Soft Computing

, Volume 22, Issue 15, pp 5115–5120 | Cite as

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

  • Velichka TranevaEmail author
  • Stoyan Tranev
  • Miroslav Stoenchev
  • Krassimir Atanassov


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.


Intuitionistic fuzzy index matrix Intuitionistic fuzzy pair Operation 


Compliance with ethical standards


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.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Computer and Information Technologies“Prof. Asen Zlatarov” UniversityBurgasBulgaria
  2. 2.Department of Economics and Management“Prof. Asen Zlatarov” UniversityBurgasBulgaria
  3. 3.Department of Bioinformatics and Mathematical ModellingBulgarian Academy of SciencesSofiaBulgaria

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