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Abstract

In the paper authors try to convince readers that application of multidimensional fuzzy arithmetic (MFAr) is useful because this arithmetic delivers more precise solutions of uncertain problems than low-dimensional fuzzy arithmetic, which is mostly used at present.

Keywords

Fuzzy arithmetic RDM fuzzy arithmetic Horizontal membership function Granular computing Multidimensional fuzzy arithmetic 

References

  1. 1.
    Aliev, R.A.: Operations on Z-numbers with acceptable degree of specificity. Procedia Comput. Sci. 120, 9–15 (2017)CrossRefGoogle Scholar
  2. 2.
    Aliev, R.A., Huseynov, O.H., Aliyev, R.R.: A sum of a large number of Z-numbers. Procedia Comput. Sci. 120, 16–22 (2017)CrossRefGoogle Scholar
  3. 3.
    Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: An introduction to the arithmetic of Z- numbers by using horizontal membership functions. Procedia Comput. Sci. 120, 349–356 (2017)CrossRefGoogle Scholar
  4. 4.
    Allahviranloo, T., Ghanbari, M.: On the algebraic solution of fuzzy linear systems based on interval theory. Appl. Math. Model. 36, 5360–5379 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dymova, L.: Soft Computing in Economics and Finance. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-17719-4CrossRefGoogle Scholar
  6. 6.
    Mazandarani, M., Pariz, N., Kamyad, A.V.: Granular differentiability of fuzzy-number-valued functions. IEEE Trans. Fuzzy Syst. 26(1), 310–323 (2018)CrossRefGoogle Scholar
  7. 7.
    Mazandarani, M., Zhao, Y.: Fuzzy bang-bang control problem under granular differentiability. J. Frankl. Inst.-Eng. Appl. Math. 355(12), 4771–5350 (2018)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Najariyan, M., Zhao, Y.: Fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives. IEEE Trans. Fuzzy Syst. 26(4), 2273–2288 (2018)CrossRefGoogle Scholar
  9. 9.
    Piegat, A., Landowski, M.: Two interpretations of multidimensional RDM interval arithmetic - multiplication and division. Int. J. Fuzzy Syst. 15(4), 488–496 (2013)MathSciNetGoogle Scholar
  10. 10.
    Piegat, A., Plucinski, M.: Fuzzy number addition with application of horizontal membership functions. Sci. World J. 2015, 16 (2015).  https://doi.org/10.1155/2015/367214. Article no. ID367214CrossRefzbMATHGoogle Scholar
  11. 11.
    Piegat, A., Landowski, M.: Horizontal membership function and examples of its applications. Int. J. Fuzzy Syst. 17(1), 22–30 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zeinalova, L.M.: Application of RDM interval arithmetic in decision making problem under uncertainty. Procedia Comput. Sci. 120, 788–796 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Computer ScienceWest Pomeranian University of TechnologySzczecinPoland
  2. 2.Department of Mathematical MethodsMaritime University of SzczecinSzczecinPoland

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