Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

doi:10.1007/s40305-018-0234-2

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (1): 131-149.doi: 10.1007/s40305-018-0234-2

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Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

Sumit Kumar Maiti¹, Sankar Kumar Roy²

1 School of Applied Sciences and Humanities, Haldia Institute of Technology, Purba Midnapore, WB 721 657, India;
2 Department of Applied Mathematics with Oceanology and Computer, Programming, Vidyasagar University, Midnapore, WB 721 102, India

Received:2018-03-23 Revised:2018-10-10 Online:2021-03-11 Published:2021-03-11
Contact: Sankar Kumar Roy, Sumit Kumar Maiti E-mail:sankroy2006@gmail.com;sumitmaiti123@gmail.com

Abstract

Abstract: This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy parameters. Intuitionistic fuzzy number is considered in many real-life situations, so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy numbers. In this paper, intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number. A defuzzification method is introduced based on the proportional probability density function associated with the corresponding membership function, as well as the complement of non-membership function. Using the proposed ranking technique, a methodology is presented for solving bi-level programming for Stackelberg game. An application example is provided to demonstrate the applicability of the proposed methodology, and the achieved results are compared with the existing methods.

Key words: Bi-level programming, Triangular intuitionistic fuzzy number, Ranking function, Nonlinear programming, Optimal solution

CLC Number:

Sumit Kumar Maiti, Sankar Kumar Roy. Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach[J]. Journal of the Operations Research Society of China, 2021, 9(1): 131-149.

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References

[1] Von, H.:The Theory of the Market Economic. Oxford University Press, New York (1952)
[2] Kiyota, S., Aiyishi, E.:A new computational method for Stackelberg and min-max problem use of a penalty method. IEEE Trans. Autom. Control 26(2), 460-466(1981)
[3] Maiti, S.K., Roy, S.K.:Multi-choice stochastic bi-level programming problem in co-operative nature via fuzzy programming approach. J. Ind. Eng. Int. 12(3), 287-298(2016)
[4] Roy, S.K., Maiti, S.K.:Stochastic bi level programming with multi-choice for Stackelberg game via fuzzy programming. Int. J. Oper. Res. 29(4), 508-530(2017)
[5] Zhang, G., Lu, J., Dillon, T.:Decentralized multi-objective bi-level decision making with fuzzy demand. Knowl. Based Syst. 20(5), 495-507(2007)
[6] Lachhwani, K., Poonia, M.P.:Mathematical solution of multi-level fractional programming problem with fuzzy goal programming approach. J. Ind. Eng. Int. 8(16), 1-11(2012)
[7] Shih, H.S., Lee, E.S.:Compensatory fuzzy multiple level decision making. Fuzzy Sets Syst. 114(1), 71-87(2000)
[8] Sinha, S.:Fuzzy programming approach to multi-level programming problems. Fuzzy Sets Syst. 136(2), 189-202(2003)
[9] Roy, S.K.:Fuzzy programming techniques for Stackelberg game. Tamsui Oxford J. Manag. Sci. 22(3), 43-56(2006)
[10] Mahapatra, D.R., Roy, S.K., Biswal, M.P.:Multi-choice stochastic transportation problem involving extreme value distribution. Appl. Math. Model. 37(4), 2230-2240(2013)
[11] Roy, S.K.:Multi-choice stochastic transportation problem involving Weibull distribution. Int. J. Oper. Res. 21(1), 38-58(2014)
[12] Maity, G., Roy, S.K.:Solving a multi-objective transportation problem with non-linear cost and multichoice demand. Int. J. Manag. Sci. Eng. Manag. 11(1), 62-70(2015)
[13] Roy, S.K.:Transportation problem with multi-choice cost and demand and stochastic supply. J. Oper. Res. Soc. China 4(2), 193-204(2016)
[14] Roy, S.K., Maity, G., Weber, G.W., Gök, S.Z.A.:Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Ann. Oper. Res. 253(1), 599-620(2017)
[15] Roy, S.K.:Lagrange's interpolation polynomial approach to solve multi-choice transportation problem. Int. J. Appl. Comput. Math. 1(4), 639-649(2015)
[16] Sakawa, M., Nishizaki, I., Uemura, Y.:Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. Fuzzy Sets Syst. 109(1), 03-19(2000)
[17] Atanassov, K.T.:Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87-96(1986)
[18] Bhaumik, A., Roy, S.K., Li, D.F.:Analysis of triangular intuitionistic fuzzy matrix games using robust ranking. J. Intell. Fuzzy Syst. 33(1), 327-336(2017)
[19] Li,D.F.:Multiattributedecisionmakingmodelsandmethodsusingintuitionisticfuzzysets.J.Comput. Syst. Sci. 70(1), 73-85(2005)
[20] Roy, S.K., Ebrahimnejad, A., Verdegay, J.L., Das, S.:New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana 43(1), 3(2018)
[21] Hassan, M.N.:A new ranking method for intuitionistic fuzzy numbers. Int. J. Fuzzy Syst. 12(1), 80-86(2010)
[22] Parvathi, R., Malathi, C.:Intuitionistic fuzzy linear optimization. Notes Intuit. Fuzzy Set 18(1), 48-56(2012)
[23] Varghese, A., Kuriakose, S.:Centroid of an intuitionistic fuzzy number. Notes Intuit. Fuzzy Sets 18(1), 19-24(2012)
[24] Wan, S.P., Wang, Q.Y., Dong, J.Y.:The extended VIKOR method for multiattribute group decision making with triangular intuitionistic fuzzy numbers. Knowl. Based Syst. 52(3), 65-77(2013)
[25] Debnath, L.:Integral Transforms and Their Applications. CRC Press, New York (1965)
[26] Zadeh, L.A.:Fuzzy sets. Inf. Control 8(2), 338-353(1965)
[27] Mitchel, H.B.:Ranking intuitionistic fuzzy numbers. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 12(3), 377-386(2004)
[28] Nishad, A.K., Singh, S.R.:Linear programming problem with intuitionistic fuzzy number. Int. J. Comput. Appl. 106(8), 22-28(2014)

Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

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