Soft Computing

, Volume 23, Issue 14, pp 5289–5305 | Cite as

EQ-algebras based on fuzzy hyper EQ-filters

  • M. Hamidi
  • Arsham Borumand SaeidEmail author


This paper introduces and applies the notion of fuzzy hyper EQ-subalgebras as a generalization of the notation of fuzzy EQ-subalgebras and constructs extendable fuzzy EQ-subalgebras via these concepts. Moreover, by using the fuzzy hyper EQ-filters, it defines a congruence relation on hyper EQ-algebras that under some conditions is strongly regular and the quotient of any hyper EQ-algebra via this relation is an EQ-algebra.


(Hyper)EQ-algebra Fundamental relation Hyper EQ-filter 



We wish to thank the reviewers for excellent suggestions that have been incorporated into the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Bashford JD, Jarvis PD (2000) The genetic code as a periodic table: algebraic aspects. BioSystems 57:147–161CrossRefGoogle Scholar
  2. Borzooei RA, Saffar BG, Ameri R (2013) On hyper EQ-algebras. Ital J Pure Appl Math 31:77–96MathSciNetzbMATHGoogle Scholar
  3. Chvalina J, Mayerova SH, Nezhad AD (2013) General actions of hyperstructures and some applications. An St Univ Ovidius Constanta 21(1):59–82MathSciNetGoogle Scholar
  4. Corsini P, Leoreanu V (2002) Applications of hyperstructure theory. Kluwer, DordrechtzbMATHGoogle Scholar
  5. Dyba M, Novák V (2015) EQ-logics with delta connective. Iran J Fuzzy Syst 12(2):41–61MathSciNetzbMATHGoogle Scholar
  6. El-Zekey M (2010) Representable good EQ-algebras. Soft Comput 14:1011–1023CrossRefzbMATHGoogle Scholar
  7. El-Zekey M, Novák V, Mesiar R (2011) On good EQ-algebras. Fuzzy Sets Syst 178(1):1–23MathSciNetCrossRefzbMATHGoogle Scholar
  8. Frappat L, Sciarrino A, Sorba P (2001) Crystalizing the genetic code. J Biol Phys 27:1–34CrossRefzbMATHGoogle Scholar
  9. Hamidi M, Saeid A (2018) Borumand EQ-algebras based on hyper EQ-algebras. Bol Soc Mat Mex 24:11–35MathSciNetCrossRefzbMATHGoogle Scholar
  10. Jun YB, Song SZ (2015) Hesitant fuzzy prefilters and filters of EQ-algebras. Appl Math Sci 9(11):515–532Google Scholar
  11. Kinyon MK, Sagle AA (1995) Quadratic dynamical systems and algebras. J Differ Equ 117:67–126MathSciNetCrossRefzbMATHGoogle Scholar
  12. Novák V (2006) EQ-algebras: primary concepts and properties. In: Proceedings of the Czech Japan seminar, ninth meeting. Kitakyushu & Nagasaki, August 18–22, 2006, Graduate School of Information, Waseda University, pp 219–223Google Scholar
  13. Novák V, de Baets B (2009) EQ-algebras. Fuzzy Sets Syst 160:2956–2978MathSciNetCrossRefzbMATHGoogle Scholar
  14. Novák V, Dyba M (2009) Non-commutative EQ-logics and their extensions. Fuzzy Sets Syst 160:2956–2978CrossRefGoogle Scholar
  15. Saanchez R, Grau R, Morgado E (2006) A novel Lie algebra of the genetic code over the Galois field of four DNA bases. Math Biosci 202:156–174MathSciNetCrossRefzbMATHGoogle Scholar
  16. Tian JJ, Li BL (2004) Coalgebraic structure of genetics inheritance. Math Biosci Eng 1:243–266MathSciNetCrossRefzbMATHGoogle Scholar
  17. Tourlakis G (2008) Mathematical logic. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  18. Xin XL, He PF, Yang YW (2014) Characterizations of some fuzzy prefilters (filters) in EQ-algebras. Sci World J 2014:829527Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of MathematicsPayame Noor UniversityTehranIran
  2. 2.Mahani Mathematical research centerShahid Bahonar University of KermanKermanIran
  3. 3.Department of Pure Mathematics, Faculty of Mathematics and ComputerShahid Bahonar University of KermanKermanIran

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