Kybernetika 57 no. 2, 372-382, 2021

Note on ``construction of uninorms on bounded lattices"

Xiu-Juan Hua, Hua-Peng Zhang and Yao OuyangDOI: 10.14736/kyb-2021-2-0372

Abstract:

In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.

Keywords:

uninorms, bounded lattices, closure operators, interior operators

Classification:

03B52, 06B20, 03E72

paper.pdf

References:

  1. G. Birkhoff: Lattice Theory. AMS Colloquium Publishers, Providence,Rhode Island 1973.   CrossRef
  2. G. D. Çaylı and F. Karaçal: Construction of uninorms on bounded lattices. Kybernetika 53 (2017), 394-417.   DOI:10.14736/kyb-2017-3-0394
  3. G. D.Çaylı, F. Karaçal and R. Mesiar: On a new class of uninorms on bounded lattices. Inf. Sci. 367 - 368 (2016), 221-231.   DOI:10.1016/j.ins.2016.05.036
  4. Y. X. Dan and B. Q. Hu: A new structure for uninorms on bounded lattices. Fuzzy Sets Syst. 386 (2020), 77-94.   DOI:10.1016/j.fss.2019.02.001
  5. B. De Baets and R. Mesiar: Triangular norm on product lattices. Fuzzy Sets Syst. 104 (1999), 61-75.   DOI:10.1016/S0165-0114(98)00259-0
  6. G. De Cooman and E. E. Kerre: Order norms on bounded partially ordered sets. J. Fuzzy Math. 2 (1994), 281-310.   CrossRef
  7. C. A. Drossos and M. Navara: Generalized t-conorms and closure operators. In: Proc. EUFIT '96, Aachen 1996, pp. 22-26.   CrossRef
  8. C. J. Everett: Closure operators and Galois theory in lattices. Trans. Amer. Math. Soc. 55 (1944), 514-525.   DOI:10.1090/S0002-9947-1944-0010556-9
  9. W. Ji: Constructions of uninorms on bounded lattices by means of t-subnorms and t-subconorms. Fuzzy Sets Syst. 403 (2021), 38-55.   DOI:10.1016/j.fss.2019.12.003
  10. F. Karaçal and R. Mesiar: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43.   DOI:10.1016/j.fss.2014.05.001
  11. Y. Ouyang and H. P. Zhang: Constructing uninorms via closure operators on a bounded lattice. Fuzzy Sets Syst. 395 (2020), 93-106.   DOI:10.1016/j.fss.2019.05.006
  12. B. Schweizer and A. Sklar: Statistical metric space. Pac. J. Math. 10 (1960), 313-334.   DOI:10.2140/pjm.1960.10.313
  13. A. F. Xie and S. J. Li: On constructing the largest and smallest uninorms on bounded lattices. Fuzzy Sets Syst. 386 (2020), 95-104.   DOI:10.1016/j.fss.2019.04.020
  14. R. R. Yager and A. Rybalov: Uninorms aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120.   DOI:10.1016/0165-0114(95)00133-6