专家系统中证据的合成,传播与修正

在专家系统中，由于证据的不确定性和推理规则的不确定性，推理也相应地发生变化，需要对证据进行合成、传播与修正。有许多文献进行了研究［２］，［３］，［４］，但已有的方法大都是针对不同的不确定性推理给出不同的方法。“本文旨在给出不确定性推理中证据合成、传播与修正的一般公式。     

Discounted combination of unreliable evidence using degree of disagreement

When Dempster’s rule is used to implement a combination of evidence, all sources are considered equally reliable. However, in many real applications, all the sources of evidence may not have the same reliability. To resolve this problem, a number of methods for discounting unreliable sources of evidence have been proposed in which the estimation of the discounting (weighting) factors is crucial, especially when prior knowledge is unavailable. In this paper, we propose a new degree of disagreement through which discounting factors can be generated for discounting combinations of unreliable evidence. The new degree of disagreement is established using distance of evidence. It can be experimentally verified that our degree of disagreement describes the disagreements or differences among bodies of evidence well and that it can be effectively used in discounting combinations of unreliable evidence.     

Building a binary outranking relation in uncertain, imprecise and multi-experts contexts: The application of evidence theory

We consider multicriteria decision problems where the actions are evaluated on a set of ordinal criteria. The evaluation of each alternative with respect to each criterion may be uncertain and/or imprecise and is provided by one or several experts. We model this evaluation as a basic belief assignment (BBA). In order to compare the different pairs of alternatives according to each criterion, the concept of first belief dominance is proposed. Additionally, criteria weights are also expressed by means of a BBA. A model inspired by ELECTRE I is developed and illustrated by a pedagogical example.     

Evidential calibration of binary SVM classifiers

In machine learning problems, the availability of several classifiers trained on different data or features makes the combination of pattern classifiers of great interest. To combine distinct sources of information, it is necessary to represent the outputs of classifiers in a common space via a transformation called calibration. The most classical way is to use class membership probabilities. However, using a single probability measure may be insufficient to model the uncertainty induced by the calibration step, especially in the case of few training data. In this paper, we extend classical probabilistic calibration methods to the evidential framework. Experimental results from the calibration of SVM classifiers show the interest of using belief functions in classification problems.     

The fifty percent rule revisited

Combinatorial reasoning is applied to the analysis of two kinds of dynamic storage allocation system to derive results about the degree and characteristics of memory fragmentation. The simple first-fit scheme with immediate replacement, discussed by Knuth, is analyzed further, providinginter alia a new derivation of the fifty percent rule. Next a system with garbage collections is considered, and the mean and variance of the number of holes following a garbage collection are determined, along with other results. The cell distributions resulting from these two idealized policies are contrasted.This research was supported in part by the National Science and Engineering Research Council of Canada under an operating grant.     

The capacity of majority rule

Let 𝔹ⁿ={−1, 1}ⁿ denote the vertices of the n-dimensional cube. Let U(m) be a random m-element subset of 𝔹ⁿ and suppose w ∈𝔹ⁿ is a vertex closest to the centroid of U(m). Using a large deviation, multivariate local limit theorem due to Richter, we show that n/π log n is a threshold function for the property that the convex hull of U(m) is contained in the positive half-space determined by w . The decision problem considered here is an instance of binary integer programming, and the algorithm selecting w as the vertex closest to the centroid of U(m) has been previously dubbed majority rule in the context of learning binary weights for a perceptron. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 83–109, 1998     

The lagrange multiplier rule for multi-dimensional problems of optimal control

In this paper a modified form of Pontryagin's maximum principle is developed, which also holds for problems of optimal control with respect to functions of several independent variables.     

Belief functions combination without the assumption of independence of the information sources

This paper considers the problem of combining belief functions obtained from not necessarily independent sources of information. It introduces two combination rules for the situation in which no assumption is made about the dependence of the information sources. These two rules are based on cautious combinations of plausibility and commonality functions, respectively. The paper studies the properties of these rules and their connection with Dempster’s rules of conditioning and combination and the minimum rule of possibility theory.     

群逆的仿射组合表示

In this paper, we first give two equalities in the operation of determinant. Using the expression of group inverse with full-rank factorization Ag = F（GF）^-2G and the Cramer rule of the nonsingular linear system Ax = b, we present a new method to prove the representation of group inverse with arlene combination
Ag=∑（I,J）∈N（A） 1/υ^2det（A）IJ ajd AJI.
A numerical example is given to demonstrate that the formula is efficient.     

