Semi-t-operators on a finite totally ordered set

Yong Su; Hua-Wen Liu

Kybernetika (2015)

  • Volume: 51, Issue: 4, page 667-677
  • ISSN: 0023-5954

Abstract

top
Recently, Drygaś generalized nullnorms and t-operators and introduced semi-t-operators by eliminating commutativity from the axiom of t-operators. This paper is devoted to the study of the discrete counterpart of semi-t-operators on a finite totally ordered set. A characterization of semi-t-operators on a finite totally ordered set is given. Moreover, The relations among nullnorms, t-operators, semi-t-operators and pseudo-t-operators (i. e., commutative semi-t-operators) on a finite totally ordered set are shown.

How to cite

top

Su, Yong, and Liu, Hua-Wen. "Semi-t-operators on a finite totally ordered set." Kybernetika 51.4 (2015): 667-677. <http://eudml.org/doc/271832>.

@article{Su2015,
abstract = {Recently, Drygaś generalized nullnorms and t-operators and introduced semi-t-operators by eliminating commutativity from the axiom of t-operators. This paper is devoted to the study of the discrete counterpart of semi-t-operators on a finite totally ordered set. A characterization of semi-t-operators on a finite totally ordered set is given. Moreover, The relations among nullnorms, t-operators, semi-t-operators and pseudo-t-operators (i. e., commutative semi-t-operators) on a finite totally ordered set are shown.},
author = {Su, Yong, Liu, Hua-Wen},
journal = {Kybernetika},
keywords = {fuzzy connectives; finite chain; t-operator; semi-t-operator; pseudo-t-operator; fuzzy connectives; finite chain; t-operator; semi-t-operator; pseudo-t-operator},
language = {eng},
number = {4},
pages = {667-677},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Semi-t-operators on a finite totally ordered set},
url = {http://eudml.org/doc/271832},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Su, Yong
AU - Liu, Hua-Wen
TI - Semi-t-operators on a finite totally ordered set
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 4
SP - 667
EP - 677
AB - Recently, Drygaś generalized nullnorms and t-operators and introduced semi-t-operators by eliminating commutativity from the axiom of t-operators. This paper is devoted to the study of the discrete counterpart of semi-t-operators on a finite totally ordered set. A characterization of semi-t-operators on a finite totally ordered set is given. Moreover, The relations among nullnorms, t-operators, semi-t-operators and pseudo-t-operators (i. e., commutative semi-t-operators) on a finite totally ordered set are shown.
LA - eng
KW - fuzzy connectives; finite chain; t-operator; semi-t-operator; pseudo-t-operator; fuzzy connectives; finite chain; t-operator; semi-t-operator; pseudo-t-operator
UR - http://eudml.org/doc/271832
ER -

References

top
  1. Baets, B. De, Mesiar, R., 10.1016/s0165-0114(98)00259-0, Fuzzy Sets and Systems 104 (1999), 61-75. Zbl0935.03060MR1685810DOI10.1016/s0165-0114(98)00259-0
  2. Baets, B. De, Fodor, J., Ruiz-Aguilera, D., Torrens, J., 10.1142/s021848850900570x, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 17 (2009), 1-14. Zbl1178.03070MR2514519DOI10.1142/s021848850900570x
  3. Calvo, T., Baets, B. De, Fodor, J., 10.1016/s0165-0114(99)00125-6, Fuzzy Sets and Systems 120 (2001), 385-394. Zbl0977.03026MR1829256DOI10.1016/s0165-0114(99)00125-6
  4. Drygaś, P., 10.1016/j.fss.2014.09.003, Fuzzy Sets and Systems 264 2015, 100-109. MR3303666DOI10.1016/j.fss.2014.09.003
  5. Fodor, J., 10.1109/91.890343, IEEE Trans. on Fuzzy Systems 8 (2000), 6, 791-795. DOI10.1109/91.890343
  6. Klement, E. P., Mesiar, R., Pap, E., 10.1007/978-94-015-9540-7, Kluwer Academic Publ., Dordrecht 2000. Zbl1087.20041MR1790096DOI10.1007/978-94-015-9540-7
  7. Kolesarova, A., Mayor, G., Mesiar, R., 10.1016/j.ins.2007.03.003, Information Sciences 177 (2007), 3822-3830. Zbl1124.03028MR2337214DOI10.1016/j.ins.2007.03.003
  8. Li, G., Liu, H-w., Fodor, J., 10.1002/int.21694, Int. J. Intelligent Systems 30 (201), 421-440. DOI10.1002/int.21694
  9. Mas, M., Mayor, G., Torrens, J., 10.1002/(SICI)1098-111X(199909)14:9<909::AID-INT4>3.0.CO;2-B, Int. J. Intelligent Systems 14 (1999), 909-922. Zbl0948.68173MR1691482DOI10.1002/(SICI)1098-111X(199909)14:9<909::AID-INT4>3.0.CO;2-B
  10. Mas, M., Mayor, G., Torrens, J., 10.1142/s0218488599000039, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 7 (1999), 31-50. Zbl1005.03047MR1691482DOI10.1142/s0218488599000039
  11. Mas, M., Mayor, G., Torrens, J., 10.1016/s0165-0114(01)00123-3, Fuzzy Sets and Systems 128 (2002), 209-225. Zbl1005.03047MR1908427DOI10.1016/s0165-0114(01)00123-3
  12. Mayor, G., Torrens, J., 10.1002/int.4550080703, Int. J. Intelligent Systems 8 (1993), 771-778. Zbl0785.68087DOI10.1002/int.4550080703
  13. Mayor, G., Torrens, J., Triangular Norms on Discrete Settings., In: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms (E. P. Klement and R. Mesiar, eds.), Elsevier, Amsterdam (2005). Zbl1079.03012MR2165236
  14. Riera, J. V., Torrens, J., 10.2991/eusflat.2011.137, In: EUSFLAT Conf. 2011, pp. 59-66. Zbl1254.03106DOI10.2991/eusflat.2011.137
  15. Ruiz-Aguilera, D., Torrens, J., 10.1016/j.fss.2014.10.020, Fuzzy Sets and Systems 268 (2015), 44-58. MR3320246DOI10.1016/j.fss.2014.10.020
  16. Torrens, J., Estudi de models matemktics per a connectius en logica multivaluada., Ph.D. Thesis, Palma de Mallorca Universitat de les IIIes Balears, 1990. 
  17. Trillas, E., Alsina, C., 10.1016/0165-0114(93)90518-m, Fuzzy Sets and Systems 5 (1993), 3, 1-13. MR1198778DOI10.1016/0165-0114(93)90518-m

NotesEmbed ?

top

You must be logged in to post comments.