Title of paper:

Solving Ifuzzy 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, Delhi110078, India

abha@ipu.ac.in

Aparna Mehra

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi110016, India

apmehra@maths.iitd.ac.in

Suresh Chandra

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi110016, India

chandras@maths.iitd.ac.in

Imran Khan

University School of Basic and Applied Sciences, Guru Gobind, Singh Indraprastha University, Delhi110078, India

imranalig_khan@yahoo.co.in


Published in:

"Notes on IFS", Volume 23, 2017, Number 5, pages 85—101

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PDF (296 Kb Kb, Info)

Abstract:

This paper proposes an extension of Tanaka and Asai approach to study Atanassov’s Ifuzzy linear programming problems where problem parameters are prescribed by Ifuzzy numbers. In literature, there are various indices based ranking function approaches for solving such Ifuzzy 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 nonlinear programming problem. A small numerical example is included as an illustration.

Keywords:

Ifuzzy set, Triangular Ifuzzy numbers, Ifuzzy mathematical programming, Ifuzzy parameters.

AMS Classification:

90C72

References:

 Aggarwal, A., Dubey, D., Chandra, S. & Mehra, A. (2012) Application of Atanassov’s Ifuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs, Fuzzy Information and Engineering, 4, 401–414.
 Aggarwal, A., Chandra, S. & Mehra, A. (2014) Solving Matrix Games with Ifuzzy Payoffs: Paretooptimal Security Strategies Approach approach, Fuzzy Information and Engineering, 6, 167–192.
 Aliev, R. A., Huseynov, O. H. & Serdaroglu, R. (2016) Ranking of Znumbers and its applications in decision making, Internatioanl Journal of Information Technology and Decision Making, 15, 1503–1519.
 Angelov, P. P. (1997) Optimization in an intuitionistic fuzzy environment, Fuzzy Sets and Systems, 86, 299–306.
 Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
 Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg.
 Atanassov, K. T. (1989) More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33, 37–45.
 Atanassov, K. T. (1986) New operations defined over intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
 Bector, C. R. & Chandra, S. (2005) Fuzzy mathematical programming and fuzzy matrix games, Berlin, Springer.
 Bellman, R. E. & Zadeh, L. A. (1970) Decision making in fuzzy environment, Management Sciences, 17, 141–164.
 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.
 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.
 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.
 De, S. K., Biswas, R. & Roy, A. R. (2001) An application ofintuitionistic fuzzy sets in medical diagonsis, Fuzzy Sets and Systems, 117, 209–213.
 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.
 Dubois. D. & Prade, H. (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
 Dubey, D., Chandra, S. & Mehra, A. (2012) Fuzzy linear programming under interval uncertainity based on IFS representation, Fuzzy Sets and Systems, 188, 68–87.
 Dubey, D. & Mehra, A. (2011) Fuzzy linear programming with triangular intuitionistic fuzzy numbers, Advances in Intelligent System Research, EUSFLATLFA, 563–569.
 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.
 Hurwicz, L. (1952) A criterion for DecisionMaking Under Uncertainity, Technical Report 355, Cowels Commission.
 Gasimov, Rafail, N. & Yenilmez, K¨urs¸at. (2002) Solving Fuzzy Linear Programming Problems with Linear Membership Functions, Turk J Math, 26, 375–396.
 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.
 Nehi, H. M. (2010) A new ranking method for intutionistic fuzzy numbers, International Journal of Fuzzy Systems, 12, 80–86.
 Szmidt, E. & Kacprzyk, J. (1996) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on Intuitionistic Fuzzy Sets, 2, 2–31.
 Tanaka, H. & Asai, K. (1984) Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13, 1–10.
 Vlachos, I. K. & Sergiadis, G. D. (2007) Intuitionistic fuzzy informationapplications to pattern recognition, Pattern Recognition Letter, 28, 197–206.
 Wu, H. C. (2003) Duality theorems in fuzzy mathematical programming problemd based on the concept of ncesssity, Fuzzy Sets and Systems, 139, 363–377.
 Yager, R. (1981) A procedure for ordering fuzzy numbers of the unit interval, Information Sciences, 24, 143–161.
 Zimmermann, H. J. (1978) Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45–55.

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