Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Novel Developments in Uncertainty Representation and Processing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 401))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Amo, A., Gómez, D., Montero, J., Biging, G.: Relevance and redundancy in fuzzy classification systems. Mathw. Soft Comput. 8, 203–216 (2001)

    MathSciNet  MATH  Google Scholar 

  2. Amo, A., Montero, J., Biging, G., Cutello, V.: Fuzzy classification systems. Eur. J. Oper. Res. 156, 495–507 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Anal. 72, 1488–1499 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  8. Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23, 866–877 (2008)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dubois, D., Prade, H.: Gradualness, uncertainty and bipolarity—making sense of fuzzy sets. Fuzzy Sets Syst. 192, 3–24 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic, Dordrecht, Boston (1994)

    Book  MATH  Google Scholar 

  12. Franco, C., Rodríguez, J.T., Montero, J.: Building the meaning of preference from logical paired structures. Knowl.-Based Syst. 83, 32–41 (2015)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Likert, R.: A technique for the measurement of attitudes. Arch. Psychol. 140, 1–55 (1932)

    Google Scholar 

  15. Montero, J.: Comprehensive fuzziness. Fuzzy Sets Syst. 20, 79–86 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. Montero, J.: Extensive fuzziness. Fuzzy Sets Syst. 21, 201–209 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  17. Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Syst. 158, 2429–2442 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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 paper

    Google Scholar 

  19. Osgood, C.E., Suci, G.J., Tannenbaum, P.H.: The Measurement of Meaning. University of Illinois Press, Urbana (1957)

    Google Scholar 

  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. Rodríguez, J.T., Franco, C., Montero, J.: On the semantics of bipolarity and fuzziness. Proc. Eurofuse 193–205, 2011 (2011)

    Google Scholar 

  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. Rodríguez, J.T., Turunen, E., Ruan, D., Montero, J.: Another paraconsistent algebraic semantics for Lukasiewicz-Pavelka logic. Fuzzy Sets Syst. 242, 132–147 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ruspini, E.H.: A new approach to clus8tering. Inf. Control 15, 22–32 (1969)

    Article  MATH  Google Scholar 

  25. Slovic, P., Peters, E., Finucane, M.L., MacGregor, D.G.: Affect, risk, and decision making. Health Psychol. 24, 35–40 (2005)

    Article  Google Scholar 

  26. de Soto, A.R., Trillas, E.: On antonym and negate in fuzzy logic. Int. J. Intell. Syst. 14, 295–303 (1999)

    Article  MATH  Google Scholar 

  27. Trillas, E.: On the use of words and fuzzy sets. Inf. Sci. 176, 1463–1487 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  28. Trillas, E., Moraga, C., Guadarrama, S., Cubillo, S., Castineira, E.: Computing with antonyms. Forg. New Front. Fuzzy Pioneers I 217, 133–153 (2007)

    Article  Google Scholar 

  29. Turunen, E., Öztürk, M., Tsoukiàs, A.: Paraconsistent semantics for Pavelka style fuzzy sentential logic. Fuzzy Sets Syst. 161, 1926–1940 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgment

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

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Complutense University, 28040, Madrid, Spain

    J. Tinguaro Rodríguez & Javier Montero

  2. IFRO, Faculty of Science, University of Copenhagen, Copenhagen, Denmark

    Camilo Franco

  3. Faculty of Statistics, Complutense University, 28040, Madrid, Spain

    Daniel Gómez

Authors
  1. J. Tinguaro Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Camilo Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Javier Montero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Tinguaro Rodríguez .

Editor information

Editors and Affiliations

  1. Inst. of Biophy. & Biomedical Eng., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Division of Graduate Studies, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Sys Res Intit of Polish Acad of Science, Intelligent Systems Laboratory, Warsaw, Poland

    Janusz Kacprzyk

  4. Warsaw School of Information Technology, Polish Academy of Sciences, Warsaw, Poland

    Maciej Krawczak

  5. Div of Gdu Stud,CalzTecn sn,Fra.TomAqu, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  6. Intelligent Systems Laboratory, Asen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

  7. Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University, Burgas, Bulgaria

    Evdokia Sotirova

  8. Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland

    Eulalia Szmidt

  9. Dept. of Tele. & Info. Processing, Ghent University, Gent, Belgium

    Guy De Tré

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Tinguaro Rodríguez, J., Franco, C., Gómez, D., Montero, J. (2016). Paired Structures, Imprecision Types and Two-Level Knowledge Representation by Means of Opposites. In: Atanassov, K., et al. Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol 401. Springer, Cham. https://doi.org/10.1007/978-3-319-26211-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26211-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26210-9

  • Online ISBN: 978-3-319-26211-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation