Improving Euclidean’s Consensus Degrees in Group Decision Making Problems Through a Uniform Extension

In a Group Decision Making problem, several people try to reach a single common decision by selecting one of the possible alternatives according to their respective preferences. So, a consensus process is performed in order to increase the level of accord amongst people, called experts, before obtaining the final solution. Improving the consensus degree as much as possible is a very interesting task in the process. In the evaluation of the consensus degree, the measurement of the distance representing disagreement among the experts’ preferences should be considered. Different distance functions have been proposed to implement in consensus models. The Euclidean distance function is one of the most commonly used. This paper analyzes how to improve the consensus degrees, obtained through the Euclidean distance function, when the preferences of the experts are slightly modified by using one of the properties of the Uniform distribution. We fulfil an experimental study that shows the betterment in the consensus degrees when the Uniform extension is applied, taking into account different number of experts and alternatives.

The chain of embedded invariant submodels for conic motions

The equations of continuum mechanics are invariant in relation to the Galilean group generalized by extention. Its 11-dimensional Lie algebra has many subalgebras, which form the optimal system of dissimilar subalgebras. Subalgebras from the optimal system form the graph of embedded subalgebras. There are many chains of subalgebras in the graph. We consider the chain of embedded subalgebras containing operators of space and time translation, the rotation and uniform extension of all independent variables for the models of the continuous medium mechanics. We choose concordant invariants for each subalgebra from the chain. The chain of invariant submodels is constructed in a cylindrical coordinates based on chosen invariants. It is proved that solutions of a submodel constructed on a subalgebra of higher dimension will be part of solutions of submodels constructed on subalgebra of smaller dimensions for the considered chain. Thus, the chain of embedded invariant submodels is constructed by the example of equations of ideal gas dynamics.

Субструктура интерметаллического соединения Cu-=SUB=-3-=/SUB=-Sn в тонкопленочном состоянии

The crystalline structure of intermetallic Cu_3Sn synthesized by successively condensing thin layers of copper and tin on a substrate at 150°C has been studied. Cu_3Sn compound exists in a very narrow homogeneity range and has a long-period close-packed ordered D0_19 superstructure. It has been found that the crystal lattice exhibits many slip traces associated with dislocation motion. The dislocation motion is due to the stressed state of the crystal, which can be characterized as uniform extension. Electron micrographs show that slip traces in the Cu_3Sn crystal are parallel to the ( $$\bar {1}\bar {1}21$$ ) and ( $$11\bar {2}1$$ ) planes belonging to pyramidal slip system II, which is a main slip system along with pyramidal and basal ones. Slip traces result from the motion of partial dislocations, as indicated by the amount of slip, which is equal to half the interplanar distance. Since the crystal is ordered, slip is accomplished by a pair of superpartial dislocations and a slip trace may be a superstructural or complex stacking fault.

Exact Analysis of Stress Fields in Composite Laminates under Extension

Exact analysis of displacements and stresses in 2-D orthotopic laminates under extension is conducted. On the basis of the Hamiltonian state space approach and the transfer matrix method, a complete solution, in the context of generalized strain, which exactly satisfies the state space equation, the traction-free BC on the top and bottom surfaces of the rectangular section, the interfacial continuity conditions in multi-layered laminates, and the end conditions on free edges, is obtained by combing the eigensolutions and the particular solution. Evaluating of the stresses in the boundary layer for verification shows that the stress decay in laminates under uniform extension may be slow and the edge effects may be pronounced.