dissimilarity metric learning in the belief function framework the evidential k nearest neighbor ek nn method provided a global treatment of imperfect knowledge regarding the class membership of training patterns it has outperformed traditional k nn rules in many applications but still shares some of their basic limitations e g 1 classification accuracy depends heavily on how to quantify the dissimilarity between different patterns and 2 no guarantee for satisfactory performance when training patterns contain unreliable imprecise and or uncertain input features in this paper we propose to address these issues by learning a suitable metric using a low dimensional transformation of the input space so as to maximize both the accuracy and efficiency of the ek nn classification to this end a novel loss function to learn the dissimilarity metric is constructed it consists of two terms the first one quantifies the imprecision regarding the class membership of each training pattern while by means of feature selection the second one controls the influence of unreliable input features on the output linear transformation the proposed method has been compared with some other metric learning methods on several synthetic and real datasets it consistently led to comparable performance with regard to testing accuracy and class structure visualization

different complex zfs leading to different complex znn models for time varying complex generalized inverse matrices as a special class of recurrent neural network zhang neural network znn has been recently proposed since 2001 for solving various time varying problems and has shown high efficiency and excellent performance for solving the problems in the real domain in this paper to solve online the time varying complex generalized inverse in most cases the pseudoinverse problem in the complex domain a new type of complex valued znn is further proposed and investigated the design of such a complex znn is based on a complex zhang function zf which is indefinite and quite different from the usual error function specially the scalar valued energy function in the studies of conventional algorithms by introducing five different complex zfs five different complex znn models termed complex znn i znn ii znn iii znn iv and znn v models are proposed developed and investigated for the online solution of the time varying complex generalized inverse matrices theoretical results of convergence analysis are presented to show the desirable properties of complex znn models in addition we discover the link between the proposed complex znn models and the getz marsden dynamic system in the complex domain computer simulation results further demonstrate the effectiveness of complex znn models based on different complex zfs for the time varying complex generalized inverse matrices

a new efficient conjugate gradient method for unconstrained optimization we propose a nonlinear conjugate gradient method for unconstrained optimization based on solving a new optimization problem our optimization problem combines the good features of the linear conjugate gradient method using some penalty parameters we show that the new method is a subclass of dai liao family the fact that enables us to analyze the family closely as a consequence we obtain an optimal bound for dai liao parameter the global convergence of the new method is investigated under mild assumptions numerical results show that the new method is efficient and robust and outperforms cg descent

interpolation and extrapolation of strictly singular operators between l p spaces we study the interpolation and extrapolation properties of strictly singular operators between different lp spaces to this end the structure of strictly singular non compact operators between l p lq spaces is analyzed among other things we clarify the relation between strict singularity and the l characteristic set of an operator in particular krasnoselskii s interpolation theorem for compact operators is extended to the class of strictly singular operators c 2017 elsevier inc

credal classification rule for uncertain data based on belief functions abstract in this paper we present a new credal classification rule ccr based on belief functions to deal with the uncertain data ccr allows the objects to belong with different masses of belief not only to the specific classes but also to the sets of classes called meta classes which correspond to the disjunction of several specific classes each specific class is characterized by a class center i e prototype and consists of all the objects that are sufficiently close to the center the belief of the assignment of a given object to classify with a specific class is determined from the mahalanobis distance between the object and the center of the corresponding class the meta classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes the selection of meta classes depends on the application and the context and a measure of the degree of indistinguishability between classes is introduced in this new ccr approach the objects assigned to a meta class should be close to the center of this meta class having similar distances to all the involved specific classes centers and the objects too far from the others will be considered as outliers noise ccr provides robust credal classification results with a relatively low computational burden several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this ccr method with respect to other classification methods

