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.
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Landowski, M. (2021). Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers. In: Atanassov, K., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives. IWIFSGN 2018. Advances in Intelligent Systems and Computing, vol 1081. Springer, Cham. https://doi.org/10.1007/978-3-030-47024-1_7
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