基于相似度和改进雷达图的概率犹豫模糊多属性决策方法

为了解决属性权重未知的概率犹豫模糊多属性决策问题,构建基于相似度和改进雷达图的多属性决策方法。首先基于概率犹豫模糊元的信息完全度构建概率犹豫模糊集的距离测度和灰色关联系数,然后基于灰色关联理想解法定义了概率犹豫模糊集的相似度,最后根据概率犹豫模糊集的相似度和改进雷达图构建多属性决策模型,并通过案例进行了验证分析。     

基于概率语言术语集的服务外包风险评估方法

考虑服务外包风险评估的不确定性,采用概率语言术语集获取FMEA方法所需的专家评价信息,通过给语言集赋予不同的概率以表达偏好的程度。针对传统FMEA方法没有考虑风险间的相互影响关系,风险严重度评估不够准确的问题,采用广义Choquet积分分析风险间的相互影响关系,得到修正后的风险严重度。考虑严重度、发生度和难检度直接相乘准确性低的问题,采用概率语言VIKOR方法对风险的三个因子进行综合评估。最后以公共体育场馆服务外包风险评估为例,验证了所提方法的有效性。     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

Theory of the dynamics of the Hopfield model of associative memory

We present an analysis of the parallel dynamics of the Hopfield model of the associative memory of a neural network without recourse to the replica formalism. A probabilistic method based on the signal-to-noise ratio is employed to obtain a simple recursion relation for the zero temperature as well as the finite temperature dynamics of the network. The fixed points of the recursion relation and their basins of attraction are found to be in fairly satisfactory agreement with the numerical simulations of the model. We also present some new numerical results which support our recursion relation and throw light on the nature of the ensemble of the network states which are optimized with respect to single spin flips.     

How many maxima can there be?

Let C be a planar region. Choose n points p₁,,p_nI.I.D. from the uniform distribution over C. Let M^C_n be the number of these points that are maximal. If C is convex it is known that either E(M^C_n)=Θ(√n)> or E(M^C_n)=O(log n). In this paper we will show that, for general C, there is very little that can be said, a-priori, about E(M^C_n). More specifically we will show that if g is a member of a large class of functions then there is always a region C such that E(M^C_n)=Θ(g(n)). This class contains, for example, all monotically increasing functions of the form g(n)= nln^βn, where 0<<1 and β0. This class also contains nondecreasing functions like g(n)=ln^*n. The results in this paper remain valid in higher dimensions.     

On the parallel dynamics of theQ-state Potts andQ-Ising neural networks

Using a probabilistic approach, the parallel dynamics of theQ-state Potts andQ-Ising neural networks are studied at zero and at nonzero temperatures. Evolution equations are derived for the first time step and arbitraryQ. These formulas constitute recursion relations for the exact parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis, including dynamical capacity-temperature diagrams and the temperature dependence of the overlap, is carried out forQ=3. Both types of models are compared.On leave of absence from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia.     

Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements, and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.     

Asymmetric Binary Covering Codes

An asymmetric binary covering code of length n and radius R is a subset of the n-cube Q_n such that every vector xQ_n can be obtained from some vector c by changing at most R 1's of c to 0's, where R is as small as possible. K⁺(n,R) is defined as the smallest size of such a code. We show K⁺(n,R)Θ(2ⁿ/n^R) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K⁺(n,n− )= +1 for constant coradius iff n ( +1)/2. These two results are extended to near-constant R and , respectively. Various bounds on K⁺ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n,R]⁺-code) is determined to be min{0,n−R}. We conclude by discussing open problems and techniques to compute explicit values for K⁺, giving a table of best-known bounds.     

Exponential convergence of Toom's probabilistic cellular automata

We obtain cluster expansions for small random perturbations of deterministic Toom's automata in the one-dimensional case. Exponential convergence follows. Analyticity of invariant measures is examined as well as the simplest multidimensional case.