A number of decision making problems consist in selecting and ranking alternatives (projects, candidates, policies, etc.) that are characterized by multiple attributes in order to satisfy multiple objectives. Furthermore, this process generally necessitate coping with many stakeholders opinion regarding the importance to assign to each attribute and/or each objective. Given an objective, there will be attributes that act in the sens of realization of this objective (supporting attributes), those working against the achievement of this objective (rejecting attributes) and finally some attributes may be neutral regarding the achievement of this objective. Building on such distinction of attributes, we propose in this paper an approach, based on satisficing game theory, that firstly determine satisficing alternatives, those alternatives for which the selectability measure (determined based on supporting attributes and stakeholders preferences) exeeds the rejectability mesaure (computed from rejecting attributes and stakeholders preferences) and secondly assign priorities to those satisficing alternatives so that an overall selectability exeeds an overall rejectability. An interesting thing to be noticed about this approach compared to existing ones is that it allows non homogeneity of attributes (all the alternatives do not need be characterized by the same attributes).

This paper first discusses the structure of abstract smoothing splines associated with bounded linear operators. The minimum-norm property and the representation of the operator smoothing spline are obtained by introducing a new inner product. Then the smoothing approximate solution with interpolating errors of operator equation T x=y is studied, and the error estimates are also given.

In this paper, we consider the approximate stabilization of a class of switched nonlinear system composed of a finite family of subsystems. We show that there exists a piecewise constant feedback controller such that the system can achieve the approximate stabilization property under arbitrary switching signal. We also discuss the numerical computation problem in determining the control input value at the sampling instant or switching instant and present a method to solve the problem.

This paper presents modified projective synchronization of two different hyperchaotic systems using active and adaptive control method. The proposed technique is applied to achieve chaos modified projective synchronization for hyperchaotic LÜ system and hyperchaotic Rössler system. Numerical simulations results are presented to demonstrate the effectiveness of the method.

In this paper, we prove that under some conditions, A two-dimension vectorial Sturm-Liouville Problem can only have finitely many eigenvalues of multiplicity two. Using this result, we imply that the spectral of two Sturm-Liouville Problem of dimension one , or two string equation, have finitely many ,such that the eigenvalues of the elements in common. And then we find a bound