Have a personal or library account? Click to login
A Decomposition Approach to Type 2 Interval Arithmetic Cover
Open Access
|Apr 2020

References

  1. Abolmasoumi, S. and Alavi, M. (2014). A method for calculating interval linear system, Journal of Mathematics and Computer Science8(3): 193–204.10.22436/jmcs.08.03.02
  2. Allahviranloo, T. and Babakordi, F. (2017). Algebraic solution of fuzzy linear system as: AX + BX = Y, Soft Computing21(24): 7463–7472.10.1007/s00500-016-2294-8
  3. De Figueiredo, L.H. and Stolphi, J. (2004). Affine arithmetic: Concepts and applications, Numerical Algorithms37(1–4): 147–158.10.1023/B:NUMA.0000049462.70970.b6
  4. Dymowa, L. (2011). Soft Computing in Economics and Finance, Springer, Berlin/Heidelberg.10.1007/978-3-642-17719-4
  5. Kaucher, E. (1980). Interval analysis in the extended interval space IR, in G. Alefeld and R.O. Grigorieff (Eds), Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis), Springer, Vienna, pp. 33–49.10.1007/978-3-7091-8577-3_3
  6. Lala, Z.M. (2017). Application of RDM interval arithmetic in decision making problem under uncertainty, Procedia Computer Science120: 788–796.10.1016/j.procs.2017.11.309
  7. Landowski, M. (2015). Differences between Moore and RDM interval arithmetic, in P. Angelov et al. (Eds), Intelligent Systems’2014, Springer, Heidelberg/New York, NY, pp. 331–340.10.1007/978-3-319-11313-5_30
  8. Lodwick, W.A. (1999). Constrained interval arithmetic, CCM report, University of Colorado at Denver, Denver, CO, http://www-math.ucdenver.edu/ccm/reports/index.shtml.
  9. Lodwick, W.A. and Dubois, D. (2015). Interval linear systems as a necessary step in fuzzy linear systems, Fuzzy Sets and Systems281(15): 227–251.10.1016/j.fss.2015.03.018
  10. Mazandarani, M., Pariz, N. and Kamyad, A.V. (2018). Granular differentiability of fuzzy-number-valued functions, IEEE Transactions on Fuzzy Systems26(1): 310–323.10.1109/TFUZZ.2017.2659731
  11. Moore, R. (1966). Interval Analysis, Prentice-Hall, Englewood Cliff, NJ.
  12. Najariyan, M. and Zhao, Y. (2017). Fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives, IEEE Transactions on Fuzzy Systems26(4): 2273–2288.10.1109/TFUZZ.2017.2783895
  13. Piegat, A. and Landowski, M. (2013). Two interpretations of multidimensional RDM interval arithmetic: Multiplication and division, International Journal of Fuzzy Systems15(4): 486–496.
  14. Piegat, A. and Landowski, M. (2015). Horizontal membership function and examples of its applications, International Journal of Fuzzy Systems17(1): 22–30.10.1007/s40815-015-0013-8
  15. Piegat, A. and Landowski, M. (2017). Is an interval the right result of arithmetic operations on intervals?, International Journal of Applied Mathematics and Computer Science27(3): 575–590, DOI: 10.1515/amcs-2017-0041.10.1515/amcs-2017-0041
  16. Piegat, A. and Landowski, M. (2018). Solving different practical granular problems under the same system of equations, Granular Computing3(1): 39–48.10.1007/s41066-017-0054-5
  17. Piegat, A. and Pluciński, M. (2015). Fuzzy number addition with the application of horizontal membership functions, Scientific World Journal2015, Article ID: 367214, DOI: 10.1155/2015/367214.10.1155/2015/367214449331226199953
  18. Piegat, A. and Pluciński, M. (2017). Fuzzy number division and the multi-granularity phenomenon, Bulletin of the Polish Academy of Sciences: Technical Sciences65(4): 497–511.10.1515/bpasts-2017-0055
  19. Pluciński, M. (2015). Solving Zadeh’s challenge problems with the application of RDM-arithmetic, International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland, pp. 239–248.
  20. Sharghi, P., Jabbarova, K. and Aliyeva, K. (2017). RDM interval arithmetic based decision making on port selection, Procedia Computer Science120: 572–579.10.1016/j.procs.2017.11.281
  21. Stolphi, J. and De Figueiredo, L. (2003). An introduction to affine arithmetic, Trends in Applied and Computational Mathematics4(3): 297–312.10.5540/tema.2003.04.03.0297
  22. Sunaga, T. (2009). Theory of an interval algebra and its application to numerical analysis, Japan Journal of Industrial and Applied Mathematics26(2–3): 125–143.10.1007/BF03186528
  23. Warmus, M. (1956). Calculus of approximations, Bulletin de l’Academie Polonaise de Sciences4(5): 253–257.
DOI: https://doi.org/10.34768/amcs-2020-0015 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 185 - 201
Submitted on: May 9, 2018
Accepted on: Oct 8, 2019
Published on: Apr 3, 2020
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Andrzej Piegat, Larisa Dobryakova, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.