Skip to main content
Erschienen in: International Journal of Machine Learning and Cybernetics 6/2016

01.12.2016 | Original Article

Applications of repeat degree to coverings of neighborhoods

verfasst von: Hua Yao, William Zhu

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 6/2016

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Covering of neighborhoods is an important concept in covering-based rough sets. There are many unsolved issues related to coverings of neighborhoods. The concept of repeat degree is proposed to study under what condition a covering of neighborhoods is a partition. It enables us to deal with many issues related to coverings of neighborhoods when coverings are incomplete. This paper applies repeat degree to solve some fundamental issues in coverings of neighborhoods. First, we investigate under what condition a covering of neighborhoods is equal to the reduct of the covering which induces the covering of neighborhoods. Then we study under what condition two coverings induce the same relation and the same covering of neighborhoods. Finally, we propose an approach to calculate coverings through repeat degree.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Weitere Produktempfehlungen anzeigen
Literatur
1.
Zurück zum Zitat Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107:149–167MathSciNetCrossRefMATH Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107:149–167MathSciNetCrossRefMATH
2.
Zurück zum Zitat Bryniarski E (1989) A calculus of rough sets of the first order. Bull Polish Acad Sci 37:71–78MathSciNetMATH Bryniarski E (1989) A calculus of rough sets of the first order. Bull Polish Acad Sci 37:71–78MathSciNetMATH
3.
Zurück zum Zitat Chen D, Zhang W, Yeung D, Tsang E (2006) Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf Sci 176:1829–1848MathSciNetCrossRefMATH Chen D, Zhang W, Yeung D, Tsang E (2006) Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf Sci 176:1829–1848MathSciNetCrossRefMATH
4.
Zurück zum Zitat Chen J, Li J, Lin Y (2013) On the structure of definable sets in covering approximation spaces. Int J Mach Learn Cybernet 4:195–206CrossRef Chen J, Li J, Lin Y (2013) On the structure of definable sets in covering approximation spaces. Int J Mach Learn Cybernet 4:195–206CrossRef
5.
Zurück zum Zitat Dai J (2005) Logic for rough sets with rough double stone algebraic semantics. In: Rough sets, fuzzy sets, data mining, and granular computing, vol 3641 of LNCS, pp 141–148 Dai J (2005) Logic for rough sets with rough double stone algebraic semantics. In: Rough sets, fuzzy sets, data mining, and granular computing, vol 3641 of LNCS, pp 141–148
7.
Zurück zum Zitat Du Y, Hu Q, Zhu P, Ma P (2011) Rule learning for classification based on neighborhood covering reduction. Inf Sci 181:5457–5467MathSciNetCrossRef Du Y, Hu Q, Zhu P, Ma P (2011) Rule learning for classification based on neighborhood covering reduction. Inf Sci 181:5457–5467MathSciNetCrossRef
9.
Zurück zum Zitat Fan N, Hu G, Xiao X, Zhang W (2012) Study on conditions of neighborhoods forming a partition. In: International Conference on fuzzy systems and knowledge discovery, 256–259 Fan N, Hu G, Xiao X, Zhang W (2012) Study on conditions of neighborhoods forming a partition. In: International Conference on fuzzy systems and knowledge discovery, 256–259
11.
Zurück zum Zitat Kazanci O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178:2349–2359MathSciNetCrossRefMATH Kazanci O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178:2349–2359MathSciNetCrossRefMATH
13.
14.
15.
Zurück zum Zitat Lin TY (1988) Neighborhood systems and relational databases. In: ACM sixteenth annual conference on computer science, p 725 Lin TY (1988) Neighborhood systems and relational databases. In: ACM sixteenth annual conference on computer science, p 725
17.
21.
Zurück zum Zitat Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, BostonCrossRefMATH Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, BostonCrossRefMATH
22.
Zurück zum Zitat Pomykala JA (1987) Approximation operations in approximation space. Bull Polish Acad Sci Math 35:653–662MathSciNetMATH Pomykala JA (1987) Approximation operations in approximation space. Bull Polish Acad Sci Math 35:653–662MathSciNetMATH
23.
