 (1969)CrossRefzbMATHGoogle Scholar
  25. 25.
    Slovic, P., Peters, E., Finucane, M.L., MacGregor, D.G.: Affect, risk, and decision making. Health Psychol. 24, 35–40 (2005)CrossRefGoogle Scholar
  26. 26.
    de Soto, A.R., Trillas, E.: On antonym and negate in fuzzy logic. Int. J. Intell. Syst. 14, 295–303 (1999)CrossRefzbMATHGoogle Scholar
  27. 27.
    Trillas, E.: On the use of words and fuzzy sets. Inf. Sci. 176, 1463–1487 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Trillas, E., Moraga, C., Guadarrama, S., Cubillo, S., Castineira, E.: Computing with antonyms. Forg. New Front. Fuzzy Pioneers I 217, 133–153 (2007)CrossRefGoogle Scholar
  29. 29.
    Turunen, E., Öztürk, M., Tsoukiàs, A.: Paraconsistent semantics for Pavelka style fuzzy sentential logic. Fuzzy Sets Syst. 161, 1926–1940 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • J. Tinguaro Rodríguez
    • 1
    Email author
  • Camilo Franco
    • 2
  • Daniel Gómez
    • 3
  • Javier Montero
    • 1
  1. 1.Faculty of MathematicsComplutense UniversityMadridSpain
  2. 2.IFRO, Faculty of ScienceUniversity of CopenhagenCopenhagenDenmark
  3. 3.Faculty of StatisticsComplutense UniversityMadridSpain

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