analytic hierarchy process for multi sensor data fusion based on belief function theory abstract multi sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined the data derived from multiple sensors can however be uncertain imperfect and conflicting the present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection sensor readings represented by belief functions have to be fused according to their corresponding weights previous studies have often estimated the weights of sensor readings based on a single criterion mono criteria approaches for the assessment of sensor reading weights are however often unreliable and inadequate for the reflection of reality accordingly this work opts for the use of a multi criteria decision aid a modified analytical hierarchy process ahp that incorporates several criteria is proposed to determine the weights of a sensor reading set the approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency it assesses the weight of each sensor reading and fuses the weighed readings obtained using a modified average combination rule the efficiency of this approach is evaluated in a target recognition context several tests sensitivity analysis and comparisons with other approaches available in the literature are described

combining ambiguous evidence with respect to ambiguous a priori knowledge part ii fuzzy logic abstract this paper describes fuzzy conditioned dempster shafer fcds theory a probability based calculus for dealing with possibly imprecise and vague evidence when the underlying a priori knowledge base is itself possibly imprecise and vague fcds has the same general form as existing fuzzy dempster shafer theories fcds however employs a finite level zadeh fuzzy logic and a dempster shafer like combination operator which is conditioned to reflect the influence of any a priori knowledge base which can be modeled by a belief measure on finite level fuzzy sets we show that fcds is grounded in probability theory specifically in the theory of random fuzzy sets we also show that it is a generalization of bayesian theory to the case when both evidence and a priori knowledge are imprecise and vague we show that fcds is consistent with the lattice structure of zadeh s min max fuzzy logic and that in particular it possesses an analog of the familiar mobius transform

an euler newton continuation method for tracking solution trajectories of parametric variational inequalities a finite dimensional variational inequality parameterized by t in 0 1 is studied under the assumption that each point of the graph of its generally set valued solution mapping is a point of strongly regularity it is shown that there are finitely many lipschitz continuous functions on 0 1 whose graphs do not intersect each other such that for each value of the parameter the set of values of the solution mapping is the union of the values of these functions moreover the property of strong regularity is uniform with respect to the parameter along any such function graph an euler newton continuation method for tracking a solution trajectory is introduced and demonstrated to have l infty accuracy of order o h 4 thus generalizing a known error estimate for equations two examples of tracking economic equilibrium parametrically illustrate the theoretical results a correction is attached

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

presentation error analysis and numerical experiments on a group of 1 step ahead numerical differentiation formulas in order to achieve higher computational precision in approximating the first order derivative of the target point the 1 step ahead numerical differentiation formulas are presented these formulas greatly remedy some intrinsic weaknesses of the backward numerical differentiation formulas and overcome the limitation of the central numerical differentiation formulas in addition a group of formulas are proposed to obtain the optimal step length moreover the error analysis of the 1 step ahead numerical differentiation formulas and the backward numerical differentiation formulas is further investigated numerical studies show that the proposed optimal step length formulas are effective and the performance of the 1 step ahead numerical differentiation formulas is much better than that of the backward numerical differentiation formulas in the first order derivative approximation

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

the combination of evidence in the transferable belief model a description of the transferable belief model which is used to quantify degrees of belief based on belief functions is given the impact of open and closed world assumption on conditioning is discussed the nature of the frame of discernment on which a degree of belief will be established is discussed a set of axioms justifying dempster s rule for the combination of belief functions induced by two distinct evidences is presented

on interpolation of strictly co singular linear operators on montre que la propriete des operateurs lineaires d etre dans l enveloppe surjective de l ideal des operateurs strictement singuliers entre les espaces de banach est une propriete d interpolation par rapport a la methode d interpolation reelle avec les parametres 0 1 et 1 p

conditional belief functions as lower envelopes of conditional probabilities in a finite setting the aim is to provide a characterization of full conditional measures on a finite boolean algebra obtained as lower envelope of the extensions of a full conditional probability defined on another finite boolean algebra such conditional measures are conditional belief functions defined by means of a generalized bayesian conditioning rule relying on a linearly ordered class of belief functions this notion of bayesian conditioning for belief functions is compared with other well known conditioning rules by looking for those conditional measures that can be seen as lower conditional probabilities

