Calculation of pessimistic, optimistic and intermediate strategies in the analysis of a Stackelberg competition under conditions of uncertainty

In this paper ‎a bi-level game problem with L-R fuzzy coefficients is studied‎. ‎Using the concept of alpha-cut‎, ‎this problem is converted to a bi-level problem with nonfuzzy coefficients‎. ‎Three kinds of optimistic‎, ‎pessimistic and intermediate ‎solution‎ are introduced for the problem‎, ‎by considering the status of decision makers‎, ‎and in each case‎, ‎the bi-level problem is converted to a single-level problem using the Karush–Kuhn–Tucker optimality conditions‎. ‎Finally‎, ‎an interactive algorithm is proposed that obtains the appropriate solution for the decision maker‎. ‎At the end of the paper‎, ‎an economic example and a case study for the production of polyethylene bags are presented and solved by the proposed algorithm.