implicit and unobserved errors and vulnerabilities issues usually arise in cryptographic protocols and especially in authentication protocols. this may enable an attacker to make serious damages to the desired system, such as having the access to or changing secret documents, interfering in bank transactions, having access to users’ accounts, or may be having the control all over the syste...

abstract this thesis includes five chapter : the first chapter assign to establish fuzzy mathematics requirement and introduction of liner programming in thesis. the second chapter we introduce a multilevel linear programming problems. the third chapter we proposed interactive fuzzy programming which consists of two phases , the study termination conditions of algorithm we show a satisfac...

abstract: in this thesis, we focus to class of convex optimization problem whose objective function is given as a linear function and a convex function of a linear transformation of the decision variables and whose feasible region is a polytope. we show that there exists an optimal solution to this class of problems on a face of the constraint polytope of feasible region. based on this, we dev...