a parametric nonconvex decomposition algorithm for real time and distributed nmpc a novel decomposition scheme to solve parametric nonconvex programs as they arise in nonlinear model predictive control nmpc is presented it consists of a fixed number of alternating proximal gradient steps and a dual update per time step hence the proposed approach is attractive in a real time distributed context assuming that the nonlinear program nlp is semi algebraic and that its critical points are strongly regular contraction of the sequence of primal dual iterates is proven implying stability of the sub optimality error under some mild assumptions moreover it is shown that the performance of the optimality tracking scheme can be enhanced via a continuation technique the efficacy of the proposed decomposition method is demonstrated by solving a centralized nmpc problem to control a dc motor and a distributed nmpc program for collaborative tracking of unicycles both within a real time framework furthermore an analysis of the sub optimality error as a function of the sampling period is proposed given a fixed computational power

d map distributed maximum a posteriori probability estimation of dynamic systems this paper develops a framework for the estimation of a time varying random signal using a distributed sensor network given a continuous time model sensors collect noisy observations and produce local estimates according to the discrete time equivalent system defined by the sampling period of observations estimation is performed using a maximum a posteriori probability estimator map within a given window of interest to mediate the incorporation of information from other sensors we introduce lagrange multipliers to penalize the disagreement between neighboring estimates we show that the resulting distributed d map algorithm is able to track dynamical signals with a small error this error is characterized in terms of problem constants and vanishes with the sampling time as long as the log likelihood function which is assumed to be log concave satisfies a smoothness condition we implement the d map algorithm for a linear and a nonlinear system model to show that the performance corroborates with theoretical findings

dynamic estimation of the discernment frame in belief function theory classification or estimation problems deal with decisions among different hypotheses in several applications the set of hypotheses may evolve with time and or with context then this work focuses on the problem of dynamic estimation and update of the discernment frame in the framework of belief function theory belief function theory is widely used in decision systems because of its ability to model both the imprecision and the uncertainty now the problem of the discernment frame estimation is even more critical as the set of handled hypotheses is the power set of the discernment frame this study describes a solution to update and adjust the discernment frame in a sequential way as new sources provide new pieces of information besides incompleteness it is assumed that the current discernment frame may contain duplicated or spurious hypotheses we thus propose new update mechanisms and we show on a practical application namely video surveillance how these mechanisms may be applied

inexact restoration method for nonlinear optimization without derivatives a derivative free optimization method is proposed for solving a general nonlinear programming problem it is assumed that the derivatives of the objective function and the constraints are not available the new method is based on the inexact restoration scheme where each iteration is decomposed in two phases in the first one the violation of the feasibility is reduced in the second one the objective function is minimized onto a linearization of the nonlinear constraints at both phases polynomial interpolation models are used in order to approximate the objective function and the constraints at the first phase a derivative free solver for box constrained optimization can be used for the second phase we propose a new method ad hoc based on trust region strategy that uses the projection of the simplex gradient on the tangent space under suitable assumptions the algorithm is well defined and convergence results are proved a numerical implementation is described and numerical experiments are presented to validate the theoretical results

lindley s paradox 1982 lindley s paradox journal of the american statistical association vol 77 no 378 pp 325 334

modeling vague beliefs using fuzzy valued belief structures abstract this paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory we adopt as a starting point the non probabilistic interpretation of belief functions provided by smets transferable belief model as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions we then introduce the concepts of interval valued and fuzzy valued belief structures defined respectively as crisp and fuzzy sets of belief structures verifying hard or elastic constraints we then proceed with a generalization of various concepts of dempster shafer theory including those of belief and plausibility functions combination rules and normalization procedures most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist making the whole scheme computationally tractable we discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data

conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization conjugate gradient methods have been paid attention to because they can be directly applied to large scale unconstrained optimization problems in order to incorporate second order information of the objective function into conjugate gradient methods dai and liao 2001 proposed a conjugate gradient method based on the secant condition however their method does not necessarily generate a descent search direction on the other hand hager and zhang 2005 proposed another conjugate gradient method which always generates a descent search direction in this paper combining dai liao s idea and hager zhang s idea we propose conjugate gradient methods based on secant conditions that generate descent search directions in addition we prove global convergence properties of the proposed methods finally preliminary numerical results are given

