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EQ-algebras based on fuzzy hyper EQ-filters

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Abstract

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.

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References

  • Bashford JD, Jarvis PD (2000) The genetic code as a periodic table: algebraic aspects. BioSystems 57:147–161

    Article  Google Scholar 

  • Borzooei RA, Saffar BG, Ameri R (2013) On hyper EQ-algebras. Ital J Pure Appl Math 31:77–96

    MathSciNet  MATH  Google Scholar 

  • Chvalina J, Mayerova SH, Nezhad AD (2013) General actions of hyperstructures and some applications. An St Univ Ovidius Constanta 21(1):59–82

    MathSciNet  Google Scholar 

  • Corsini P, Leoreanu V (2002) Applications of hyperstructure theory. Kluwer, Dordrecht

    MATH  Google Scholar 

  • Dyba M, Novák V (2015) EQ-logics with delta connective. Iran J Fuzzy Syst 12(2):41–61

    MathSciNet  MATH  Google Scholar 

  • El-Zekey M (2010) Representable good EQ-algebras. Soft Comput 14:1011–1023

    Article  MATH  Google Scholar 

  • El-Zekey M, Novák V, Mesiar R (2011) On good EQ-algebras. Fuzzy Sets Syst 178(1):1–23

    Article  MathSciNet  MATH  Google Scholar 

  • Frappat L, Sciarrino A, Sorba P (2001) Crystalizing the genetic code. J Biol Phys 27:1–34

    Article  MATH  Google Scholar 

  • Hamidi M, Saeid A (2018) Borumand EQ-algebras based on hyper EQ-algebras. Bol Soc Mat Mex 24:11–35

    Article  MathSciNet  MATH  Google Scholar 

  • Jun YB, Song SZ (2015) Hesitant fuzzy prefilters and filters of EQ-algebras. Appl Math Sci 9(11):515–532

    Google Scholar 

  • Kinyon MK, Sagle AA (1995) Quadratic dynamical systems and algebras. J Differ Equ 117:67–126

    Article  MathSciNet  MATH  Google Scholar 

  • 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 219–223

  • Novák V, de Baets B (2009) EQ-algebras. Fuzzy Sets Syst 160:2956–2978

    Article  MathSciNet  MATH  Google Scholar 

  • Novák V, Dyba M (2009) Non-commutative EQ-logics and their extensions. Fuzzy Sets Syst 160:2956–2978

    Article  Google Scholar 

  • 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 202:156–174

    Article  MathSciNet  MATH  Google Scholar 

  • Tian JJ, Li BL (2004) Coalgebraic structure of genetics inheritance. Math Biosci Eng 1:243–266

    Article  MathSciNet  MATH  Google Scholar 

  • Tourlakis G (2008) Mathematical logic. Wiley, New York

    Book  MATH  Google Scholar 

  • Xin XL, He PF, Yang YW (2014) Characterizations of some fuzzy prefilters (filters) in EQ-algebras. Sci World J 2014:829527

    Google Scholar 

Download references

Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Payame Noor University, Tehran, Iran

    M. Hamidi

  2. Mahani Mathematical research center, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

  3. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

Authors
  1. M. Hamidi
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  2. Arsham Borumand Saeid
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Correspondence to Arsham Borumand Saeid.

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Communicated by A. Di Nola.

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Hamidi, M., Borumand Saeid, A. EQ-algebras based on fuzzy hyper EQ-filters. Soft Comput 23, 5289–5305 (2019). https://doi.org/10.1007/s00500-018-3456-7

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  • DOI: https://doi.org/10.1007/s00500-018-3456-7

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