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

  • Sumit Kumar Maiti
  • Sankar Kumar RoyEmail author


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.


Bi-level programming Triangular intuitionistic fuzzy number Ranking function Nonlinear programming Optimal solution 

Mathematics Subject Classification

90C05 90C70 90C30 



The authors are very much thankful to the Associate Editor, Prof. Dong-Lei Du and the anonymous reviewers for their valuable comments to increase the novelty and overall quality of the paper.


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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Applied Sciences and HumanitiesHaldia Institute of TechnologyPurba MidnaporeIndia
  2. 2.Department of Applied Mathematics with Oceanology and ComputerProgramming, Vidyasagar UniversityMidnaporeIndia

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