Title: Analysing interval and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy programming

Authors: Sumit Kumar Maiti; Sankar Kumar Roy

Addresses: School of Applied Sciences and Humanities, Haldia Institute of Technology, Purba Midnapore – 721 157, WB, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore – 721 102, WB, India

Abstract: The aim of this paper is to provide a computational algorithm for solving interval-valued and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy approach. It also includes the cost parameters of upper and lower-level objective functions corresponding to interval numbers and multi-choice types while the parameters of constraints are intuitionistic fuzzy numbers. The interval-valued and multi-choice types objective functions are converted into deterministic form using interval programming and a general transformation technique respectively. Again, the intuitionistic fuzzy parameters of constraints are reduced to an interval by taking expected value of intuitionistic fuzzy number. A conflicting nature between the objective functions is resolved with the help of intuitionistic fuzzy programming by considering nonlinear degree of membership and non-membership functions respectively. The resultant max-min problem is solved with LINGO 15.0 iterative scheme. The developed algorithm is illustrated by an application example and Pareto optimality test is performed as well. The conclusions and an outlook of future study are described at last.

Keywords: bi-level programming; interval programming; multi-choice programming; intuitionistic fuzzy programming; Pareto-optimal.

DOI: 10.1504/IJMOR.2020.106919

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.3, pp.354 - 375

Received: 05 Jul 2018
Accepted: 25 Dec 2018
Published online: 27 Apr 2020 *

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