Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2015 | OriginalPaper | Chapter

Rough Sets and Other Mathematics: Ten Research Programs

Author : Piero Pagliani

Published in: Facets of Uncertainties and Applications

Publisher: Springer India

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Since its inception, interesting connections between Rough Set Theory and different mathematical and logical topics have been investigated. This paper is a survey of some less known although highly interesting connections, which extend from Rough Set Theory to other mathematical and logical fields. The survey is primarily thought of as a guide for new directions to be explored.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter Correction to: Dealing with Uncertainty: From Rough Sets to Interactive Rough-Granular Computing
next chapter Dealing with Uncertainty: From Rough Sets to Interactive Rough-Granular Computing
Footnotes
1
Except for [7], this book is the only work of the author’s that will be cited. The story of the results can be found in the mentioned chapters.
 
Literature
1.
2.
Cattaneo, G., Ciucci, D.: Lattices with Interior and Closure Operators and Abstract Approximation Spaces. Transactions on Rough Sets X. Springer (2009)
3.
4.
Gabbay, D.M.: Labelled Deductive Systems. Oxford University Press (1997)
5.
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multi-criteria decision analysis. Euro. J. Op. Res. 129(1), 1–47 (2001)CrossRef
6.
Huang, A., Zhu, W.: Topological characterizations for three covering approximation operators. In: Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, LNCS, 8170, pp. 277–284, Springer (2013)
7.
8.
Johnstone, P.T.: Conditions related to De Morgan’s law. In: Fourman, M.P., Mulvey C.J., Scott, D.S., (eds.), Applications of Sheaves (Durham 1977), LNM 753, pp. 479–491, Springer-Verlag (1979)
9.
Khan, M.A., Banerjee, M.: A Study of Multiple-Source Approximation Systems. Transactions on rough sets. XII. Springer (2010)
10.
Lawvere, F.W.: Intrinsic co-heyting boundaries and the Leibniz rule in certain toposes. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds.), Category Theory (Como 1990), LNM 1488, pp. 279–297, Springer (1991)
11.
Miglioli, P.A., Moscato, U., Ornaghi, M., Usberti, U.: A constructivism based on classical truth. Notre Dame J. Formal Logic 30(1), 67–90 (1989)MathSciNetCrossRef
12.
Mundici, D.: The \(C^{\ast }\)-algebras of three-valued logic. In: Ferro, R., et al. (eds.) Logic Colloquium’88, pp. 61–67. North-Holland, Amstedam (1989)
13.
Mundici, D.: Ulam’s games, Łukasiewicz logic and AF \(C^*\)-algebras. Fundamenta Informaticae 18, 151–161 (1993)MathSciNetMATH
14.
Nagarajan, E.K.R., Umadevi, D.: A method of representing rough sets system determined by quasi orders. Order 30(1), 313–337 (2013)MathSciNetCrossRef
15.
Orłowska, E.: Kripke models with relative accessibility and their applications to inferences from incomplete information. In: Mirkowska, G., Rasiowa, H. (eds.), Mathematical Problems in Computation Theory, p. 329–339, Banach Center Publications, 21 PWN—Polish Scientific Publishers, Warsaw (1988)
16.
Pagliani, P., Chakraborty, M.K.: A geometry of Approximation. Trends in Logic, 27. Springer (2008)
17.
V. de Paiva, V.: A dialectica-like model of linear logic. In: Proceedings of the Conference on Category Theory and Computer Science, LNCS, 389, pp. 341–356. Springer (1989)
18.
Pratt, V.: Chu spaces as a semantic bridge between linear logic and mathematics. Theor. Comput. Sci. 294, 439–471 (1998)MathSciNetCrossRef
19.
20.
Sambin, G.: Intuitionistic formal spaces—a first communication. In: Skordev, D. (ed.) Mathematical Logic and Its Applications, pp. 187–204. Plenum, New York (1987)CrossRef
21.
Sambin, G.: The semantics of pretopologies. In: Schroeder-Heister, P., Dosen, K. (eds.) Substructural Logics, pp. 293–307. Clarendon, Oxford (1993)
22.
Sambin, G., Gebellato, S.: A preview of the basic picture: a new perspective on formal topology. In: Proceedings of the TYPES ’98. International Workshop on Types for Proofs and Programs, LNCS 1657, pp. 194–207, Springer (1999)
23.
Sen, J., Chakraborty, M.K.: A study of interconnections between rough and 3-valued Łukasiewicz logics. Fundamenta Informaticae 51, 311–324 (2002)MathSciNetMATH
24.
Spinks, M., Veroff, R.: Constructive Logic with Strong Negation is a Substructural Logic—I and II. Studia Logica, 88, pp. 325–348 and 89, 401–425 (2008)
25.
Metadata
Title
Rough Sets and Other Mathematics: Ten Research Programs
Author
Piero Pagliani
Copyright Year
2015
Publisher
Springer India
Book
Facets of Uncertainties and Applications

Print ISBN: 978-81-322-2300-9

Electronic ISBN: 978-81-322-2301-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-81-322-2301-6_1

Premium Partner

    Image Credits