nach oben

Granular Computing

Erschienen in:

11.10.2018 | Original Paper

Operation properties and algebraic properties of multi-covering rough sets

verfasst von: Qingzhao Kong, Xiawei Zhang, Weihua Xu

Erschienen in: Granular Computing | Ausgabe 3/2019

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The multi-covering rough sets (MCRSs) are a popular aspect of rough sets. It is easy to see that classical rough sets, covering rough sets (CRSs) and multi-granulation rough sets (MGRSs) are all the special cases of the MCRSs. Recently, the algebraic theory of these rough set models mentioned above have been researched in detail. However, the algebraic theory of MCRSs has not been studied until now. It is necessary for researchers to explore the algebraic theory of MCRSs. In this paper, we focus on the operation and algebraic theories of two types of MCRS models. First, the properties of the two types of multi-covering set approximations are discussed. Especially, the properties of multi-covering approximation operators based on the unary coverings are deeply researched. Second, the operation properties with respect to intersection and union of MCRSs are researched. Meanwhile, to compute the intersection and union of MCRSs, several algorithms are constructed. Finally, on the basis of the operation properties of MCRSs, many meaningful algebraic properties of MCRSs are deeply studied.

Vorheriger Artikel Three-way decisions with reflexive probabilistic rough fuzzy sets

Nächster Artikel Probabilistic decision making based on rough sets in interval-valued fuzzy information systems

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren

Apolloni B, Bassis S, Rota J, Galliani GL, Gioia M, Ferrari L (2016) A neurofuzzy algorithm for learning from complex granules. Granul Comput 1(4):225–246CrossRef

Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf Sci 177:3500–3518MathSciNetCrossRefMATH

Chen J, Lin Y, Lin G (2017) Attribute reduction of civering decision systems by hypergraph model. Knowl Based Syst 118:93–104CrossRef

Dai J, Huang D, Su H (2014) Uncertainty measurement for covering rough sets. J Unc Fuzz Knowl Based Syst 22(2):217–233MathSciNetCrossRefMATH

D’eer L, Restrepo M, Cornelis C (2016) Neighborhood operators for covering-based rough sets. Inf Sci 336:21–44CrossRefMATH

Ge X, Wang P, Yun Z (2017) The rough membership functions on four types of covering-based rough sets and their applications. Inf Sci 390:1–14MathSciNetCrossRef

Iwiński T (1987) Algebraic approach to rough sets. Bull Pol Acad Sci (Math) 35(9–10):673–683MathSciNetMATH

Kong Q, Wei Z (2017) Further study of multi-granulation fuzzy rough sets. J Intell Fuzzy Syst 32:2413–2424CrossRefMATH

Kong Q, Xu W (2018) The comparative study of covering rough sets and multi-granulation rough sets. Soft Comput. https://doi.org/10.1007/s00500-018-3205-y

Kong Q, Xu W (2018b) Operation properties and algebraic application of covering rough sets. Fundam Inf 160:385–408MathSciNetCrossRefMATH

Lang G, Li Q, Cai M (2015) Characteristic matrixes-based knowledge reduction in dynamic covering decision systems. Knowl Based Syst 85:1–26CrossRef

Lang G, Miao D (2016) Knowledge reduction of dynamic covering decision information systems when varying covering cardinalities. Inf Sci 346:236–260CrossRefMATH

Lang G, Miao D, Cai M, Zhang Z (2017) Incremental approaches for updating reducts in dynamic covering information systems. Knowl Based Syst 134:85–104CrossRef

Lang G, Cai M, Fujita H, Xiao Q (2018) Related families-based attribute reduction of dynamic covering decision information systems. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2018.05.019

Li D (2002) Algebraic aspects and knowledge reduction in rough set theory, Xi’an Jiaotong University Doctor Paper

Li J, Ren Y, Mei C (2016) A comparative study of multi-granulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164CrossRef

Li J, Huang C, Qi J, Qian Y, Liu W (2017) Three-way cognitive concept learning via multi-granulaity. Inf Sci 378:244–263CrossRef

Liang M, Mi J, Feng T (2018) Optimal granulation selection for multi-label based on multi-granulation rough sets. Granul Comput. https://doi.org/10.1007/s41066-018-0110-9

Lin G, Qian Y, Li J (2012) NMGRS: neighborhood-based multi-granulation rough sets. Int J Approx Reason 53(7):1080–1093CrossRefMATH

Lin G, Liang J, Qian Y (2013) Multigranulation rough sets: from partition to covering. Inf Sci 241:101–118MathSciNetCrossRefMATH

Liu C, Miao D, Qian J (2014) On multi-granulation covering rough sets. Int J Approx Reason 55:1404–1418MathSciNetCrossRefMATH

Pagliani P (1996) Gough sets and Nelson algebras. Fundam Inf 27:205–219MathSciNetMATH

Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356CrossRefMATH

Pedrycz W, Chen SM (2011) Granular computing and intelligent systems: design with information granules of higher order and higner type. Springer, HeidelbergCrossRef

Pedrycz W, Chen SM (2015a) Granular computing and decision-making: interactive and interactive approaches. Springer, HeidelbergCrossRef

Pedrycz W, Chen SM (2015b) Information granularity, big data, and computational intelligence. Springer, HeidelbergCrossRef

