On reverses of some binary operators

Michal Šabo; Peter Strežo

Kybernetika (2005)

  • Volume: 41, Issue: 4, page [435]-450
  • ISSN: 0023-5954

Abstract

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The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.

How to cite

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Šabo, Michal, and Strežo, Peter. "On reverses of some binary operators." Kybernetika 41.4 (2005): [435]-450. <http://eudml.org/doc/33765>.

@article{Šabo2005,
abstract = {The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.},
author = {Šabo, Michal, Strežo, Peter},
journal = {Kybernetika},
keywords = {reverse of binary operations; fuzzy preference structures; reverse of binary operations; fuzzy preference structures},
language = {eng},
number = {4},
pages = {[435]-450},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On reverses of some binary operators},
url = {http://eudml.org/doc/33765},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Šabo, Michal
AU - Strežo, Peter
TI - On reverses of some binary operators
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 4
SP - [435]
EP - 450
AB - The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.
LA - eng
KW - reverse of binary operations; fuzzy preference structures; reverse of binary operations; fuzzy preference structures
UR - http://eudml.org/doc/33765
ER -

References

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  1. Baets B. De, Fodor J., Twenty years of fuzzy preference structures (1978 – 1997), Belg. J. Oper. Res. Statist. Comput. Sci. 37 (1997), 61–81 (1997) Zbl0926.91012MR1619319
  2. Baets B. De, Fodor J., Generator triplets of additive preference structures, Academia Press, Gent 2003, pp. 15–25 
  3. Baets B. De, Mayer H. De, The Frank family in fuzzy similarity measurement, In: Proc. Eusflat, Leicester 2001, pp. 15–23 
  4. Fodor J., Roubens M., Fuzzy Preference Modeling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht 1994 
  5. Fodor J., Jenei S., On reversible triangular t-norms, Fuzzy Sets and Systems 104 (1999), 1, 43–51 (1999) MR1685808
  6. Frank M. J., 10.1007/BF02189866, Aequationes Math. 19 (1979), 194–226 (1979) Zbl0444.39003MR0556722DOI10.1007/BF02189866
  7. Jenei S., Fibred triangular norms, Fuzzy Sets and Systems 103 (1999), 68–82 (1999) Zbl0946.26017MR1674034
  8. Kimberling C., On a class of associative function, Publ. Math. Debrecen 20 (1973), 21–39 (1973) MR0333504
  9. Klement E. P., Mesiar, R., Pap E., On some geometric tranformations of t-norms, Mathware & Soft Computing 5 (1998), 57–67 (1998) MR1632763
  10. Klement E. P., Mesiar, R., Pap E., Invariant copulas, Kybernetika 38 (2002), 275–285 MR1944309
  11. Klement E. P., Mesiar, R., Pap E., 10.1016/j.fss.2003.10.028, Fuzzy Sets and Systems 142 (2004), 3–14 Zbl1046.28011MR2045339DOI10.1016/j.fss.2003.10.028
  12. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  13. Kolesárová A., Mordelová J., 1-Lipschitz and kernel aggregation operators, In: Proc. Summmer School on Aggregation Operators and their Applications, Oviedo 2001, pp. 71–75 
  14. Lazaro J., Rückschlossová, T., Calvo T., 10.1016/j.fss.2003.10.031, Fuzzy Sets and Systems 142 (2004), 51–62 Zbl1081.68106MR2045342DOI10.1016/j.fss.2003.10.031
  15. Mesiarová A., Continuous triangular subnorms, Fuzzy Sets and Systems 142 (2004), 75–83 Zbl1043.03018MR2045344
  16. Moyniham R., On τ T semigroups of probability distributions II, Aequationes Math. 17 (1978), 19–40 (1978) 
  17. Nelsen R. B., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics 139.) Springer, New York 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
  18. Šabo M., On t-reverse of t-norms, Tatra Mt. Math. Publ. 12 (1997), 35–40 (1997) Zbl0954.03060MR1607131
  19. Šabo M., Fuzzy preference structures and t-reversible t-norm, Busefal 76 (1998), 29–33 (1998) 
  20. Schweizer B., Sklar A., Probabilistic Metric Spaces, North–Holland, New York 1963 Zbl0546.60010MR0790314
  21. Walle B. Van de, Baets, B. De, Kerre E. E., A comparative study of completeness conditions in fuzzy preference structures, In: Proc. IFSA’97, Prague, Vol. III, pp. 74–79 

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