31
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values

&
Pages 1192-1209 | Received 20 May 2015, Accepted 13 Oct 2015, Published online: 13 Nov 2015

References

  • R. Moore, “Interval analysis,” Prentice Hall, Englewood Cliffs, New Jork (1966).
  • R. Moore, R. Kearfott and M. Cloud, “Introduction to interval analysis,” Society for Industrial and Applied Mathematics, Philadelphia (2009).
  • L. Zadeh, “Computing with Words,” Springer, Heidelberg, New York (2012).
  • S. Liu and Y. Lin, “Grey systems, theory and applications,” Springer Verlag, Berlin, Heidelberg (2010).
  • W. Pedrycz, A. Skowron and V. Kreinovicz (eds), “Handbook of granular computing,” J. Wiley, Chichester, England (2008).
  • Y. Yoshimura, “Mathematical model for manoeuvring ship motion (MMG model),” Proceedings of Workshop on Mathematical Models for Operations Involving Ship-Ship Interaction, 1–6, Tokyo (2005).
  • M. Hanss, “Applied fuzzy arithmetic,” Springer Verlag, Berlin, Heidelberg (2005).
  • A. Kaufmann and M. Gupta, “Introduction to fuzzy arithmetic,” Van Nostrand Reinhold, New York (1991).
  • A. Piegat, “Fuzzy modeling and control,” Physica Verlag, Heidelberg-New York (2001).
  • S. Jaroszewicz and M. Korzen´, “Arithmetic operations on independent random variables: a numerical approach,” SIAM Journal of Scientific Computing, 34(3), 1241–1265 (2012). doi: 10.1137/110839680
  • S. Jaroszewicz and M. Korzen´, “Pacal: a Python package for arithmetic computations with random variables,” http://pacal.sourceforge.net (2012).
  • R. Williamson, “Probabilistic arithmetic,” PhD thesis, Department of Electrical Engineering, University of Queensland (1989).
  • R. Aliev, W. Pedrycz, B. Fazlollahi, O. Huseynov, A. Alizadeh and B. Guirimov, “Fuzzy logic-based generalized decision theory with imperfect information,” Information Sciences, 189, 18–42 (2012). doi: 10.1016/j.ins.2011.11.027
  • L. Zadeh, “From computing with numbers to computing with words – from manipulation of measurements to manipulation of perceptions,” International Journal of Applied Mathematics and Computer Science, 12(3), 307–324 (2002).
  • L. Martinez, D. Ruan and F. Herrera, “Computing with Words in decision support dystems: an overview on models and applications,” International Journal of Computational Intelligence Systems, 3(4), 382–395 (2010). doi: 10.1080/18756891.2010.9727709
  • J. Liu, L. Martinez, H. Wang, R. Rodriguez and V. Novozhilov, “Computing with Words in risk assessment,” International Journal of Computational Intelligence Systems, 3(4), 396–419 (2010). doi: 10.1080/18756891.2010.9727710
  • H. Bustince, “Interval-valued fuzzy sets in soft computing,” International Journal of Computational Intelligence Systems, 3(2), 215–222 (2010). doi: 10.1080/18756891.2010.9727692
  • H. Liu and C. Li, “Fully implicational methods for interval-valued fuzzy reasoning with multi-antecedent rules,” International Journal of Computational Intelligence Systems, 4(5),929–945 (2011). doi: 10.1080/18756891.2011.9727843
  • R. Gonzalez-del-Campo, L. Garmendia and R. Yager, “Specificity for interval-valued fuzzy sets,” International Journal of Computational Intelligence Systems, 5(3), 452–459 (2012). doi: 10.1080/18756891.2012.696908
  • J. Kacprzyk, “Computational intelligence and soft computing: some thoughts on already explored and not yet explored paths,” International Journal of Computational Intelligence Systems, 3(2), 223–236 (2010). doi: 10.1080/18756891.2010.9727693
  • L. Dymova, “Soft computing in economics and finance,” Springer Verlag, Berlin, Heidelberg (2011).
  • A. Sengupta and T. Pal, “Fuzzy preference ordering of interval numbers in decision problems,” Springer Verlag, Berlin, Heidelberg (2009).
  • R. Gonzalez-del-Campo, L. Garmendia and J. Recasens, “Transitive closure of interval-valued fuzzy relations,” International Journal of Computational Intelligence Systems, 6(4), 648–657 (2013). doi: 10.1080/18756891.2013.802117
  • X. Zhang, “On interval soft sets with applications,” International Journal of Computational Intelligence Systems, 7(1), 186–196 (2014). doi: 10.1080/18756891.2013.862354
  • X. Wang, S. Li and T. Denoeux, “Interval-valued linear model,” International Journal of Computational Intelligence Systems, 8(1), 114–127 (2015). doi: 10.1080/18756891.2014.967010
  • F. Meng, C. Tan and X. Chen, “An approach to Atanassov's interval-valued intuitionistic fuzzy multiattribute decision making based on prospect theory,” International Journal of Computational Intelligence Systems, 8(3), 591–605 (2015). doi: 10.1080/18756891.2015.1036224
  • P. Sevastjanov and L. Dymova, “A new method for solving interval and fuzzy equations: linear case,” Information Sciences, 17, 925–937 (2009). doi: 10.1016/j.ins.2008.11.031
  • P. Sevastjanov, L. Dymova and P. Bartosiewicz, “A framework for rule-base evidential reasoning in the interval settings applied to diagnosing type 2 diabetes,” Expert Systems with Applications, 39, 4190–4200 (2012). doi: 10.1016/j.eswa.2011.09.115
  • A. Piegat and M. Landowski, “Is the conventional interval-arithmetic correct?” Journal of Theoretical and Applied Computer Science, 6(2), 27–44 (2012).
  • A. Piegat and M. Landowski, “Multidimensional approach to interval-uncertainty calculations,” New Trends in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, vol. II: Applications, System Research Institute of Polish Academy of Sciences, Warsaw, Poland, 137–152 (2013).
  • A. Piegat and M. Landowski, “Two interpretations of multidimensional RDM arithmetic: multiplication and division,” International Journal of Fuzzy Systems, 15(4), 486–496 (2013).
  • A. Piegat and K. Tomaszewska, “Decision-making under uncertainty using Info-Gap theory and a new multidimensional RDM interval arithmetic,” Electrical Review, 89(8), 71–76 (2013).
  • A. Piegat and M. Landowski, “Correctness-checking of uncertain-equation solutions on example of the interval-modal method,” Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, vol. 1, eds.: K. Atanassov et al., 159–170 (2013).
  • M. Landowski, “Differences between Moore's and RDM interval arithmetic,” Proceedings of Thirteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, Warsaw, Poland (2014).
  • K. Tomaszewska and A. Piegat, “Application of horizontal membership function to the uncertain displacement calculation of a composite massless rod under a tensile load,” Soft Computing in Computer and Information Science, 63–72 (2015).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.