Zurück zum Zitat Pomykala JA (1988) On definability in the nondeterministic information system. Bull Polish Acad Sci Math 36:193–210MathSciNetMATH Pomykala JA (1988) On definability in the nondeterministic information system. Bull Polish Acad Sci Math 36:193–210MathSciNetMATH
24.
Zurück zum Zitat Qin K, Gao Y, Pei Z (2007) On covering rough sets. in: Rough set and knowledge technology, vol 4481 of LNAI, pp 34–41 Qin K, Gao Y, Pei Z (2007) On covering rough sets. in: Rough set and knowledge technology, vol 4481 of LNAI, pp 34–41
25.
Zurück zum Zitat Samanta P, Chakraborty MK (2009) Covering based approaches to rough sets and implication lattices. In: Rough sets, fuzzy sets, data mining and granular computing, vol 5908 of LNAI, pp 127–134 Samanta P, Chakraborty MK (2009) Covering based approaches to rough sets and implication lattices. In: Rough sets, fuzzy sets, data mining and granular computing, vol 5908 of LNAI, pp 127–134
26.
Zurück zum Zitat Shi Z, Gong Z (2010) The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models. Inf Sci 180:3745–3763MathSciNetCrossRefMATH Shi Z, Gong Z (2010) The further investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models. Inf Sci 180:3745–3763MathSciNetCrossRefMATH
28.
Zurück zum Zitat Wang C, Chen D, Sun B, Hu Q (2012) Communication between information systems with covering based rough sets. Inf Sci 216:17–33MathSciNetCrossRefMATH Wang C, Chen D, Sun B, Hu Q (2012) Communication between information systems with covering based rough sets. Inf Sci 216:17–33MathSciNetCrossRefMATH
30.
Zurück zum Zitat Wang S, Zhu Q, Zhu W, Min F (2012) Matroidal structure of rough sets and its characterization to attribute reduction. Knowl Based Syst 35:155–161MathSciNetCrossRef Wang S, Zhu Q, Zhu W, Min F (2012) Matroidal structure of rough sets and its characterization to attribute reduction. Knowl Based Syst 35:155–161MathSciNetCrossRef
31.
Zurück zum Zitat Wang S, Zhu Q, Zhu W, Min F (2013) Quantitative analysis for covering-based rough sets through the upper approximation number. Inf Sci 220:483–491MathSciNetCrossRefMATH Wang S, Zhu Q, Zhu W, Min F (2013) Quantitative analysis for covering-based rough sets through the upper approximation number. Inf Sci 220:483–491MathSciNetCrossRefMATH
32.
33.
34.
Zurück zum Zitat Xu Z, Wang Q (2005) On the properties of covering rough sets model. J Henan Normal Univ (Nat Sci) 33:130–132MathSciNetMATH Xu Z, Wang Q (2005) On the properties of covering rough sets model. J Henan Normal Univ (Nat Sci) 33:130–132MathSciNetMATH
36.
Zurück zum Zitat Yang T, Li Q, Zhou B (2013) Related family: a new method for attribute reduction of covering information systems. Inf Sci 228:175–191MathSciNetCrossRefMATH Yang T, Li Q, Zhou B (2013) Related family: a new method for attribute reduction of covering information systems. Inf Sci 228:175–191MathSciNetCrossRefMATH
38.
Zurück zum Zitat Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259MathSciNetCrossRefMATH Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259MathSciNetCrossRefMATH
40.
Zurück zum Zitat Yun Z, Ge X, Bai X (2011) Axiomatization and conditions for neighborhoods in a covering to form a partition. Inf Sci 181:1735–1740MathSciNetCrossRefMATH Yun Z, Ge X, Bai X (2011) Axiomatization and conditions for neighborhoods in a covering to form a partition. Inf Sci 181:1735–1740MathSciNetCrossRefMATH
41.
42.
43.
Zurück zum Zitat Zhu P (2011) Covering rough sets based on neighborhoods: an approach without using neighborhoods. Int J Approx Reason 52:461–472MathSciNetCrossRefMATH Zhu P (2011) Covering rough sets based on neighborhoods: an approach without using neighborhoods. Int J Approx Reason 52:461–472MathSciNetCrossRefMATH
45.
47.
Zurück zum Zitat Zhu W, Wang S (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybernet 2(4):273–279CrossRef Zhu W, Wang S (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybernet 2(4):273–279CrossRef
Metadaten
Titel
Applications of repeat degree to coverings of neighborhoods
verfasst von
Hua Yao
William Zhu
Publikationsdatum
01.12.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 6/2016
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-014-0287-4

Weitere Artikel der Ausgabe 6/2016

International Journal of Machine Learning and Cybernetics 6/2016 Zur Ausgabe

Neuer Inhalt