Nearness relations in linear spaces

Martin Kalina

Kybernetika (2004)

  • Volume: 40, Issue: 4, page [441]-458
  • ISSN: 0023-5954

Abstract

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In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.

How to cite

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Kalina, Martin. "Nearness relations in linear spaces." Kybernetika 40.4 (2004): [441]-458. <http://eudml.org/doc/33710>.

@article{Kalina2004,
abstract = {In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.},
author = {Kalina, Martin},
journal = {Kybernetika},
keywords = {nearness relation; pseudo-arithmetic mean; geometric mean; nearness-convergence; continuous t-norm; nearness relation; pseudo-arithmetic mean; geometric mean; nearness-convergence; continuous -norm},
language = {eng},
number = {4},
pages = {[441]-458},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nearness relations in linear spaces},
url = {http://eudml.org/doc/33710},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Kalina, Martin
TI - Nearness relations in linear spaces
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 4
SP - [441]
EP - 458
AB - In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.
LA - eng
KW - nearness relation; pseudo-arithmetic mean; geometric mean; nearness-convergence; continuous t-norm; nearness relation; pseudo-arithmetic mean; geometric mean; nearness-convergence; continuous -norm
UR - http://eudml.org/doc/33710
ER -

References

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  2. Dobrakovová J., Nearness, convergence and topology, Busefal 80 (1999), 17–23 (1999) 
  3. Dobrakovová J., Nearness based topology, Tatra Mount. Math. Publ. 21 (2001), 163–170 Zbl0993.54006MR1904907
  4. Janiš V., Fixed points of fuzzy functions, Tatra Mount. Math. Publ. 12 (1997), 13–19 (1997) Zbl0946.54036MR1607143
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  7. Kalina M., Fuzzy smoothness and sequences of fuzzy smooth functions, Fuzzy Sets and Systems 105 (1999), 233–239 (1999) Zbl0955.26011MR1695578
  8. Kalina M., Dobrakovová J., Relation of fuzzy nearness in Banach space, In: Proc. East-West Fuzzy Colloquium, Zittau 2002, pp. 26–32 
  9. Klement E. P., Mesiar, R., Pap E., Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms, Fuzzy Sets and Systems 104 (1999), 3–13 (1999) Zbl0953.26008MR1685803
  10. Klement E. P., Mesiar, R., Pap E., Triangular norms, Trends in Logic, Studia Logica Library 8, Kluwer 2000 Zbl1087.20041MR1790096
  11. Kolesárová A., On the comparision of quasi-arithmetic means, Busefal 80 (1999), 30–34 (1999) 
  12. Mesiar R., Komorníková M., Aggregation operators, In: Proc. PRIM’96, XI Conference on Applied Mathematics 1996, pp. 193-211 (1996) 
  13. Micháliková–Rückschlossová T., Some constructions of aggregation operators, J. Electrical Engrg. 12 (2000), 29–32 Zbl0973.26018
  14. Viceník P., Noncontinuous Additive Generators of Triangular Norms (in Slovak), Ph. D. Thesis. STU Bratislava 2002 

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