Title:
|
On the direct product of uninorms on bounded lattices (English) |
Author:
|
Aşıcı, Emel |
Author:
|
Mesiar, Radko |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
57 |
Issue:
|
6 |
Year:
|
2021 |
Pages:
|
989-1004 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices and properties of introduced order are deeply investigated. Moreover, we obtain some results concerning orders induced by uninorms acting on the unit interval $ [0,1] $. (English) |
Keyword:
|
uninorm |
Keyword:
|
direct product |
Keyword:
|
partial order |
MSC:
|
03B52 |
MSC:
|
03E72 |
idZBL:
|
Zbl 07478651 |
idMR:
|
MR4376872 |
DOI:
|
10.14736/kyb-2021-6-0989 |
. |
Date available:
|
2022-02-04T08:48:38Z |
Last updated:
|
2022-02-24 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149352 |
. |
Reference:
|
[1] Aşıcı, E.: An order induced by nullnorms and its properties..Fuzzy Sets Syst. 325 (2017), 35-46. MR 3690353, |
Reference:
|
[2] Aşıcı, E.: The equivalence of uninorms induced by the $ U $-partial order..Hacet. J. Math. Stat. 48 (2019), 2, 439-450. MR 3974553, |
Reference:
|
[3] Aşıcı, E.: Construction methods for triangular norms and triangular conorms on appropriate bounded lattices..Iran. J. Fuzzy Syst. 18 (2021), 81-98. MR 4284673, |
Reference:
|
[4] Aşıcı, E., Karaçal, F.: On the $ T $-partial order and properties..Inform. Sci. 267 (2014), 323-333. MR 3177320, |
Reference:
|
[5] Aşıcı, E., Mesiar, R.: Alternative approaches to obtain t-norms and t-conorms on bounded lattices..Iran. J. Fuzzy Syst. 17 (2020), 121-138. MR 4155854, |
Reference:
|
[6] Aşıcı, E., Mesiar, R.: On generating uninorms on some special classes of bounded lattices.Fuzzy Sets Syst. |
Reference:
|
[7] Aşıcı, E., Mesiar, R.: On the construction of uninorms on bounded lattices..Fuzzy Sets Syst. 408 (2021), 65-85. MR 4210984, |
Reference:
|
[8] Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners..Studies in Fuzziness and Soft Computing, vol. 221, Springer, Berlin, Heidelberg 2007. MR 3382259 |
Reference:
|
[9] Birkhoff, G.: Lattice Theory. Third edition..Providence 1967. MR 0227053 |
Reference:
|
[10] Calvo, T., Baets, B. De, Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms..Fuzzy Sets Syst. 120 (2001), 385-394. Zbl 0977.03026, MR 1829256, |
Reference:
|
[11] Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: New Trends and Applications..Studies in Fuzziness and Soft Computing, vol. 97, Springer, Berlin, Heidelberg 2002. MR 1936384 |
Reference:
|
[12] Casasnovas, J., Mayor, G.: Discrete t-norms and operations on extended multisets..Fuzzy Sets Syst. 159 (2008), 1165-1177. Zbl 1176.03023, MR 2416385, |
Reference:
|
[13] Çaylı, G. D.: New methods to construct uninorms on bounded lattices..Int. J. Approximate Reason. 115 (2019), 254-264. MR 4018632, |
Reference:
|
[14] Çaylı, G. D.: Uninorms on bounded lattices with the underlying t-norms and t-conorms..Fuzzy Sets and Systems 395 (2020), 107-129. MR 4109064, |
Reference:
|
[15] Çaylı, G. D.: Alternative approaches for generating uninorms on bounded lattices..Inform. Sci. 488 (2019), 111-139. MR 3924420, |
Reference:
|
[16] Baets, B. De, Mesiar, R.: Triangular norms on product lattices..Fuzzy Sets Syst. 104 (1999), 61-75. Zbl 0935.03060, MR 1685810, |
Reference:
|
[17] Drewniak, J., Drygaś, P., Rak, E.: Distributivity between uninorms and nullnorms..Fuzzy Sets Syst. 159 (2008), 1646-1657. MR 2419975, |
Reference:
|
[18] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms..Inform. Sci. 330 (2016), 315-327. |
Reference:
|
[19] Fodor, J. C., Yager, R. R., Rybalov, A.: Structure of uninorms..Int. J. Uncertain Fuzz. Knowl.-Based Syst. 5 (1997), 411-427. Zbl 1232.03015, MR 1471619, 10.1142/S0218488597000312 |
Reference:
|
[20] Fodor, J., Baets, B. De: A single-point characterization of representable uninorms..Fuzzy Sets Syst. 202 (2012), 89-99. Zbl 1268.03027, MR 2934788, |
Reference:
|
[21] Kalina, M.: On uninorms and nullnorms on direct product of bounded lattices..Open Phys. 14 (2016), 321-327. |
Reference:
|
[22] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices..Fuzzy Sets Syst. 261 (2015), 33-43. MR 3291484, |
Reference:
|
[23] Karaçal, F., Kesicioğlu, M. N.: A T-partial order obtained from t-norms..Kybernetika 47 (2011), 300-314. Zbl 1245.03086, MR 2828579, |
Reference:
|
[24] Kesicioğlu, M. N., Karaçal, F., Ertuğrul, Ü.: An equivalence relation based on the $ U $-partial order..Inform. Sci. 411 (2017), 39-51. MR 3659313, |
Reference:
|
[25] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms..Kluwer Academic Publishers, Dordrecht 2000. Zbl 1087.20041, MR 1790096 |
Reference:
|
[26] Klir, G. J., Yuan, B.: Fuzzy Sets and Fuzzy Logic, Theory and Application..Prentice Hall PTR, Upper Saddle River, New Jersey 1995. MR 1443433 |
Reference:
|
[27] Saminger, S.: On ordinal sums of triangular norms on bounded lattices..Fuzzy Sets Syst. 157 (2006), 1403-1416. Zbl 1099.06004, MR 2226983, |
Reference:
|
[28] Yager, R. R., Rybalov, A.: Uninorm aggregation operators..Fuzzy Sets Syst. 80 (1996), 111-120. Zbl 0871.04007, MR 1389951, |
. |