Skip to main content

2018 | OriginalPaper | Buchkapitel

Multi-criteria Decision Making on Lattice Ordered Multisets

verfasst von : V. S. Anusuya Ilamathi, J. Vimala

Erschienen in: Intelligent Systems Technologies and Applications

Verlag: Springer International Publishing

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

search-config
loading …

Abstract

The crucial aspect of a multiset is the recurrence of its objects which we get it from a set and it is a new interesting mathematical notion. In this paper, lattice theory is applied to the multiset in context. We introduce a new concept for sorting things, demonstrated with lots of quantitative and qualitative attributes, and may endure in several copies. We then investigate few of the properties relevent to them. Moreover, we propose 0 and 1 as multiset depiction and identify how they play an application role in the lattice (anti-lattice) ordered multisets, where some sorting exists amid the attributes are analysed.

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!

Literatur
1.
Zurück zum Zitat Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)MATH Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)MATH
2.
Zurück zum Zitat Chen, S., Liu, J., Wang, H., Augusto, J.C.: Ordering based decision making-a survey. Inf. Fusion 14(4), 521–531 (2013)CrossRef Chen, S., Liu, J., Wang, H., Augusto, J.C.: Ordering based decision making-a survey. Inf. Fusion 14(4), 521–531 (2013)CrossRef
4.
Zurück zum Zitat Girish, K.P., John, S.J.: General relations between partially ordered multisets and their chains and antichains. Math. Commun. 14(2), 193–206 (2009)MathSciNetMATH Girish, K.P., John, S.J.: General relations between partially ordered multisets and their chains and antichains. Math. Commun. 14(2), 193–206 (2009)MathSciNetMATH
5.
Zurück zum Zitat Gratzer, G.: General Lattice Theory, 2nd edn. Birkhauser, Boston (2003)MATH Gratzer, G.: General Lattice Theory, 2nd edn. Birkhauser, Boston (2003)MATH
7.
Zurück zum Zitat Liu, J., Xu, Y., Ruan, D., Martinez, L.: A lattice-valued linguistic-based decision making method. In: The Proceedings of 2005 IEEE Conference on Granular Computing, Beijing, China, pp. 199–202 (2005) Liu, J., Xu, Y., Ruan, D., Martinez, L.: A lattice-valued linguistic-based decision making method. In: The Proceedings of 2005 IEEE Conference on Granular Computing, Beijing, China, pp. 199–202 (2005)
8.
Zurück zum Zitat Nazmul, S., Majumdar, P., Samanta, S.K.: On multisets and multigroups. Ann. Fuzzy Math. Inf. 6(3), 643–656 (2013)MathSciNetMATH Nazmul, S., Majumdar, P., Samanta, S.K.: On multisets and multigroups. Ann. Fuzzy Math. Inf. 6(3), 643–656 (2013)MathSciNetMATH
9.
Zurück zum Zitat Natarajan, R., Vimala, J.: Distributive l-ideal in commutative Lattice ordered group. Acta Cienc. Indica 33(2), 517 (2007)MathSciNetMATH Natarajan, R., Vimala, J.: Distributive l-ideal in commutative Lattice ordered group. Acta Cienc. Indica 33(2), 517 (2007)MathSciNetMATH
10.
Zurück zum Zitat Natarajan, R., Vimala, J.: Distributive convex l- subgroup. Acta Ciencia Indica XXXIII(4), 1795 (2007)MathSciNetMATH Natarajan, R., Vimala, J.: Distributive convex l- subgroup. Acta Ciencia Indica XXXIII(4), 1795 (2007)MathSciNetMATH
11.
Zurück zum Zitat Singh, D., Ibrahim, A.M., et al.: An overview of the applications of multisets. Novi Sad J. Math. 37(2), 73–92 (2007)MathSciNetMATH Singh, D., Ibrahim, A.M., et al.: An overview of the applications of multisets. Novi Sad J. Math. 37(2), 73–92 (2007)MathSciNetMATH
12.
Zurück zum Zitat Syropoulos, A.: Mathematics of multisets. In: Calude, C., Paun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. Lecture Notes in Computer Science, vol. 2235, pp. 347–358. Springer, Heidelberg (2001)CrossRef Syropoulos, A.: Mathematics of multisets. In: Calude, C., Paun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. Lecture Notes in Computer Science, vol. 2235, pp. 347–358. Springer, Heidelberg (2001)CrossRef
13.
Zurück zum Zitat Triantaphyllou, E.: Multi-Criteria Decision Making: A Comparative Study. Kluwer Academic Publishers, Dordrecht (2000). p. 320. ISBN 0-7923-6607-7. (now Springer)CrossRefMATH Triantaphyllou, E.: Multi-Criteria Decision Making: A Comparative Study. Kluwer Academic Publishers, Dordrecht (2000). p. 320. ISBN 0-7923-6607-7. (now Springer)CrossRefMATH
14.
Zurück zum Zitat Chen, T.Y.: Comparative analysis of SAW and TOPSIS based on interval valued fuzzy sets: discussions on score functions and weight constraints. Expert Syst. Appl. 39, 1848–1861 (2012)CrossRef Chen, T.Y.: Comparative analysis of SAW and TOPSIS based on interval valued fuzzy sets: discussions on score functions and weight constraints. Expert Syst. Appl. 39, 1848–1861 (2012)CrossRef
15.
Zurück zum Zitat Gayatri, V., Misal Chetan, S.: Comparative study of different multi criteria decision making methods. Int. J. Adv. Comput. Theory Eng. 2(4), 2319–2526 (2013) Gayatri, V., Misal Chetan, S.: Comparative study of different multi criteria decision making methods. Int. J. Adv. Comput. Theory Eng. 2(4), 2319–2526 (2013)
Metadaten
Titel
Multi-criteria Decision Making on Lattice Ordered Multisets
verfasst von
V. S. Anusuya Ilamathi
J. Vimala
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-68385-0_34