global optimization algorithm for mixed integer quadratically constrained quadratic program abstract mixed integer quadratic programs with quadratic constraints miqqp occur frequently in various areas of engineering practice and management science but most solution methods for this kind of problems are often designed for its special cases in this paper we present a simple global optimization algorithm for solving problem miqqp we first convert problem miqqp into an equivalent generalized bilinear programming problem with integer variables eiqqp we next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region finally by incorporating the reduction correction techniques and sampling strategies into the branch and bound scheme the proposed algorithm is developed for solving miqqp convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and minlplib2 are carried out to validate the performance of the proposed algorithm

log sigmoid nonlinear lagrange method for nonlinear optimization problems over second order cones this paper analyzes the rate of local convergence of the log sigmoid nonlinear lagrange method for nonconvex nonlinear second order cone programming under the componentwise strict complementarity condition the constraint nondegeneracy condition and the second order sufficient condition we show that the sequence of iteration points generated by the proposed method locally converges to a local solution when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter finally we report numerical results to show the efficiency of the method

shape from silhouette using dempster shafer theory this work proposes a novel shape from silhouette sfs algorithm using the dempster shafer ds theory for dealing with inconsistent silhouettes standard sfs methods makes assumptions about consistency in the silhouettes employed however total consistency hardly ever happens in realistic scenarios because of inaccuracies in the background subtraction or occlusions thus leading to poor reconstruction outside of controlled environments our method classify voxels using the ds theory instead of the traditional intersection of all visual cones sensors reliability is modelled taking into account the positional relationships between camera pairs and voxels this information is employed to determine the degree in which a voxel belongs to a foreground object finally evidences collected from all sensors are fused to choose the best hypothesis that determines the voxel state experiments performed with synthetic and real data show that our proposal outperforms the traditional sfs method and other techniques specifically designed to deal with inconsistencies in addition our method includes a parameter for adjusting the precision of the reconstructions so that it could be adapted to the application requirements

a nonfeasible gradient projection recurrent neural network for equality constrained optimization problems in this paper a recurrent neural network for both convex and nonconvex equality constrained optimization problems is proposed which makes use of a cost gradient projection onto the tangent space of the constraints the proposed neural network constructs a generically nonfeasible trajectory satisfying the constraints only as t rarr infin local convergence results are given that do not assume convexity of the optimization problem to be solved global convergence results are established for convex optimization problems an exponential convergence rate is shown to hold both for the convex case and the nonconvex case numerical results indicate that the proposed method is efficient and accurate

general four step discrete time zeroing and derivative dynamics applied to time varying nonlinear optimization abstract time varying nonlinear optimization tvno problems are considered as important issues in various scientific disciplines and industrial applications in this paper the continuous time derivative dynamics ctdd model is developed for obtaining the real time solutions of tvno problems furthermore aiming to remedy the weaknesses of ctdd model a continuous time zeroing dynamics ctzd model is presented and investigated for potential digital hardware realization by using bilinear transform a general four step zhang et al discretization zead formula is proposed and applied to the discretization of both ctdd and ctzd models a general four step discrete time derivative dynamics general four step dtdd model and a general four step discrete time zeroing dynamics general four step dtzd model are proposed on the basis of this general four step zead formula further theoretical analyses indicate that the general four step dtzd model is zero stable consistent and convergent with the truncation error of o g 4 which denotes a vector with every entries being o g 4 with g denoting the sampling period theoretical analyses also indicate that the maximal steady state residual error mssre has an o g 4 pattern confirmedly the efficacy and accuracy of the general four step dtdd and dtzd models are further illustrated by numerical examples

