Submit your research to the International Journal "Notes on Intuitionistic Fuzzy Sets". Contact us at nifs.journal@gmail.com

Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.

Issue:Solving I-fuzzy number linear programming problems via Tanaka and Asai approach

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/23/5/85-101
Title of paper: Solving I-fuzzy number linear programming problems via Tanaka and Asai approach
Author(s):
Abha Aggarwal
University School of Basic and Applied Sciences, Guru Gobind, Singh Indraprastha University, Delhi-110078, India
abha@ipu.ac.in
Aparna Mehra
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
apmehra@maths.iitd.ac.in
Suresh Chandra
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
chandras@maths.iitd.ac.in
Imran Khan
University School of Basic and Applied Sciences, Guru Gobind, Singh Indraprastha University, Delhi-110078, India
imranalig_khan@yahoo.co.in
Published in: "Notes on IFS", Volume 23, 2017, Number 5, pages 85—101
Download:  PDF (296 Kb  Kb, Info)
Abstract: This paper proposes an extension of Tanaka and Asai approach to study Atanassov’s I-fuzzy linear programming problems where problem parameters are prescribed by I-fuzzy numbers. In literature, there are various indices based ranking function approaches for solving such I-fuzzy linear programming problems, e.g., Li [26], Li et al. [27], Dubey and Mehra [18] and Dubey et al. [19]. One major issue with these approaches is that the solution so obtained depends on the specific choice of the ranking function. The primary advantage of the proposed method is that, it is independent of any transformation and also provides the precise degrees of belief and disbelief of the optimal solution in achieving the goals set by the decision maker. It is shown that solving such an optimization problem is equivalent to solving a non-linear programming problem. A small numerical example is included as an illustration.
Keywords: I-fuzzy set, Triangular I-fuzzy numbers, I-fuzzy mathematical programming, I-fuzzy parameters.
AMS Classification: 90C72
References:
  1. Aggarwal, A., Dubey, D., Chandra, S. & Mehra, A. (2012) Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs, Fuzzy Information and Engineering, 4, 401–414.
  2. Aggarwal, A., Chandra, S. & Mehra, A. (2014) Solving Matrix Games with I-fuzzy Payoffs: Pareto-optimal Security Strategies Approach approach, Fuzzy Information and Engineering, 6, 167–192.
  3. Aliev, R. A., Huseynov, O. H. & Serdaroglu, R. (2016) Ranking of Z-numbers and its applications in decision making, Internatioanl Journal of Information Technology and Decision Making, 15, 1503–1519.
  4. Angelov, P. P. (1997) Optimization in an intuitionistic fuzzy environment, Fuzzy Sets and Systems, 86, 299–306.
  5. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
  6. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg.
  7. Atanassov, K. T. (1989) More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33, 37–45.
  8. Atanassov, K. T. (1986) New operations defined over intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
  9. Bector, C. R. & Chandra, S. (2005) Fuzzy mathematical programming and fuzzy matrix games, Berlin, Springer.
  10. Bellman, R. E. & Zadeh, L. A. (1970) Decision making in fuzzy environment, Management Sciences, 17, 141–164.
  11. Bector, C. R., Chandra, S. & Vidyottama, V. (2004) Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs, Fuzzy Sets and Systems, 146, 253–269.
  12. Clemente, M., Fernandez, F. R. & Puerto, J. (2011) Pareto optimal security strategies in matrix games with fuzzy payoffs, Fuzzy Sets and Systems, 176, 36–45.
  13. Das, S. K., Mandal, T. & Edalatpanah, S. A. (2017) A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers, Applied Intelligence, 46, 509–519.
  14. De, S. K., Biswas, R. & Roy, A. R. (2001) An application ofintuitionistic fuzzy sets in medical diagonsis, Fuzzy Sets and Systems, 117, 209–213.
  15. Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J. & Prade, H. (2005) Terminological difficulties in fuzzy set theory the case of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 156, 485–491.
  16. Dubois. D. & Prade, H. (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
  17. Dubey, D., Chandra, S. & Mehra, A. (2012) Fuzzy linear programming under interval uncertainity based on IFS representation, Fuzzy Sets and Systems, 188, 68–87.
  18. Dubey, D. & Mehra, A. (2011) Fuzzy linear programming with triangular intuitionistic fuzzy numbers, Advances in Intelligent System Research, EUSFLAT-LFA, 563–569.
  19. Dubey. D., Chandra. S. & Mehra, A. (2015) Computing a Pareto optimal solution for multiobjective flexible linear programming in a bipolar framework, International Journal of General Systems, 44, 457–470.
  20. Hurwicz, L. (1952) A criterion for Decision-Making Under Uncertainity, Technical Report 355, Cowels Commission.
  21. Gasimov, Rafail, N. & Yenilmez, K¨urs¸at. (2002) Solving Fuzzy Linear Programming Problems with Linear Membership Functions, Turk J Math, 26, 375–396.
  22. Grzegorzewski, P. & Mrowka, E. (2005) Some notes on Atanassov’s multiobjective fuzzy sets, Fuzzy Sets and Systems, 156, 492–495. nonlinear programming approach to matrix games with payoffs of Atanassov’s intutionistic fuzzy sets, International Journal of Uncertainity, Fuzziness and Knowledge based Systems, 17, 585–607.
  23. Nehi, H. M. (2010) A new ranking method for intutionistic fuzzy numbers, International Journal of Fuzzy Systems, 12, 80–86.
  24. Szmidt, E. & Kacprzyk, J. (1996) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on Intuitionistic Fuzzy Sets, 2, 2–31.
  25. Tanaka, H. & Asai, K. (1984) Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13, 1–10.
  26. Vlachos, I. K. & Sergiadis, G. D. (2007) Intuitionistic fuzzy information-applications to pattern recognition, Pattern Recognition Letter, 28, 197–206.
  27. Wu, H. C. (2003) Duality theorems in fuzzy mathematical programming problemd based on the concept of ncesssity, Fuzzy Sets and Systems, 139, 363–377.
  28. Yager, R. (1981) A procedure for ordering fuzzy numbers of the unit interval, Information Sciences, 24, 143–161.
  29. Zimmermann, H. J. (1978) Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45–55.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.