Prediction of future observations using belief functions: A likelihood-based approach

We study a new approach to statistical prediction in the Dempster–Shafer framework. Given a parametric model, the random variable to be predicted is expressed as a function of the parameter and a pivotal random variable. A consonant belief function in the parameter space is constructed from the likelihood function, and combined with the pivotal distribution to yield a predictive belief function that quantifies the uncertainty about the future data. The method boils down to Bayesian prediction when a probabilistic prior is available. The asymptotic consistency of the method is established in the iid case, under some assumptions. The predictive belief function can be approximated to any desired accuracy using Monte Carlo simulation and nonlinear optimization. As an illustration, the method is applied to multiple linear regression.     

The modular branching rule for affine Hecke algebras of type A

For the affine Hecke algebra of type A at roots of unity, we make explicit the correspondence between geometrically constructed simple modules and combinatorially constructed simple modules and prove the modular branching rule. The latter generalizes work by Vazirani (2002) [22].     

Birmbaum信息与多个测验分数的最佳组合法

本文用现代教育、心理测量的ＩＲＴ（项目反应理论）中的Ｂｉｒｍｂａｕｍ信息函数，对经典教育、心理测量（ＣＴＴ）中的真实分数模型Ｘ＝Ｔ＋ｅ给出了一种多个测量分数的最佳组合法。该组合获得最大信息，并突破了ＩＲＴ和ＣＴＴ的局限性。     

Exploring the VCG mechanism in combinatorial auctions: The threshold revenue and the threshold-price rule

We explore interesting potential extensions of the Vickrey–Clarke–Groves (VCG) rule under the assumption of players with independent and private valuations and no budget constraints. First, we apply the VCG rule to a coalition of bidders in order to compute the second price of the coalition. Then, we introduce and formulate the problem of determining that partition of players into coalitions which maximize the auctioneer’s revenue in the case whereby such coalitions take part to a VCG auction each one as a single agent; in particular, we provide an integer linear formulation of this problem. We also generalize this issue by allowing players to simultaneously belong to distinct coalitions in the case that players’ valuation functions are separable. Finally, we propose some applications of these theoretical results. For instance, we exploit them to provide a class of new payment rules and to decide which bids should be defined as the highest losing ones in combinatorial auctions.     

Medical diagnosis: Fuzzy sets and degrees of belief

A model simulating the medical diagnostic process is presented. Diagnostic groups are considered as fuzzy sets. Partial knowledge is quantified by belief functions. The process is considered as the evaluation by the clinician of his degree of belief concerning the belonging of his patient to a fuzzy set given fuzzy and partial informations.     

The duality property of the Discrete Fourier Transform based on Simpson's rule

The classical Discrete Fourier Transform (DFT) satisfies a duality property that transforms a discrete time signal to the frequency domain and back to the original domain. In doing so, the original signal is reversed to within a multiplicative factor, namely the dimension of the transformation matrix. In this paper, we prove that the DFT based on Simpson's method satisfies a similar property and illustrate its effect on a real discrete signal. The duality property is particularly useful in determining the components of the transformation matrix as well as components of its positive integral powers. Copyright © 2012 John Wiley & Sons, Ltd.     

Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians

We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenvalues of the uncoupled system disappear and establish a limiting absorption principle above this level of energy. We rely on a positive commutator approach introduced by Skibsted and pursued by Georgescu-Gérard-Møller. We complete some results obtained so far by Dereziński-Jakši? on one side and by Bach-Fröhlich-Sigal-Soffer on the other side.     

Stefenssen''s inequality and estimates of error in trapezoidal rule

In this paper, a sharp estimate for a slight modification of the classical trapezoidal rule is obtained by using Stefenssen's inequality.     

The reduction and fusion of fuzzy covering systems based on the evidence theory

This paper studies reduction of a fuzzy covering and fusion of multi-fuzzy covering systems based on the evidence theory and rough set theory. A novel pair of belief and plausibility functions is defined by employing a method of non-classical probability model and the approximation operators of a fuzzy covering. Then we study the reduction of a fuzzy covering based on the functions we presented. In the case of multiple information sources, we present a method of information fusion for multi-fuzzy covering systems, by which objects can be well classified in a fuzzy covering decision system. Finally, by using the method of maximum flow, we discuss under what conditions, fuzzy covering approximation operators can be induced by a fuzzy belief structure.