bilevel programming

Defender-attacker game is a model for conflicting between a defender and an attacker. Defender tries to prevent attacking an opponent by assigning limited security resources. In real world the utility values of the defender-attacker game are assigned by experts which usually are uncertain. According to that the assigned values by several experts may be slightly different and conflicting, we consider a set of all their viewpoints. This approach is similar to hesitant fuzzy environment. Also, each of the experts may have the different weights; AHP method is used to determine the weights of each of the experts. A weighted sum method is applied to obtain a game with aggregated payoffs. An expected value of the fuzzy numbers is introduced to convert the problem into defender-attacker game with interval payoffs. According to this, we proposed a method to solve security game in fuzzy environment. It is shown that the optimal solution of the expected value model is the optimal solution of the original model. Finally, a practical example is illustrated to solve by the proposed method.

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

This paper presents a Taylor series approach for solving linear fractional de- centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with a single decision maker at the upper level and multiple decision makers at the lower level. In the proposed approach, the membership functions associated with each objective(s) of the level(s) of LFDBL-MODM are transformed by using a Taylor series and then they are unified. On using the Kuhn-Tucker conditions, the problem is finally reduced to a single objective. Numerical example is given in order to illustrate the efficiency and superiority of the proposed approach.

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose the initial probleminto two subproblems to names RMP and SP. The lower and upper bound providedfrom the RMP and SP are updated in each iteration. The algorithm converges whenthe dierence between the upper and lower bound is less than an arbitrary tolerance.Finally, we give some numerical examples are presented in order to show the eciencyof algorithm.

Bilevel linear programming is a decision making problem with a two-level decentralized organization. The textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. Making a decision at one level affects that at the other one. In this paper, bilevel linear programming with inexact parameters has been studied and a method is proposed to solve a fuzzy bilevel linear programming using interval bilevel linear programming.