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A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem Cover

A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

Open Access
|Sep 2017

References

  1. Atanassov, K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1): 87–96.10.1016/S0165-0114(86)80034-3
  2. Atanassov, K.T. and Gargov, G. (1989). Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31(3): 343–349.10.1016/0165-0114(89)90205-4
  3. Ben Aicha, F., Bouani, F. and Ksouri, M. (2013). A multivariable multiobjective predictive controller, International Journal of Applied Mathematics and Computer Science23(1): 35–45, DOI: 10.2478/amcs-2013-0004.10.2478/amcs-2013-0004
  4. Chanas, S. and Kuchta, D. (1996). Multi objective programming in optimization of interval objective functions—A generalized approach, European Journal of Operational Research94(3): 594–598.10.1016/0377-2217(95)00055-0
  5. Chinneck, J.W. and Ramadan, K. (2000). Linear programming with interval coefficients, Journal of the Operational Research Society51(2): 209–220.10.1057/palgrave.jors.2600891
  6. Deng-Feng, L. (2010). A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications1(6): 1557–1570.10.1016/j.camwa.2010.06.039
  7. Dębski, R. (2016). An adaptive multi-spline refinement algorithm in simulation based sailboat trajectory optimization using onboard multi-core computer systems, International Journal of Applied Mathematics and Computer Science26(2): 351–365, DOI: 10.1515/amcs-2016-0025.10.1515/amcs-2016-0025
  8. Dwyer, P.S. (1951). Linear Computation, Wiley, New York, NY.
  9. Ganesan, K. and Veeramani, P. (2005). On arithmetic operations of interval numbers, International Journal of Uncertainty Fuzziness and Knowledge-based Systems13(6): 619–631.10.1142/S0218488505003710
  10. Ida, M. (1999). Necessary efficient test in interval multi objective linear programming, Proceedings of the 8th International Fuzzy Systems Association World Congress, Taipei, Taiwan, pp. 500–504.
  11. Inuiguchi, M. and Sakawa, M. (1995). Minimax regret solution to linear programming problems with an interval objective function, European Journal of Operational Research86(3): 526–536.10.1016/0377-2217(94)00092-Q
  12. Irene Hepzibah, R. and Vidhya, R. (2015). Modified new operations for interval valued intuitionistic fuzzy numbers (IVIFNs): Linear programming problem with triangular intuitionistic fuzzy numbers, Proceedings of the National Conference on Frontiers in Applied Sciences and Computer Technology, NIT, Trichy, Tamil Nadu, India, pp. 35–43.
  13. Ishibuchi, H. and Tanaka, H. (1990). Multi objective programming in optimization of the interval objective function, European Journal of Operational Research48(2): 219–225.10.1016/0377-2217(90)90375-L
  14. Moore, R.E. (1966). Interval Analysis, Prentice Hall, Englewood Cliffs, NJ.
  15. Oliveira, C. and Antunes, C.H. (2007). Multiple objective linear programming models with interval coefficients—An illustrated overview, European Journal of Operational Research181(3): 1434–1463.10.1016/j.ejor.2005.12.042
  16. Rardin, R.L. (2003). Optimization in Operations Research, Pearson Education, Singapore.
  17. Sengupta, A., Pal, T.K. and Chakraborty, D. (2001). Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems119(1): 129–138.10.1016/S0165-0114(98)00407-2
  18. Smoczek, J. (2013). Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control, International Journal of Applied Mathematics and Computer Science23(4): 749–759, DOI: 10.2478/amcs-2013-0056.10.2478/amcs-2013-0056
  19. Timothy, J.R. (2010). Fuzzy Logic with Engineering Applications, 3rd Edn., Wiley, New York, NY.
  20. Wang, M.L. and Wang, H.F. (2001). Interval analysis of a fuzzy multi objective linear programming, International Journal of Fuzzy Systems3(4): 558–568.
  21. Yun, Y.S. and Lee, B. (2013). The one-sided quadrangular fuzzy sets, Journal of the Chungcheong Mathematical Society26(2): 297–308.10.14403/jcms.2013.26.2.297
DOI: https://doi.org/10.1515/amcs-2017-0040 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 563 - 573
Submitted on: Aug 11, 2016
Accepted on: May 2, 2017
Published on: Sep 23, 2017
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2017 Rajendran Vidhya, Rajkumar Irene Hepzibah, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.