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Issue:Intuitionistic fuzzy T-sets based solution technique for multiple objective linear programming problems under imprecise environment

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Title of paper: Intuitionistic fuzzy T-sets based solution technique for multiple objective linear programming problems under imprecise environment
Author(s):
Arindam Garai
Department of Mathematics, Sonarpur Mahavidyalaya, West Bengal, India, Pin 700149
fuzzy_arindam@yahoo.com
Palash Mandal
Department of Mathematics, IIEST, Shibpur, Howrah, West Bengal, India, Pin 711103
palashmandalmbss@gmail.com
Tapan Kumar Roy
Department of Mathematics, IIEST, Shibpur, Howrah, West Bengal, India, Pin 711103
roy_t_k@yahoo.co.in
Published in: "Notes on IFS", Volume 21, 2015, Number 4, pages 104–123
Download:  PDF (146  Kb, Info)
Abstract: Technique to find Pareto-optimal solutions to multiple objective linear programming problems under imprecise environment is discussed in this paper. In 1997, Angelov formulated an optimization technique under intuitionistic fuzzy environment. Several other researchers have worked on it in recent years. In optimization technique under imprecise environment, it is observed that the prime intention to maximize up-gradation of most misfortunate is better served if some constraints present in existing, well established techniques are removed. In classical intuitionistic fuzzy optimization techniques, it is also observed that membership functions and non-membership functions are not utilised in the way they are defined; and in some cases, constraints in those existing techniques may make the problem infeasible. Hence in this paper, new functions: T(+)-characteristic functions and T(–)-characteristic functions, are introduced to supersede membership functions and non-membership functions respectively; and subsequently new set: Intuitionistic fuzzy T-set is introduced to supersede intuitionistic fuzzy set to represent impreciseness. Moreover in this paper, one general algorithm has been developed to find Pareto optimal solutions to multiple objective linear programming problems under imprecise environment. A real life industrial application model further illustrates the limitations of existing technique as well as advantages of using proposed technique. Finally conclusions are drawn.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy optimization, T(+)-characteristic functions, T(–)-characteristic functions, Intuitionistic fuzzy T-sets.
AMS Classification: 03E72, 90C70, 58E17, 90C05.
References:
  1. Angelov, P. P. (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems, 86, 299–306.
  2. Atanassov, K. T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
  3. Bellman, R. E., & Zadeh, L. A. (1970) Decision making in a fuzzy environment. Management Science, 17, 141–164.
  4. Dubois, D., & Fortemps, P. (1999) Computing improved optimal solutions to max–min flexible constraint satisfaction problems. European Journal of Operational Research, 118, 95–126.
  5. Gao, Z., & Tang, L. (2003) A multi-objective model for purchasing of bulk raw materials of a large-scale integrated steel plant. International Journal of Production Economics, 83, 325–334.
  6. Guu, S.-M., & Wu, Y.-K. (1997) Weighted coefficients in two-phase approach for solving the multiple objective programming problems. Fuzzy Sets and Systems, 85, 45–48.
  7. Guu, S.-M., & Wu, Y.-K. (1999) Two phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107, 191–195.
  8. Jiménez, M., & Bilbao, A. (2009) Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 150, 2714–2721.
  9. Sakawa, M., Yano, H., & Yumine, T. (1987) An interactive fuzzy satisficing method for multi-objective linear-programming problems and its application. IEEE Transactions on Systems, Man and Cybernetics, SMC-17, 654–661.
  10. Sakawa, M., Yano, H., & Nishizaki, I. (2013) Linear and Multi-objective Programming with Fuzzy Stochastic Extensions. Springer Science Business Media New York.
  11. Tanaka, H., Okuda, T., & Asai, K. (1974) On fuzzy mathematical programming. Journal of Cybernetics, 3, 37–46.
  12. Wu, Y.-K., Liu, C.-C., & Lur, Y.-Y. (2015) Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals. Fuzzy Optimum Decision Making, 43–55.
  13. Zimmermann, H.-J. (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45–55.
  14. Zimmermann, H.-J. (1985) Applications of fuzzy set theory to mathematical programming. Information Sciences, 36, 29–58.
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