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

adaptive imputation of missing values for incomplete pattern classification in classification of incomplete pattern the missing values can either play a crucial role in the class determination or have only little influence or eventually none on the classification results according to the context we propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory at first we try to classify the object incomplete pattern based only on the available attribute values as underlying principle we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information in this case the object is committed to this particular class however if the object cannot be classified without ambiguity it means that the missing values play a main role for achieving an accurate classification in this case the missing values will be imputed based on the k nearest neighbor k nn and self organizing map som techniques and the edited pattern with the imputation is then classified the original or edited pattern is classified according to each training class and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification the object is allowed to belong with different masses of belief to the specific classes and meta classes which are particular disjunctions of several single classes the credal classification captures well the uncertainty and imprecision of classification and reduces effectively the rate of misclassifications thanks to the introduction of meta classes the effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets highlightsmissing values are adaptively imputed in classification according to context som and k nn are used for the imputation with admissible computation burden ensemble classifier is introduced for credal classification the imprecision of classification can be well captured using belief functions the proposed method has been tested by artificial and real data sets

generalized jeffrey s rule of conditioning and evidence combining rule for a priori probabilistic knowledge in conditional evidence theory in bayesian probabilistic approach for uncertain reasoning one basic assumption is that a priori knowledge about the uncertain variable is modeled by a probability distribution when new evidence representable by a constant set is available the bayesian conditioning is used to update a priori knowledge in the conventional d s evidence theory all bodies of evidence about the uncertain variable are imprecise and uncertain all bodies of evidence are combined by so called dempster s rule of combination to achieve a combined body of evidence without considering a priori knowledge from our point of view when identifying the true value of an uncertain variable bayesian approach and evidence theory can cooperate to deal with uncertain reasoning firstly all imprecise and uncertain bodies of evidence about the uncertain variable are fused to achieve a combined evidence based on a priori knowledge then the a posteriori probability distribution is achieved from a priori probability distribution by conditioning on the combined evidence in this paper we firstly deal with the knowledge updating problem where a priori knowledge is represented by a probability distribution and new evidence is represented by a random set then we review the conditional evidence theory which resolves the knowledge combining problem based on a priori probabilistic knowledge finally we discuss the close relationship between knowledge updating procedure and knowledge combining procedure presented in this paper we show that a posteriori probability conditioned on fused body of evidence satisfies the bayesian parallel combination rule

the combination of multiple classifiers using an evidential reasoning approach in many domains when we have several competing classifiers available we want to synthesize them or some of them to get a more accurate classifier by a combination function in this paper we propose a class indifferent method for combining classifier decisions represented by evidential structures called triplet and quartet using dempster s rule of combination this method is unique in that it distinguishes important elements from the trivial ones in representing classifier decisions makes use of more information than others in calculating the support for class labels and provides a practical way to apply the theoretically appealing dempster shafer theory of evidence to the problem of ensemble learning we present a formalism for modelling classifier decisions as triplet mass functions and we establish a range of formulae for combining these mass functions in order to arrive at a consensus decision in addition we carry out a comparative study with the alternatives of simplet and dichotomous structure and also compare two combination methods dempster s rule and majority voting over the uci benchmark data to demonstrate the advantage our approach offers

a class of prediction correction methods for time varying convex optimization this paper considers unconstrained convex optimization problems with time varying objective functions we propose algorithms with a discrete time sampling scheme to find and track the solution trajectory based on prediction and correction steps while sampling the problem data at a constant rate of 1 h where h is the sampling period the prediction step is derived by analyzing the iso residual dynamics of the optimality conditions the correction step adjusts for the distance between the current prediction and the optimizer at each time step and consists either of one or multiple gradient steps or newton steps which respectively correspond to the gradient trajectory tracking gtt or newton trajectory tracking ntt algorithms under suitable conditions we establish that the asymptotic error incurred by both proposed methods behaves as o h 2 and in some cases as o h 4 which outperforms the state of the art error bound of o h for correction only methods in the gradient correction step moreover when the characteristics of the objective function variation are not available we propose approximate gradient and newton tracking algorithms agt and ant respectively that still attain these asymptotical error bounds numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude

medical diagnosis fuzzy sets and degrees of belief abstract 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

representation and fusion of heterogeneous fuzzy information in the 3d space for model based structural recognition application to 3d brain imaging we present a novel approach to model based pattern recognition where structural information and spatial relationships have a most important role it is illustrated in the domain of 3d brain structure recognition using an anatomical atlas our approach performs segmentation and recognition of the scene simultaneously the solution of the recognition task is progressive processing successively different objects and using different pieces of knowledge about the object and about relationships between objects therefore the core of the approach is the knowledge representation part and constitutes the main contribution of this paper we make use of a spatial representation of each piece of information as a spatial fuzzy set representing a constraint to be satisfied by the searched object thanks in particular to fuzzy mathematical morphology operations fusion of these constraints allows us to select segment and recognize the desired object

real time nonlinear optimization as a generalized equation we establish results for the problem of tracking a time dependent manifold arising in real time optimization by casting this as a parametric generalized equation we demonstrate that if points along a solution manifold are consistently strongly regular it is possible to track the manifold approximately by solving a single linear complementarity problem lcp at each time step we derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the lcp is solved only approximately we use these results to derive a fast augmented lagrangian tracking algorithm and demonstrate the developments through a numerical case study

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

decentralized dynamic optimization through the alternating direction method of multipliers this paper develops the application of the alternating direction method of multipliers admm to optimize a dynamic objective function in a decentralized multi agent system at each time slot agents in the network observe local functions and cooperate to track the optimal time varying argument of the sum objective this cooperation is based on maintaining local primal variables that estimate the value of the optimal argument and auxiliary dual variables that encourage proximity with neighboring estimates primal and dual variables are updated by an admm iteration that can be implemented in a distributed manner whereby local updates require access to local variables and the most recent primal variables from adjacent agents for objective functions that are strongly convex and have lipschitz continuous gradients the distances between the primal and dual iterates to their corresponding time varying optimal values are shown to converge to a steady state gap this gap is explicitly characterized in terms of the condition number of the objective function the condition number of the network that is defined as the ratio between the largest and smallest nonzero laplacian eigenvalues and a bound on the drifts of the optimal primal variables and the optimal gradients numerical experiments corroborate theoretical findings and show that the results also hold for non differentiable and non strongly convex primal objectives

evidential reasoning rule for evidence combination this paper aims to establish a unique evidential reasoning er rule to combine multiple pieces of independent evidence conjunctively with weights and reliabilities the novel concept of weighted belief distribution wbd is proposed and extended to wbd with reliability wbdr to characterise evidence in complement of belief distribution bd introduced in dempster shafer d s theory of evidence the implementation of the orthogonal sum operation on wbds and wbdrs leads to the establishment of the new er rule the most important property of the new er rule is that it constitutes a generic conjunctive probabilistic reasoning process or a generalised bayesian inference process it is shown that the original er algorithm is a special case of the er rule when the reliability of evidence is equal to its weight and the weights of all pieces of evidence are normalised it is proven that email protected s rule is also a special case of the er rule when each piece of evidence is fully reliable the er rule completes and enhances email protected s rule by identifying how to combine pieces of fully reliable evidence that are highly or completely conflicting through a new reliability perturbation analysis the main properties of the er rule are explored to facilitate its applications several existing rules are discussed and compared with the er rule numerical and simulation studies are conducted to show the features of the er rule

evaluating and comparing soft partitions an approach based on dempster shafer theory in evidential clustering cluster membership uncertainty is represented by dempster shafer mass functions the notion of evidential partition generalizes other soft clustering structures such as fuzzy possibilistic or rough partitions in this paper we propose two extensions of the rand index for evaluating and comparing evidential partitions called similarity and consistency indices the similarity index is suitable for measuring the closeness of two soft partitions whereas the consistency index allows one to assess the agreement or lack of conflict between a soft partition and the true hard partition simulation experiments illustrate some applications of these indices

