Note on "construction of uninorms on bounded lattices"
Kybernetika, Tome 57 (2021) no. 2, pp. 372-382 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2021-2-0372
Classification : 03B52, 03E72, 06B20
Keywords: bounded lattices; uninorms; closure operators; interior operators
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Hua, Xiu-Juan; Zhang, Hua-Peng; Ouyang, Yao. Note on "construction of uninorms on bounded lattices". Kybernetika, Tome 57 (2021) no. 2, pp. 372-382. doi: 10.14736/kyb-2021-2-0372

[1] Birkhoff, G.: Lattice Theory. AMS Colloquium Publishers, Providence,Rhode Island 1973. | MR | Zbl

[2] Çaylı, G. D., Karaçal, F.: Construction of uninorms on bounded lattices. Kybernetika 53 (2017), 394-417. | DOI | MR

[3] D.Çaylı, G., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices. Inf. Sci. 367 - 368 (2016), 221-231. | DOI | MR

[4] Dan, Y. X., Hu, B. Q.: A new structure for uninorms on bounded lattices. Fuzzy Sets Syst. 386 (2020), 77-94. | DOI | MR

[5] Baets, B. De, Mesiar, R.: Triangular norm on product lattices. Fuzzy Sets Syst. 104 (1999), 61-75. | DOI | MR

[6] Cooman, G. De, Kerre, E. E.: Order norms on bounded partially ordered sets. J. Fuzzy Math. 2 (1994), 281-310. | MR | Zbl

[7] Drossos, C. A., Navara, M.: Generalized t-conorms and closure operators. In: Proc. EUFIT '96, Aachen 1996, pp. 22-26.

[8] Everett, C. J.: Closure operators and Galois theory in lattices. Trans. Amer. Math. Soc. 55 (1944), 514-525. | DOI | MR

[9] Ji, W.: Constructions of uninorms on bounded lattices by means of t-subnorms and t-subconorms. Fuzzy Sets Syst. 403 (2021), 38-55. | DOI | MR

[10] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets Syst. 261 (2015), 33-43. | DOI | MR

[11] Ouyang, Y., Zhang, H. P.: Constructing uninorms via closure operators on a bounded lattice. Fuzzy Sets Syst. 395 (2020), 93-106. | DOI | MR

[12] Schweizer, B., Sklar, A.: Statistical metric space. Pac. J. Math. 10 (1960), 313-334. | DOI | MR

[13] Xie, A. F., Li, S. J.: On constructing the largest and smallest uninorms on bounded lattices. Fuzzy Sets Syst. 386 (2020), 95-104. | DOI | MR

[14] Yager, R. R., Rybalov, A.: Uninorms aggregation operators. Fuzzy Sets Syst. 80 (1996), 111-120. | DOI | MR

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