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

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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.

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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
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  2. Stoyan Tranev
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  3. Miroslav Stoenchev
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  4. Krassimir Atanassov
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Corresponding author

Correspondence to Velichka Traneva.

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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.

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

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Communicated by C. Kahraman.

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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”.

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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

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

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