Polkowski L, Skowron A (1998a) Rough sets and current trends in computing, vol 1424. Springer, BerlinCrossRefMATH

Polkowski L, Skowron A (1998b) Rough sets in knowledge discovery 1: methodology and applications. Studies in fussiness and soft computing, vol 18. Physica C, Heidelberg (ISBN: 978-3-7908-1884-0)CrossRefMATH

Polkowski L, Skowron A (1998c) Rough sets in knowledge discovery: applications, case studies and, software systems. Physica C, Heidelberg. https://doi.org/10.1007/978-3-7908-1883-3 (ISBN: 3790811203, 9783790811209)CrossRefMATH

Pomkala J (1988) On definability in the nondeterministic information system. Bulle Pol Acad Sci Math 36:193–210MathSciNet

Pomy Kala J, Pomy Kala JA (1988) The stone algebra of rough sets. Bulle Pol Acad Sci Math 36(7–8):495–508MathSciNet

Qian Y, Liang J, Yao Y, Dang C (2005) MGRS: a multi-granulation rough set. Inf Sci 180:949–970MathSciNetCrossRefMATH

Qian Y, Liang J, Wei W (2010) Pessimistic rough decision. In: Second international workshop on rough sets theory, Zhoushan, P.R. China, pp 440-449

Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundam Inf 27:245–253MathSciNetMATH

Slowinski R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12:331–336CrossRef

Wang L, Yang X, Wu C (2013) Multi-covering based rough set model. In: Ciucci D et al (eds) RSFDGrC 2013, LNAI 8170. Springer-Verlag, Berlin, pp 236–244

Wang C, Shao M, Sun B (2015) An improved attribute reduction scheme with covering based rough sets. Appl Soft Comput 26:235–243CrossRef

Wang G, Yang J, Xu J (2017) Granular computing: from granularity optimization to multi-granularity joint problem solving. Granul Comput 2(3):105–120CrossRef

Wu W, Zhang W (2006) Rough set approximations vs. measurable spaces. In: IEEE GrC, pp 329-332

Xu W, Zhang W (2007) Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst 158:2443–2455MathSciNetCrossRefMATH

Xu W, Sun W, Zhang X, Zhang W (2012) Multile granulation rough set approach to ordered information systems. Int J Gen Syst 41(5):471–501CrossRef

Xu W, Wang Q, Zhang X (2013) Multi-granulation rough sets based on tolerance relations. Soft Comput 17:1241–1252CrossRefMATH

Xu W, Guo X (2016) Generalized multigranulation double-quantitative decision-theoretic rough set. Knowl Based Syst 105:190–205CrossRef

Xu W, Li W, Zhang X (2017) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput. https://doi.org/10.1007/s41066-017-0042-9

Xu Z, Wang H (2016) Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul Comput 1(1):21–35CrossRef

Yang X, Song X, Chen Z, Yang J (2012) On multigranulation rough sets in incomplete information system. Int J Mach Learn Cybern 3:223–232CrossRef

Yang B, Zhu W (2014) A new type of covering-based rough sets, In: 9th International conference on rough sets and knowledge technology, Shanghai, P.R.China, pp 489–499

Yao Y, Lin T (1996) Generalization of rough sets using model logic. Intell Autom Soft Comput Int J 2:103–120CrossRef

Yao Y (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 101:239–259MathSciNetCrossRefMATH

Yao Y (2003) On generalizing rough set theory. In: Proceeding of the ninth international conference on rough sets, fuzzy sets, data mining and granular computing LNCS(LNAI) 2639, pp 44-51

Yao Y, Chen Y (2005) Subsystem based generalizations of rough set approximations. LNCS 3488:210–218MATH

Yao Y, Yao B (2012) Covering based rough set approximations. Inf Sci 200(1):91–107MathSciNetCrossRefMATH

Yao Y, She Y (2016) Rough set models in multigranulation spaces. Inf Sci 327:40–56MathSciNetCrossRefMATH

Zakowski W (1983) Approximations in the space (\(u,\pi\)). Demonstr Math 16:761–769MathSciNetMATH

Zhang N, Yao Y, Ohshima M (2003) Pecularity oriented multidatabase mining. IEEE Trans Knowl Data Eng 15(4):952–960CrossRef

Zhu W (2007) Generalized rough sets based on relations. Inf Sci 177(22):4997–5001MathSciNetCrossRefMATH

Zhu W, Wang F (2006) Covering based granular computing for conflict analysis. In: IEEE ISI vol 3975 of LNCS, pp 566-571

Zhu W, Wang S (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybern 2(4):273–279CrossRef

Titel: Operation properties and algebraic properties of multi-covering rough sets
verfasst von: Qingzhao Kong
Xiawei Zhang
Weihua Xu
Publikationsdatum: 11.10.2018
Verlag: Springer International Publishing
Erschienen in: Granular Computing / Ausgabe 3/2019
Print ISSN: 2364-4966
Elektronische ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-018-0137-y

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 3/2019

An extension of VIKOR method for multi-attribute decision-making under Pythagorean hesitant fuzzy setting

Neighborhood attribute reduction for imbalanced data

Granular computing in machine learning

Hesitant bipolar-valued fuzzy sets and bipolar-valued hesitant fuzzy sets and their applications in multi-attribute group decision making

Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications

Multi-level granularity in formal concept analysis