Skip to main content
Springer Nature Link
Log in

Variable-Range Approximate Systems Induced by Many-Valued L-Relations

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 444))

Abstract

The concept of a many-valued L-relation is introduced and studied. Many-valued L-relations are used to induce variable-range quasi-approximate systems defined on the lines of the paper (A. Šostak, Towards the theory of approximate systems: variable-range categories. Proceedings of ICTA2011, Cambridge Univ. Publ. (2012) 265–284.) Such variable-range (quasi-)approximate systems can be realized as special families of L-fuzzy rough sets indexed by elements of a complete lattice.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Birkhoff, G.: Lattice Theory. AMS, Providence (1995)

    Google Scholar 

  2. Bodenhofer, U.: Ordering of fuzzy sets based on fuzzy orderings. I: The basic approach. Mathware Soft Comput. 15, 201–218 (2008)

    MATH  MathSciNet  Google Scholar 

  3. Bodenhofer, U.: Ordering of fuzzy sets based on fuzzy orderings. II: Generalizations. Mathware Soft Comput. 15, 219–249 (2008)

    MATH  MathSciNet  Google Scholar 

  4. Brown, L.M., Ertürk, R., Dost, Ş.: Ditopological texture spaces and fuzzy topology, I. Basic concepts. Fuzzy Sets and Syst. 110, 227–236 (2000)

    Article  MATH  Google Scholar 

  5. Brown, L.M., Ertürk, R., Dost, Ş.: Ditopological texture spaces and fuzzy topology, II. Topological considerations. Fuzzy Sets and Syst. 147, 171–199 (2004)

    Article  MATH  Google Scholar 

  6. Chang, C.L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24, 182–190 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Internat. J. General Syst. 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  8. Gierz, G., Hoffman, K.H., Keimel, K., Lawson, J.D., Mislove, M.W., Scott, D.S.: Continuous Lattices and Domains. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  9. Goguen, J.A.: The fuzzy Tychonoff theorem. J. Math. Anal. Appl. 43, 734–742 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  10. Eļkins, A., Šostak, A.: On some categories of approximate systems generated by L-relations. In: 3rd Rough Sets Theory Workshop, Milan, Italy, pp. 14–19 (2011)

    Google Scholar 

  11. Sang-Eon, H., Soo, K.I., Šostak, A.: On approximate-type systems generated by L-relations. Inf. Sci. (to appear)

    Google Scholar 

  12. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Acad. Publ. (2000)

    Google Scholar 

  13. Pawlak, Z.: Rough sets. Intern. J. of Computer and Inform. Sci. 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  14. Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Syst. 126, 137–155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Rosenthal, K.I.: Quantales and Their Applications. Pirman Research Notes in Mathematics 234. Longman Scientific & Technical (1990)

    Google Scholar 

  16. Rodabaugh, S.E.: Powers-set operator based foundations for point-set lattice-theoretic (poslat) fuzzy set theories and topologies. Quaest. Math. 20, 463–530 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rodabaugh, S.E.: Power-set operator foundations for poslat fuzzy set theories and topologies. In: Höhle, U., Rodabaugh, S.E. (eds.) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, pp. 91–116. Kluwer Acad. Publ. (1999)

    Google Scholar 

  18. Schweitzer, B., Sklar, A.: Probabilistic Metric Spaces. North Holland, New York (1983)

    Google Scholar 

  19. Šostak, A.: On approximative operators and approximative systems. In: Proceedings of Congress of the International Fuzzy System Association (IFSA 2009), Lisbon, Portugal, July 20-24, pp. 1061–1066 (2009)

    Google Scholar 

  20. Šostak, A.: Towards the theory of M-approximate systems: Fundamentals and examples. Fuzzy Sets and Syst. 161, 2440–2461 (2010)

    Article  MATH  Google Scholar 

  21. Šostak, A.: Towards the theory of approximate systems: variable range categories. In: Proceedings of ICTA 2011, Islamabad, Pakistan, pp. 265–284. Cambridge University Publ. (2012)

    Google Scholar 

  22. Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Syst. 17, 313–328 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  23. Yao, Y.Y.: A comparative study of fuzzy sets and rough sets. Inf. Sci. 109, 227–242 (1998)

    Article  MATH  Google Scholar 

  24. Yao, Y.Y.: On generalizing Pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 298–307. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  25. Zadeh, L.: Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200 (1971)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Latvia, LV-1002, Riga, Latvia

    Aleksandrs Eļkins & Alexander Šostak

  2. Institute of Mathematics and CS, University of Latia, LV-1459, Riga, Latvia

    Alexander Šostak

  3. Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City, Jeonbuk, 561-756, Republic of Korea

    Sang-Eon Han

Authors
  1. Aleksandrs Eļkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sang-Eon Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Šostak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. Institute for Human Factors and Technology Management, IAT, University of Stuttgart, Nobelstraße 12, 70569, Stuttgart, Germany

    Oliver Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Eļkins, A., Han, SE., Šostak, A. (2014). Variable-Range Approximate Systems Induced by Many-Valued L-Relations. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08852-5_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics