Kybernetika 53 no. 5, 911-921, 2017

Notes on locally internal uninorm on bounded lattices

Gül Deniz Çaylı, Ümit Ertuğrul, Tuncay Köroğlu and Funda KaraçalDOI: 10.14736/kyb-2017-5-0911

Abstract:

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice $L$. We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice $L$, and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.

Keywords:

uninorm, idempotent uninorm, bounded lattice, locally internal

Classification:

03B52, 06B20, 03E72

paper.pdf

References:

  1. E. Aşıcı and F. Karaçal: Incomparability with respect to the triangular order. Kybernetika 52 (2016), 15-27.   DOI:10.14736/kyb-2016-1-0015
  2. G. Birkhoff: Lattice Theory. American Mathematical Society Colloquium Publ., Providence 1967.   DOI:10.1090/coll/025
  3. B. De Baets: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631-642.   DOI:10.1016/s0377-2217(98)00325-7
  4. B. De Baets and J. Fodor: A single-point characterization of representable uninorms. Fuzzy Sets Syst. 202 (2012), 89-99.   DOI:10.1016/j.fss.2011.12.001
  5. G. D. Çaylı, F. Karaçal and R. Mesiar: On a new class of uninorms on bounded lattices. Inform. Sci. 367-368 (2016), 221-231.   DOI:10.1016/j.ins.2016.05.036
  6. G. D. Çaylı and P. Drygaś: Some properties of idempotent uninorms on bounded lattices. Inform. Sci. 422 (2018), 352-363.   DOI:10.1016/j.ins.2017.09.018
  7. J. Drewniak and P. Drygaś: On a class of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10 (2002), 5-10.   DOI:10.1142/s021848850200179x
  8. P. Drygaś: On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums. Fuzzy Sets Syst. 161 (2010), 149-157.   DOI:10.1016/j.fss.2009.09.017
  9. P. Drygaś, D. Ruiz-Aguilera and J. Torrens: A characterization of uninorms locally internal in $A(e)$ with continuous underlying operators. Fuzzy Sets Syst. 287 (2016), 137-153.   DOI:10.1016/j.fss.2009.09.017
  10. Ü. Ertuğrul, M. N. Kesicioğlu and F. Karaçal: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327.   DOI:10.1016/j.ins.2015.10.019
  11. J. Fodor, R. R. Yager and A. Rybalov: Structure of uninorms. Int. J. Uncertain Fuzziness Knowl.-Based Syst. 5 (1997), 411-427.   DOI:10.1142/s0218488597000312
  12. M. N. Kesicioğlu and R. Mesiar: Ordering based on implications. Fuzzy Sets Syst. 276 (2014), 377-386.   DOI:10.1016/j.ins.2013.12.047
  13. M. N. Kesicioğlu, Ü. Ertuğrul and F. Karaçal: An equivalence relation based on the U-partial order. Inform. Sci. 411 (2017), 39-51.   DOI:10.1016/j.ins.2017.05.020
  14. F. Karaçal and R. Mesiar: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43.   DOI:10.1016/j.fss.2014.05.001
  15. F. Karaçal, Ü. Ertuğrul and R. Mesiar: Characterization of uninorms on bounded lattices. Fuzzy Sets Syst. 308 (2017), 54-71.   DOI:10.1016/j.fss.2016.05.014
  16. E. P. Klement, R. Mesiar and E. Pap: Triangular Norms. Dordrecht, Kluwer Acad. Publ., 2000.   DOI:10.1007/978-94-015-9540-7
  17. J. Martin, G. Mayor and J. Torrens: On locally internal monotonic operations. Fuzzy Sets Syst. 137 (2003), 27-42.   DOI:10.1016/s0165-0114(02)00430-x
  18. A. Mesiarová-Zemánková: Multi-polar t-conorms and uninorms. Inform. Sci. 301 (2015), 227-240.   DOI:10.1016/j.ins.2014.12.060
  19. R. R. Yager: Uninorms in fuzzy system modeling. Fuzzy Sets Syst. 122 (2001), 167-175.   DOI:10.1016/s0165-0114(00)00027-0
  20. R. R. Yager: Defending against strategic manipulation in uninorm-based multi-agent decision making. European J. Oper. Res. 141 (2002), 217-232.   DOI:10.1016/s0377-2217(01)00267-3
  21. R. R. Yager and A. Rybalov: Uninorms aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120.   DOI:10.1016/0165-0114(95)00133-6