Skip to main content
SpringerLink
Log in
Book cover

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2012: Advances in Computational Intelligence pp 511–520Cite as

Dual Connectives in Fuzzy Reasoning

  • Conference paper

  • 827 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

Abstract

Paper concerns applications of Duality Principle in fuzzy algebra, fuzzy logics and approximate reasoning. Examples of important dual notions from lattice theory to relation theory and from fuzzy logic to fuzzy relational equations are presented. In particular properties of dual connectives of multi-valued logic are described and properties of dual relation compositions are summarized. Finally, residuated lattices are used for description of L-valued approximate reasoning.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baczyński, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Berlin (2008)

    MATH  Google Scholar 

  2. Baldwin, J.F., Pilsworth, B.W.: Axiomatic approach to implication for approximate reasoning with fuzzy logic. Fuzzy Sets Syst. 3, 193–219 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bělohlávek, R.: Fuzzy Relational Systems. Kluwer, New York (2002)

    MATH  Google Scholar 

  4. Birkhoff, G.: Lattice Theory. AMS Coll. Publ. 25. AMS, Providence (1967)

    Google Scholar 

  5. Bustince, H., Burillo, P., Mohedano, V.: A method for inference in approximate reasoning based on normal intuitionistic fuzzy sets. Notes IFS 1, 51–55 (1995)

    MathSciNet  Google Scholar 

  6. Drewniak, J., Kula, K.: Generalized compositions of fuzzy relations. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 10, 149–164 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Drewniak, J., Król, A.: A survey of weak connectives and the preservation of their properties by aggregations. Fuzzy Sets Syst. 161(2), 202–215 (2010)

    Article  MATH  Google Scholar 

  8. Drewniak, J., Pękala, B.: Properties of powers of fuzzy relations. Kybernetika 43(2), 133–142 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Fan, Z.T.: A note on power sequence of a fuzzy matrix. Fuzzy Sets Syst. 102, 281–286 (1999)

    Article  MATH  Google Scholar 

  10. Fodor, J.C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)

    MATH  Google Scholar 

  11. Fodor, J.C., Yager, R.R., Rybalov, A.: Structure of uninorms. Internat. J. Uncertainty, Fuzzines Knowledge-Based System 5, 411–427 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18, 145–174 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Academic Press, New York (1975)

    MATH  Google Scholar 

  14. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  15. Li, P., Fang, S.: A survey on fuzzy relational equations. Fuzzy Optim. Decis. Making 8, 179–229 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu, H.: Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets. J. Syst. Eng. Electr. 21, 224–232 (2010)

    Google Scholar 

  17. Perfilieva, I., Lehmke, S.: Correct models of fuzzy IF–THEN rules are continuous. Fuzzy Sets Syst. 157, 3188–3197 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Reiser, R.H.S., Bedregal, B.C.: Obtaining representable coimplications from aggregation and dual operators. In: EUSFLAT-LFA 2011, pp. 238–245 (2011)

    Google Scholar 

  19. Ruiz, D., Torrens, J.: Residual implications and coimplications from idempotent uninorms. Kybernetika 40, 21–38 (2004)

    MathSciNet  MATH  Google Scholar 

  20. Smets, P., Magrez, P.: Implication in fuzzy logic, Internat. J. Approx. Reason. 1, 327–347 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  21. Takács, M.: Approximate reasoning in fuzzy systems based on pseudo-analysis and uninorm residuum. Acta Polytechnica Hungarica 1(2), 49–62 (2004)

    Google Scholar 

  22. Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cyber. 3, 28–44 (1973)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Rzeszów, ul. Rejtana 16a, 35-959, Rzeszów, Poland

    Józef Drewniak

Authors
  1. Józef Drewniak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Drewniak, J. (2012). Dual Connectives in Fuzzy Reasoning. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_54

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31715-6_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation