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:
Fuzzy, Intuitionistic Fuzzy, What Next? Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Intuitionistic Fuzzy Relational Equations in \(BL-\)Algebras

Author : Ketty Peeva

Published in: Imprecision and Uncertainty in Information Representation and Processing

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

We investigate direct and inverse problem resolution for intuitionistic fuzzy relational equations in some \(BL-\)algebras, when the composition for the membership degrees is a \(\sup -t-\)norm and for non-membership degrees is an \(\inf -s-\)norm. Criterion for solvability of intuitionistic fuzzy relational equation is proposed and analytical expressions for maximal solution is given.

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 One, Two and Uni-type Operators on IFSs
next chapter Intuitionistic Fuzzy Weakly Open Mappings
Literature
1.
Atanassov, K.: Intuitionistic fuzzy sets. VII ITKR’s Session, Soa, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)
2.
3.
4.
Bartl, E., Belohlavek, R.: Sup-t-norm and inf-residuum are a single type of relational equations. Int. J. Gen. Syst. 40, 599–609 (2011)MathSciNetCrossRefMATH
5.
Dinda, B., Samanta, T.K.: Relations on intuitionistic fuzzy soft sets. Gen. Math. Notes 1(2), 74–83. ISSN 2219-7184
6.
Chen, L., Wang, P.: Fuzzy relational equations (I): the general and specialized solving algorithms. Soft Comput. 6, 428–435 (2002)CrossRefMATH
7.
De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) Handbooks of Fuzzy Sets Series: Fundamentals of Fuzzy Sets, vol. 1, pp. 291–340. Kluwer Academic Publishers (2000)
8.
Belohlavek, R.: Sup-t-norm and inf-residuum are one type of relational product: unifying framework and consequences. Fuzzy Sets Syst. 197, 45–58 (2012)
9.
Burillo, P., Bustince, H.: Intuitionistic fuzzy relations (part I). Mathw. Soft Comput. 2, 5–38 (1995)MATH
10.
Di Nola, A., Pedrycz, W., Sessa, S., Sanchez, E.: Fuzzy Relation Equations and Their Application to Knowledge Engineering. Kluwer Academic Press, Dordrecht (1989)CrossRefMATH
11.
Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATH
12.
13.
Deschrijver, Gl., Kerre, E.E.: On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst. |bf 136 333–361 (2003)
14.
15.
Klir, G., Clair, U.H. St., Bo, Y.: Fuzzy Set Theory Foundations and Applications. Prentice Hall PRT (1977)
16.
17.
MacLane, S., Birkhoff, G.: Algebra. Macmillan, New York (1979)MATH
18.
Meenakshi, A.R., Gandhimathi, T.: Intuitionistic fuzzy relational equations. Adv. Fuzzy Math. 5(3), 239–244 (2010)
19.
Meenakshi, A.R., Gandhimathi, T.: System of intuitionistic fuzzy relational equations. Glob. J. Math. Sci.: Theory Pract. 4(1), 49–55 (2012) ISSN 0974-3200
20.
Peeva, K.: Resolution of composite intuitionistic fuzzy relational equations. Notes on IFS 61, 15–24 (2000)
21.
Peeva, K.: Resolution of fuzzy relational equations—method, algorithm and software with applications, information sciences 234, 44–63 (2013) ISSN 0020-0255
22.
Peeva, K., Kyosev, Y.: Fuzzy relational calculus-theory, applications and software (with CD-ROM). In the series Advances in Fuzzy Systems—Applications and Theory, vol. 22, World Scientific Publishing Company (2004)
23.
Peeva, K., Kyosev, Y.: Software for direct and inverse problem resolution in intuitionistic fuzzy relational calculus. In: Second International Workshop on IFS and Generalized Nets, Warsaw, pp. 60–68, 26–27 July 2002; in Issues in Intuitionistic Fuzzy Sets and Generalized Nets, vol. 2, Warsaw School of Information Technology Press, pp. 117–125, ISBN 83-88311-75-1, Warszawa (2004)
24.
Peeva, K., Kyosev, Y.: Solving problems in intuitionistic fuzzy relational calculus with fuzzy relational calculus toolbox. In: Eight International Conference on IFSs, Varna, pp. 37–43, 20–21 June 2004, NIFS 10 (2004)
25.
Shivanian, E.: An algorithm for finding solutions of fuzzy relation equations with max-Lukasiwicz composition. Mathw. Soft Comput. 17, 15–26 (2010)MATH
26.
Wei, Zh.: Intuitionistic fuzzy relation equations. In: 2010 International Conference on Educational and Information Technology (ICEIT), 17–19 September 2010, vol. 2, pp. V2-249–V2-251, E-ISBN:978-1-4244-8035-7, Print ISBN:978-1-4244-8033-3
27.
Metadata
Title
Intuitionistic Fuzzy Relational Equations in Algebras
Author
Ketty Peeva
Copyright Year
2016
Book
Imprecision and Uncertainty in Information Representation and Processing

Print ISBN: 978-3-319-26301-4

Electronic ISBN: 978-3-319-26302-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-26302-1_6

Premium Partner

    Image Credits