Skip to main content
Erschienen in: Soft Computing 10/2021

07.04.2021 | Foundations

Approximations of fuzzy soft sets by fuzzy soft relations with image processing application

verfasst von: Jiří Močkoř, Petr Hurtík

Erschienen in: Soft Computing | Ausgabe 10/2021

Einloggen

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

search-config
loading …

Abstract

Fuzzy soft sets represent a generalization of fuzzy sets with considerable application potential in decision-making problems, optimization, and computer science. In the paper, we use the fact that the fuzzy soft sets powerset theory is defined by the monad and, using this theory, we introduce the concept of fuzzy soft relations defined by the monad. Using that general method, we can also introduce the fuzzy soft approximation of fuzzy soft sets defined by fuzzy soft relations. We show that fuzzy soft sets and fuzzy soft approximations can be naturally used in selective color segmentation problem, where reliable and fully automated methods do not yet exist.

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 "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!

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!

Literatur
Zurück zum Zitat Boixader D, Jacas J, Recasens J (2000) Upper and lower approximations of fuzzy sets. Int J Gen Syst 29(4):555–568MathSciNetCrossRef Boixader D, Jacas J, Recasens J (2000) Upper and lower approximations of fuzzy sets. Int J Gen Syst 29(4):555–568MathSciNetCrossRef
Zurück zum Zitat Eklund P, Galán MÁ (2008) Partially ordered monads and rough sets. In: Transactions on rough sets VIII. Springer, pp 53–74 Eklund P, Galán MÁ (2008) Partially ordered monads and rough sets. In: Transactions on rough sets VIII. Springer, pp 53–74
Zurück zum Zitat Eklund P, Galán MA, Gähler W (2009) Partially ordered monads for monadic topologies, rough sets and Kleene algebras. Electron Notes Theor Comput Sci 225:67–81CrossRef Eklund P, Galán MA, Gähler W (2009) Partially ordered monads for monadic topologies, rough sets and Kleene algebras. Electron Notes Theor Comput Sci 225:67–81CrossRef
Zurück zum Zitat Gähler W (2001) Extension structures and completions in topology and algebra. Seminarberichte aus dem Fachbereich Mathematik 70:77–103 Gähler W (2001) Extension structures and completions in topology and algebra. Seminarberichte aus dem Fachbereich Mathematik 70:77–103
Zurück zum Zitat Herrlich H, Strecker GE (1979) Category theory: an introduction, vol 1. Heldermann, BerlinMATH Herrlich H, Strecker GE (1979) Category theory: an introduction, vol 1. Heldermann, BerlinMATH
Zurück zum Zitat Höhle U (2001) Partially ordered monads. In: Many valued topology and its applications. Springer, pp 29–54 Höhle U (2001) Partially ordered monads. In: Many valued topology and its applications. Springer, pp 29–54
Zurück zum Zitat Hurtík P, Močkoř J (2021) SECOI: An application based on fuzzy soft sets for producing selective-coloured images. Soft Comput (Submitted) Hurtík P, Močkoř J (2021) SECOI: An application based on fuzzy soft sets for producing selective-coloured images. Soft Comput (Submitted)
Zurück zum Zitat Kazancı O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178(10):2349–2359MathSciNetCrossRef Kazancı O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178(10):2349–2359MathSciNetCrossRef
Zurück zum Zitat Khan MJ et al (2020) The renewable energy source selection by remoteness index-based vikor method for generalized intuitionistic fuzzy soft sets. Symmetry 12:977CrossRef Khan MJ et al (2020) The renewable energy source selection by remoteness index-based vikor method for generalized intuitionistic fuzzy soft sets. Symmetry 12:977CrossRef
Zurück zum Zitat Khan MJ et al (2020) Another view on generalized interval valued intuitionistic fuzzy soft set and its applications in decision support system. J Intell Fuzzy Syst 38(4):4327–4341CrossRef Khan MJ et al (2020) Another view on generalized interval valued intuitionistic fuzzy soft set and its applications in decision support system. J Intell Fuzzy Syst 38(4):4327–4341CrossRef
