Equivalent fuzzy sets

Branimir Šešelja; Andreja Tepavčević

Kybernetika (2005)

  • Volume: 41, Issue: 2, page [115]-128
  • ISSN: 0023-5954

Abstract

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Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.

How to cite

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Šešelja, Branimir, and Tepavčević, Andreja. "Equivalent fuzzy sets." Kybernetika 41.2 (2005): [115]-128. <http://eudml.org/doc/33744>.

@article{Šešelja2005,
abstract = {Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.},
author = {Šešelja, Branimir, Tepavčević, Andreja},
journal = {Kybernetika},
keywords = {poset valued fuzzy set; cut; equivalent fuzzy sets; Dedekind- MacNeille completion; poset-valued fuzzy set; cut set; equivalent fuzzy sets; Dedekind-MacNeille completion},
language = {eng},
number = {2},
pages = {[115]-128},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Equivalent fuzzy sets},
url = {http://eudml.org/doc/33744},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Šešelja, Branimir
AU - Tepavčević, Andreja
TI - Equivalent fuzzy sets
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [115]
EP - 128
AB - Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.
LA - eng
KW - poset valued fuzzy set; cut; equivalent fuzzy sets; Dedekind- MacNeille completion; poset-valued fuzzy set; cut set; equivalent fuzzy sets; Dedekind-MacNeille completion
UR - http://eudml.org/doc/33744
ER -

References

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  10. Šešelja B., Fuzzy structures and collections of level structures, BUSEFAL 61 (1995), 5–8 (1995) 
  11. Šešelja B., Tepavčević A., 10.1016/0165-0114(94)90249-6, Fuzzy Sets and Systems 65 (1994), 85–94 (1994) DOI10.1016/0165-0114(94)90249-6
  12. Šešelja B., Tepavčević A., 10.1016/0165-0114(95)00332-0, Fuzzy Sets and Systems 83 (1996), 85–91 (1996) DOI10.1016/0165-0114(95)00332-0
  13. Šeselja B., Tepavčević A., Completion of ordered structures by cuts of fuzzy sets, An overview. Fuzzy Sets and Systems 136 (2003), 1–19 Zbl1020.06005MR1978466
  14. Šeselja B., Tepavčević A., Representing ordered structures by fuzzy sets, An overview. Fuzzy Sets and Systems 136 (2003), 21–39 Zbl1026.03039MR1978467
  15. Šeselja B., Tepavčević A., A note on natural equivalence relation on fuzzy power set, Fuzzy Sets and Systems 148 (2004), 201–210 

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