Skip to main content
SpringerLink
Log in

On the circulant intuitionistic fuzzy matrices

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, we define fuzzy matrices (FM), intuitionistic fuzzy matrices (IFM) and a new operation \( * \) defined on the set \( I_{n} = \left\{ {1,2, \ldots ,n} \right\}. \) The system \( (I_{n} , * ) \) is an abelian group. This group is pivotal in our paper. Circulant intuitionistic fuzzy matrices is defined also in this paper via the group \( (I_{n} , * ) \) as a new way for defining circulant matrices. However, we study and investigate several properties of circulant intuitionistic fuzzy matrices. The first row (column) of a circulant matrix plays an important role in our studying. From any intuitionistic fuzzy matrix R (not necessarily circulant) we can construct two circulant intuitionistic fuzzy matrices \( R_{L} \) and \( R_{U} \) such that \( R_{L} \le R \le R_{U} \). We also show that some compositions of circulant intuitionistic fuzzy matrices are also circulant. Moreover, we proved that \( RS = SR \) for two circulant intuitionistic fuzzy matrices \( R \) and \( S \). However, we give some examples to clarify our results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abualiagah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithms with genetic operators for the text clustering. J Supercomput 73(11):4773–4795

    Article  Google Scholar 

  • Abualiagah LM, Khader AT, Hanandeh ES (2018) Hybrid clustering analysis using improved Krill herd algorithm. Appl Intell 48(11):4047–4071

    Article  Google Scholar 

  • Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306

    Article  MathSciNet  Google Scholar 

  • Ashraf S, Abdullah S, Mahmood T, Ghani F, Mahmood T (2019) Spherical fuzzy sets and their applications in multi-attribute decision making problems. J Intell Fuzzy Syst 36(3):2829–2844

    Article  Google Scholar 

  • Atanasov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Atanasov KT (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–45

    Article  MathSciNet  Google Scholar 

  • Bhowmik M, Pal M, Pal A (2008) Circulant triangular fuzzy number matrices. J Phys Sci 12:141–154

    MATH  Google Scholar 

  • Cacioppo JT, Gardner WL, Bernetson GG (1997) Beyond bipolar conceptualization and measures: the case of attitudes and evaluative spaces. Pers Soc Psychol Rev 1:3–25

    Article  Google Scholar 

  • Deschrijver G, Kerre EE (2003a) On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst 136(3):333–361

    Article  MathSciNet  Google Scholar 

  • Deschrijver G, Kerre EE (2003b) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst 133(2):227–235

    Article  MathSciNet  Google Scholar 

  • Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H (2005) Terminological difficulties in fuzzy set theory—the case of “Intuitionistic Fuzzy Sets”. Fuzzy Sets Syst 156:485–491

    Article  MathSciNet  Google Scholar 

  • Dudziak U, Pekala B (2010) Equivalent bipolar fuzzy relations. Fuzzy Sets Syst 161:234–253

    Article  MathSciNet  Google Scholar 

  • Emam EG (2017) Intuitionistic circular fuzzy matrices. J Egypt Math Soc 25:272–275

    Article  Google Scholar 

  • Emam EG (2019) Group compatible intuitionistic fuzzy matrices. Comput Appl Math 1:1. https://doi.org/10.1007/s40314-019-0975-5

    Article  MathSciNet  MATH  Google Scholar 

  • Emam EG (2020) An operation on intuitionistic fuzzy matrices. Filomat 34(1):79–88

    Article  MathSciNet  Google Scholar 

  • Hashimoto H (1983) Convergence of powers of a fuzzy transitive matrix. Fuzzy Sets Syst 9:153–160

    Article  MathSciNet  Google Scholar 

  • Hemasinha R, Pal NR, Bezdek JC (1993) Iterates of fuzzy circulant matrices. Fuzzy Sets Syst 60:199–206

    Article  MathSciNet  Google Scholar 

  • Khan M, Khan F, Lenley J, Abdullah S, Hussain F (2020) Extended topsis method based on Pythagorean cubic fuzzy multi-criteria decision making with incomplete weight information. J Intell Fuzzy Syst 38(2):2285–2296

    Article  Google Scholar 

  • Kim KH, Roush FW (1980) Generalized fuzzy matrices. Fuzzy Sets Syst 4:293–315

    Article  MathSciNet  Google Scholar 

  • Pal M, Khan SK, Shyamal AK (2002) Intuitionistic fuzzy matrices. Notes Intuit Fuzzy Sets 8(2):51–62

    MathSciNet  MATH  Google Scholar 

  • Qiyas M, Abdullah S, Ashraf S (2020) Utilizing linguistic picture fuzzy aggregation operators for multiple-attribute decision-making problems. Int J Fuzzy Syst 22:310–320

    Article  Google Scholar 

  • Thomason MG (1977) Convergence of powers of a fuzzy matrix. J Math Anal Appl 57:476–480

    Article  MathSciNet  Google Scholar 

  • Vijayalakshmi V, Sattanathan R (2010) Circulant trapezoidal fuzzy number matrices. Int J Algorithms Comput Math 3(2):49–56

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3:177–200

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author is grateful to the referees and editors for their valuable comments and suggestions provided in revising the manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    E. G. Emam

Authors
  1. E. G. Emam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. G. Emam.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Research involving human participants and/or animals

This article does not contain any studies with human participants or animal performed by the author.

Informed consent

Not applicable.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Emam, E.G. On the circulant intuitionistic fuzzy matrices. Soft Comput 25, 4621–4628 (2021). https://doi.org/10.1007/s00500-020-05468-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05468-5

Keywords

Search

Navigation