Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bellman–Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (X,M models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called X,R models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example.     

On the solutions of the equation AXB = C under Toeplitz‐like and Hankel matrices constraint

In this paper, we are mainly concerned with 2 types of constrained matrix equation problems of the form AXB=C, the least squares problem and the optimal approximation problem, and we consider several constraint matrices, such as general Toeplitz matrices, upper triangular Toeplitz matrices, lower triangular Toeplitz matrices, symmetric Toeplitz matrices, and Hankel matrices. In the first problem, owing to the special structure of the constraint matrix , we construct special algorithms; necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions. In the second problem, we use von Neumann alternating projection algorithm to obtain the solutions of problem. Then we give 2 numerical examples to demonstrate the effectiveness of the algorithms.     

Random approximations and random fixed point theorems for random 1-setn-contractive non-self-maps in abstract cones

In this paper, we will prove that the random version of Fan's Theorem [6, Theorem 2] is true for a random hemicompact 1-set-contractive map defined on a closed ball, a sphere and an annulus in cones. This class of random 1-set-contractive map includes random condensing maps, random continuous semicontractive maps, random LANE maps, random nonexpansive maps and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations, improvements or stochastic versions of the recent results obtained by many authors     

利用凸优化进行多用户OFDM通信系统的简化设计

以有限发射功率、迫零均衡为限定条件,利用现代凸优化理论和算法进一步进行多用户通信系统收发器的简化设计。将半正定规划模型等效转化为二阶锥规划模型。二阶锥规划模型将更加简单而且计算复杂度获得很大的改善。借助优化软件SeDuMi的计算机仿真表明:设计的收发器比现存收发     

The Bootstrap Methodology in Statistics of Extremes—Choice of the Optimal Sample Fraction

The main objective of statistics of extremes is the prediction of rare events, and its primary problem has been the estimation of the tail index , usually performed on the basis of the largest k order statistics in the sample or on the excesses over a high level u. The question that has been often addressed in practical applications of extreme value theory is the choice of either k or u, and an adaptive estimation of . We shall be here mainly interested in the use of the bootstrap methodology to estimate adaptively, and although the methods provided may be applied, with adequate modifications, to the general domain of attraction of G, , we shall here illustrate the methods for heavy right tails, i.e. for > 0. Special relevance will be given to the use of an auxiliary statistic that is merely the difference of two estimators with the same functional form as the estimator under study, computed at two different levels. We shall also compare, through Monte Carlo simulation, these bootstrap methodologies with other data-driven choices of the optimal sample fraction available in the literature.     

Neighborhood Turnpike Theorem for Continuous-Time Optimization Models

A neighborhood turnpike theorem is proved for continuous-time, infinite-horizon optimization models with positive discounting. Our approach is a primal one and no differentiability assumption is made. The basic hypothesis is a condition of uniform concavity at the point defining the undiscounted steady state. The main novelty here is that we formulate the theorem by taking the undiscounted steady state as the turnpike.     

Effect of substituents and protonation on the mechanism of 1,3-dipolar retro-cycloaddition reaction of pyrrolidino[60]- and [70]fullerenes

The mass spectra of new substituted pyrrolidino[60]- and [70]fullerenes have been obtained using electrospray ionization conditions in the positive and negative mode of detection with two different mass spectrometers, a quadrupole ion trap and a Fourier transform ion cyclotron resonance. Radical anions M(●-) and deprotonated molecules [M-H](-) are formed under negative electrospray ionization mass spectrometry conditions, and the collision-induced dissociations of both ionic species have been studied. Either negative odd-electron ions or negative even-electron ions undergo a retro-cycloaddition process forming the corresponding fullerene product ions C(60)(●-) and C(70)(●-). The generation of fullerene radical anions from deprotonated molecules is a new exception of the "even-electron rule." In contrast, the protonated molecules [M + H](+) obtained from the positive mode of detection do not undergo this cycloreversion reaction, and the MS(n) experiment reveals a variety of eliminations of neutral molecules involving different hydrogen shifts and multiple bond cleavages that lead eventually to substituted methanofullerene fragment ions. The observed fragmentations can be correlated with the electronic character of the substituents attached to the heterocyclic moiety. The results obtained from the thermal reactions of these compounds, carried out under different pH conditions, correlate well with those obtained in gas phase. The different behaviors between protonated and unprotonated molecules and ions can be explained assuming that the retro-cycloaddition reaction takes place only when the nitrogen atom of the pyrrolidine ring (the basic center of the molecule) is unprotonated both in gas and condensed phase. The protonation of the NH group inhibits the cycloreversion process, and therefore different fragmentations take place. The detailed mechanisms of the formation and evolution of the intermediate fragments are described.