Skip to main content
SpringerLink
Log in

Picture fuzzy matrix and its application

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, the notions of picture fuzzy matrix, restricted picture fuzzy matrix and special restricted picture fuzzy matrix are established. Two types of \(\langle \theta , \phi , \psi \rangle \)-cut of special restricted square picture fuzzy matrix are introduced and corresponding properties are studied. Also, determinant and adjoint of square picture fuzzy matrix are established and some related properties are investigated. An application of picture fuzzy matrix in decision-making problem is presented here.

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

Fig. 1

Similar content being viewed by others

Abbreviations

IFS:

Intuitionistic fuzzy set

IFV:

Intuitionistic fuzzy value

IFM:

Intuitionistic fuzzy matrix

SIFM:

Square intuitionistic fuzzy matrix

PFS:

Picture fuzzy set

PFV:

Picture fuzzy value

PFM:

Picture fuzzy matrix

SPFM:

Square picture fuzzy matrix

AO:

Administrative officer

AOs:

Administrative officers

DOC:

Degree of closeness

DOCs:

Degree of closenesses

Government:

Govt.

Governments:

Govts.

References

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  Google Scholar 

  • Chang YF, Ishii H (2013) Fuzzy multiple criteria decision making approach to assess the project quality management in project. Procedia Comput Sci 22:928–936

    Article  Google Scholar 

  • Chen YW, Larbani M (2006) Two-person zero-sum game approach for fuzzy multiple attribute decision making problems. Fuzzy Sets Syst 157:34–51

    Article  MathSciNet  Google Scholar 

  • Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  • Cuong BC, Hai PV (2015) Some fuzzy logic operators for picture fuzzy sets. In: 7th International conference on knowledge and systems engineering

  • Cuong BC, Kreinovich V (2013) Picture fuzzy sets - a new concept for computational intelligence problems. In: Proceedings of the third world congress on information and communication technologies WIICT

  • Dechouniotis D (2018) Fuzzy multi-criteria based trust management in heterogeneous federated future internet testbeds. Future Internet 10(58):1–17

    Google Scholar 

  • Ejegwa PA, Akub AJ, Joshu OM (2017) Career determination using intuitionistic fuzzy multisets approach. MAYFEB J Math 1:1–10

    Google Scholar 

  • Fullerr R, Carlsson C (1996) Fuzzy multiple criteria decision making: recent developments. Fuzzy Sets Syst 78:139–153

    Article  MathSciNet  Google Scholar 

  • Hashimoto H (1983) Canonical form of a transitive matrix. Fuzzy Sets Syst 11(1–3):157–162

    Article  MathSciNet  Google Scholar 

  • Khan SK, Pal A (2007) The Generalised inverse of intuitionistic fuzzy matrices. J Phys Sci 11:62–67

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Khemiri R, Khaoula EM, Bernard G, Belhassen Z (2017) A fuzzy multi-criteria decision making approach for managing performance and risk in integrated procurement–production planning. Int J Prod Res 55(18):5305–5329

    Article  Google Scholar 

  • Kim KH, Roush FW (1980) Generalized fuzzy matrices. Fuzzy Sets Syst 4(3):293–315

    Article  MathSciNet  Google Scholar 

  • Lee HS, Shen PD, Chih WL (2004) A fuzzy multiple criteria decision making model for software selection. IEEE Int Conf Fuzzy Syst Bp Hung 3:1709–1713

    Google Scholar 

  • Lilik S, Lamalewa L, Istanto T (2019) Implementation of fuzzy multiple criteria decision making for recommendation paddy fertizer. Int J Mech Technol 10(3):236–243

    Google Scholar 

  • Mondal S, Pal M (2014) Intuitionistic fuzzy incline matrix and determinant. Ann Fuzzy Math Inf 8(1):19–32

    MathSciNet  MATH  Google Scholar 

  • Murugdas P, Sriram S, Muthuraji T (2014) Modal operator in intuitionistic fuzzy matrices. Int J Comput Appl 90(17):1–4

    Google Scholar 

  • Muthuraji T, Sriram S, Murugadas P (2016) Decomposition of intuitionistic fuzzy matrices. Fuzzy Inf Eng 8(3):345–354

    Article  MathSciNet  Google Scholar 

  • Nagar A (2011) Development of fuzzy multi criteria decision making method for selection of optimum maintenance alternative. Int J Appl Res Mech Eng 1(2):87–92

    Google Scholar 

  • Pal M (2001) Intuitionistic fuzzy determinant. V. U. J. Phys Sci 7:87–93

    Google Scholar 

  • Pal M (2015a) Fuzzy matrices with fuzzy rows and columns. J Intell Fuzzy Syst 30(1):561–573

    Article  Google Scholar 

  • Pal M (2015b) Interval valued fuzzy matrices with interval valued rows and columns. Fuzzy Inf Eng 7:335–368

    Article  MathSciNet  Google Scholar 

  • Pal M, Mondal S (2019) Bipolar fuzzy matrices. Soft Comput 23:9885–9897

    Article  Google Scholar 

  • Pradhan R, Pal M (2014) The generalized inverse of atanassov’s intuitionistic fuzzy matrices. Int J Comput Intell Syst 7(6):1083–1095

    Article  Google Scholar 

  • Pradhan R, Pal M (2017) Triangular fuzzy matrix norm and its properties. J Fuzzy Math 25(4):823–834

    MATH  Google Scholar 

  • Ragab MG, Emam EG (1994) The determinant and adjoint of a square fuzzy matrix. Fuzzy Sets Syst 61(3):297–307

    Article  MathSciNet  Google Scholar 

  • Ragab MG, Emam EG (1995) On the min–max composition of fuzzy matrices. Fuzzy Sets Syst 75(1):83–92

    Article  MathSciNet  Google Scholar 

  • Sriram S, Murugadas P (2010) On semiring of intuitionistic fuzzy matrices. Appl Math Sci 4(23):1099–1105

    MathSciNet  MATH  Google Scholar 

  • Sriram S, Murugadas P (2012) \(\langle \alpha, \alpha ^\prime \rangle \)-cut of intuitionistic fuzzy matrices. J Fuzzy Math 20(2):307–318

    MathSciNet  MATH  Google Scholar 

  • Wei G (2016) Picture fuzzy cross-entropy for multiple attribute decision making problems. J Bus Econ Manage 17(4):491–502

    Article  MathSciNet  Google Scholar 

  • Wei G (2017) Picture fuzzy aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33:713–724

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Shovan Dogra & Madhumangal Pal

Authors
  1. Shovan Dogra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Madhumangal Pal.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Additional information

Communicated by A. Di Nola.

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

Dogra, S., Pal, M. Picture fuzzy matrix and its application. Soft Comput 24, 9413–9428 (2020). https://doi.org/10.1007/s00500-020-05021-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05021-4

Keywords

Search

Navigation