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Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers

  • Marek LandowskiEmail author
Conference paper
  • 5 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1081)

Abstract

In this paper the definition of a multidimensional trapezoidal horizontal intuitionistic fuzzy number (TrHIFN) and multidimensional decomposition method (TrHIFN arithmetic) for calculations on TrHIFNs are presented. Till now, for intuitionistic fuzzy numbers (IFN) only low-dimensional approaches have been considered. The proposed arithmetic is based on multidimensional rdm interval arithmetic (RDMIA) and its extension horizontal fuzzy arithmetic (HFA). A direct result obtained with TrHIFN arithmetic is described in multidimensional space as a granule of information about the solution. From the direct solution, IFN as an indicator (a span) of the direct solution can be calculated. Moreover, in the paper the examples with basic operations on TrHIFN and the solution of intuitionistic fuzzy linear system (IFLS) are considered.

Keywords

Intuitionistic fuzzy number Intuitionistic fuzzy arithmetic Multidimensional arithmetic Decomposition method RDM arithmetic 

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© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Department of Mathematical MethodsMaritime University of SzczecinSzczecinPoland

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