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2017 | Vol. 27, no. 3 | 563--573
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.
Wydawca

Rocznik
Strony
563--573
Opis fizyczny
Bibliogr. 21 poz., tab., wykr.
Twórcy
autor
  • Research Scholar, Bharathiar University, Coimbatore 641046, Tamil Nadu, India; Department of Mathematics, AS-SALAM College of Engineering and Technology, Aduthurai, Tamil Nadu, India, vidhya14m@gmail.com
  • Research and Development Centre, Bharathiar University, Coimbatore 641046, Tamil Nadu, India; Department of Mathematics, AVC College of Engineering, Mayiladuthurai, Tamil Nadu, India, ireneraj74@gmail.com
Bibliografia
  • [1] Atanassov, K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1): 87–96.
  • [2] Atanassov, K.T. and Gargov, G. (1989). Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31(3): 343–349.
  • [3] Ben Aicha, F., Bouani, F. and Ksouri, M. (2013). A multivariable multiobjective predictive controller, International Journal of Applied Mathematics and Computer Science 23(1): 35–45, DOI: 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 Research 94(3): 594–598.
  • [5] Chinneck, J.W. and Ramadan, K. (2000). Linear programming with interval coefficients, Journal of the Operational Research Society 51(2): 209–220.
  • [6] Deng-Feng, L. (2010). A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications 1(6): 1557–1570.
  • [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 Science 26(2): 351–365, DOI: 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 Systems 13(6): 619–631.
  • [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 Research 86(3): 526–536.
  • [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 Research 48(2): 219–225.
  • [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 Research 181(3): 1434–1463.
  • [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 Systems 119(1): 129–138.
  • [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 Science 23(4): 749–759, DOI: 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 Systems 3(4): 558–568.
  • [21] Yun, Y.S. and Lee, B. (2013). The one-sided quadrangular fuzzy sets, Journal of the Chungcheong Mathematical Society 26(2): 297–308.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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Bibliografia
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