Skip to main content
SpringerLink
Log in

Scaled aggregation operations over two- and three-dimensional index matrices

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

Abstract

Index matrices (IMs) are extensions of the standard matrices. Their elements can be different objects, e.g., natural, real or complex numbers, variables or predicates. In the present paper, we discuss the case, when the elements of the IM are intuitionistic fuzzy pairs. In this case, we can aggregate these elements by some intuitionistic fuzzy operations. In the paper, a set of such operations is constructed, so that the matrix elements are well ordered, generating a scale. Some applications of the so constructed scaled operations are discussed.

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

  • Angelova N, Stoenchev M (2015–2016) Intuitionistic fuzzy conjunctions and disjunctions from first type. Ann Inf Sect Union Sci Bulg 8:1–17

  • Atanassov K (1987) Generalized index matrices. Comptes rendus de l’Academie Bulgare des Sciences 40(11):15–18

    MathSciNet  MATH  Google Scholar 

  • Atanassov K (2014a) On index matrices. Part 5: three dimensional index matrices. Advanced studies. Contemp Math 24(4):423–432

    MATH  Google Scholar 

  • Atanassov K (2014b) Index matrices: towards an augmented matrix calculus. Springer, Cham pp 110

    MATH  Google Scholar 

  • Atanassov K (2017) Intuitionistic fuzzy logics. Springer, Cham pp 138

    Book  MATH  Google Scholar 

  • Atanassov K (2018) n-Dimensional extended index matrices. Adv Stud Contemp Math 28(2):245–259

    Google Scholar 

  • Atanassov K, Pasi G, Yager R (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36(14):859–868

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K, Szmidt E, Kacprzyk J (2013) On intuitionistic fuzzy pairs. Notes Intuit Fuzzy Sets 19(3):1–13

    MATH  Google Scholar 

  • Bureva V, Traneva V, Sotirova E, Atanassov K (2017) Index matrices and OLAP-cube. Part 2: an presentation of the OLAP-analysis by index matrices. Advanced studies. Contemp Math 27(4):647–672

    MATH  Google Scholar 

  • Mendelson E (1964) Introduction to Mathematical Logic. D. Van Nostrand, Princeton pp 408

    MATH  Google Scholar 

  • Traneva V (2014) On 3-dimensional intuitionistic fuzzy index matrices. Notes Intuit Fuzzy Sets 20(4):59–64

    Google Scholar 

  • Traneva V, Atanassov K, Rangasami P (2014) On 3-dimensional index matrices. Int J Res Sci 1(2):64–68

    Google Scholar 

  • Traneva V, Sotirova E, Bureva V, Atanassov K (2015) Aggregation operations over 3-dimensional extended index matrices. Adv Stud Contemp Math 25(3):407–416

    MATH  Google Scholar 

  • Traneva V, Bureva V, Sotirova E, Atanassov K (2017a) Index matrices and OLAP-cube. Part 1: application of the index matrices to presentation of operations in OLAP-cube. Advanced studies. Contemp Math 27(2):253–278

    MATH  Google Scholar 

  • Traneva V, Tranev S, Szmidt E, Atanasov K (2017b) Three dimensional intercriteria analysis over intuitionistic fuzzy data. In: Advances in fuzzy logic and technology 2017: proceedings of the 10th conference of the European society for fuzzy logic and technology, vol 3. Springer, Poland, pp 442–449

  • Zadeh L (1988) Fuzzy logic. IEEE Comput 21(4):83–93

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Information Technologies, “Prof. Asen Zlatarov” University, “Prof. Yakimov” Blvd, 8000, Burgas, Bulgaria

    Velichka Traneva

  2. Department of Economics and Management, “Prof. Asen Zlatarov” University, “Prof. Yakimov” Blvd, 8000, Burgas, Bulgaria

    Stoyan Tranev

  3. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, 1113, Sofia, Bulgaria

    Miroslav Stoenchev & Krassimir Atanassov

Authors
  1. Velichka Traneva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stoyan Tranev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miroslav Stoenchev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Krassimir Atanassov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Velichka Traneva.

Ethics declarations

Funding

This study was funded by the Bulgarian National Science Fund under Grants Ref. No. DN-02-10 “New Instruments for Knowledge Discovery from Data, and their Modelling” and the project of Asen Zlatarov University under Ref. No. NIX-401/2017 “Modern methods of optimization and business management”.

Conflict 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 C. Kahraman.

Publisher's Note

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

The authors are thankful for the support provided by the Bulgarian National Science Fund under Grants Ref. No. DN-02-10 “New Instruments for Knowledge Discovery from Data, and their Modelling” and the project of Asen Zlatarov University under Ref. No. NIX-401/2017 “Modern methods of optimization and business management”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Traneva, V., Tranev, S., Stoenchev, M. et al. Scaled aggregation operations over two- and three-dimensional index matrices. Soft Comput 22, 5115–5120 (2018). https://doi.org/10.1007/s00500-018-3315-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3315-6

Keywords

Search

Navigation