Zurück zum Zitat Khan MJ, Kumam P, Kumam W, Ashraf W (2019) A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system. Mathematics 7:1–21MATH Khan MJ, Kumam P, Kumam W, Ashraf W (2019) A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system. Mathematics 7:1–21MATH
Zurück zum Zitat Kleisli H (1965) Every standard construction is induced by a pair of adjoint functors. Proc Am Math Soc 16(3):544–546MathSciNetCrossRef Kleisli H (1965) Every standard construction is induced by a pair of adjoint functors. Proc Am Math Soc 16(3):544–546MathSciNetCrossRef
Zurück zum Zitat Kovkov D, Kolbanov V, Molodtsov D (2007) Soft sets theory-based optimization. J Comput Syst Sci Int 46(6):872–880MathSciNetCrossRef Kovkov D, Kolbanov V, Molodtsov D (2007) Soft sets theory-based optimization. J Comput Syst Sci Int 46(6):872–880MathSciNetCrossRef
Zurück zum Zitat Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083MathSciNetCrossRef Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083MathSciNetCrossRef
Zurück zum Zitat Manes EG (2012) Algebraic theories, vol 26. Springer, BerlinMATH Manes EG (2012) Algebraic theories, vol 26. Springer, BerlinMATH
Zurück zum Zitat Manes L (1982) Book review “fuzzy sets and systems: theory and applications.” Bull (New Ser) Am Math Soc 7(3):603–612 Manes L (1982) Book review “fuzzy sets and systems: theory and applications.” Bull (New Ser) Am Math Soc 7(3):603–612
Zurück zum Zitat Močkoř J (2020) Powerset theory of fuzzy soft sets. Int J Fuzzy Log Intell Syst 20(4):298–315CrossRef Močkoř J (2020) Powerset theory of fuzzy soft sets. Int J Fuzzy Log Intell Syst 20(4):298–315CrossRef
Zurück zum Zitat Mushrif MM, Sengupta S, Ray AK (2006) Texture classification using a novel, soft-set theory based classification algorithm. In: Asian conference on computer vision. Springer, pp 246–254 Mushrif MM, Sengupta S, Ray AK (2006) Texture classification using a novel, soft-set theory based classification algorithm. In: Asian conference on computer vision. Springer, pp 246–254
Zurück zum Zitat Pei D, Miao D (2005) From soft sets to information systems. In: 2005 IEEE international conference on granular computing, vol 2. IEEE, pp 617–621 Pei D, Miao D (2005) From soft sets to information systems. In: 2005 IEEE international conference on granular computing, vol 2. IEEE, pp 617–621
Zurück zum Zitat Perfilieva I (2005) Fuzzy transforms and their applications to data compression. In: The 14th IEEE international conference on fuzzy systems, 2005. FUZZ’05. IEEE, pp 294–299 Perfilieva I (2005) Fuzzy transforms and their applications to data compression. In: The 14th IEEE international conference on fuzzy systems, 2005. FUZZ’05. IEEE, pp 294–299
Zurück zum Zitat Perfilieva I, Novák V, Dvořák A (2008) Fuzzy transform in the analysis of data. Int J Approx Reason 48(1):36–46CrossRef Perfilieva I, Novák V, Dvořák A (2008) Fuzzy transform in the analysis of data. Int J Approx Reason 48(1):36–46CrossRef
Zurück zum Zitat Roy AR, Maji P (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418CrossRef Roy AR, Maji P (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418CrossRef
Zurück zum Zitat Seal GJ (2011) On the monadic nature of categories of ordered sets. Cahiers de topologie et géométrie différentielle catégoriques 52(3):163–187MathSciNetMATH Seal GJ (2011) On the monadic nature of categories of ordered sets. Cahiers de topologie et géométrie différentielle catégoriques 52(3):163–187MathSciNetMATH
Zurück zum Zitat Xiao Z, Gong K, Zou Y (2009) A combined forecasting approach based on fuzzy soft sets. J Comput Appl Math 228(1):326–333MathSciNetCrossRef Xiao Z, Gong K, Zou Y (2009) A combined forecasting approach based on fuzzy soft sets. J Comput Appl Math 228(1):326–333MathSciNetCrossRef
Zurück zum Zitat Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945CrossRef Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945CrossRef
Metadaten
Titel
Approximations of fuzzy soft sets by fuzzy soft relations with image processing application
verfasst von
Jiří Močkoř
Petr Hurtík
Publikationsdatum
07.04.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 10/2021
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-021-05769-3

Weitere Artikel der Ausgabe 10/2021

Soft Computing 10/2021 Zur Ausgabe

Premium Partner