belief functions and parametric models the theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance in order to analyse parametric statistical problems within the framework of this theory we must specify the evidence on which the parametric model is based this article gives several examples to show how the nature of this evidence affects the analysis these examples also illustrate how the theory of belief functions can deal with problems where the evidence is too weak to support a parametric model

on interpolation of strictly singular operators strictly co singular operators and related operator ideals we improve the known results on interpolation of strictly singular operators and strictly co singular operators in several directions applications are given to embeddings between symmetric spaces

z type neural dynamics for time varying nonlinear optimization under a linear equality constraint with robot application abstract nonlinear optimization is widely important for science and engineering most research in optimization has dealt with static nonlinear optimization while little has been done on time varying nonlinear optimization problems these are generally more complicated and demanding we study time varying nonlinear optimizations with time varying linear equality constraints and adapt z type neural dynamics ztnd for solving such problems using a lagrange multipliers approach we construct a continuous ztnd model for such time varying optimizations a new four instant finite difference fifd formula is proposed that helps us discretize the continuous ztnd model with high accuracy we propose the fdztnd k and fdztnd u discrete models and compare their quality and the advantage of the fifd formula with two standard euler discretization ztnd models called edztnd k and edztnd u that achieve lower accuracy theoretical convergence of our continuous and discrete models is proved and our methods are tested in numerical experiments for a real world we apply the fdztnd u model to robot motion planning and show its feasibility in practice

taylor type 1 step ahead numerical differentiation rule for first order derivative approximation and znn discretization in order to achieve higher computational precision in approximating the first order derivative and discretize more effectively the continuous time zhang neural network znn a taylor type numerical differentiation rule is proposed and investigated in this paper this rule not only greatly remedies some intrinsic weaknesses of the backward and central numerical differentiation rules but also overcomes the limitation of the lagrange type numerical differentiation rules in znn discretization in addition a formula is proposed to obtain the optimal step length of the taylor type numerical differentiation rule moreover based on the proposed numerical differentiation rule the stability convergence and residual error of the taylor type discrete time znn dtznn are analyzed numerical experimental results further substantiate the efficacy and advantages of the proposed taylor type numerical differentiation rule for first order derivative approximation and znn discretization a formula is proposed to approximate the first order derivative an optimal step length rule for the proposed formula is investigated a taylor type znn model is derived for time varying matrix inversion

an evidential classifier based on feature selection and two step classification strategy in this paper we investigate ways to learn efficiently from uncertain data using belief functions in order to extract more knowledge from imperfect and insufficient information and to improve classification accuracy we propose a supervised learning method composed of a feature selection procedure and a two step classification strategy using training information the proposed feature selection procedure automatically determines the most informative feature subset by minimizing an objective function the proposed two step classification strategy further improves the decision making accuracy by using complementary information obtained during the classification process the performance of the proposed method was evaluated on various synthetic and real datasets a comparison with other classification methods is also presented highlightsa classifier is based on belief functions to tackle uncertain data the classifier composed by feature selection and a two step classification a new combination rule to better represent data uncertainty a new feature selection is based on minimizing uncertainty with sparse constraint two step classification improving accuracy of decision making

rigidity of composition operators on the hardy space h p abstract let be an analytic map taking the unit disk d into itself we establish that the class of composition operators f c f f exhibits a rather strong rigidity of non compact behaviour on the hardy space h p for 1 p and p 2 our main result is the following trichotomy which states that exactly one of the following alternatives holds i c is a compact operator h p h p ii c fixes a linearly isomorphic copy of l p in h p but c does not fix any copies of l 2 in h p iii c fixes a copy of l 2 in h p moreover in case iii the operator c actually fixes a copy of l p 0 1 in h p provided p 1 we reinterpret these results in terms of norm closed ideals of the bounded linear operators on h p which contain the compact operators k h p in particular the class of composition operators on h p does not reflect the quite complicated lattice structure of such ideals

an information fusion approach by combining multigranulation rough sets and evidence theory multigranulation rough set mgrs theory provides two kinds of qualitative combination rules that are generated by optimistic and pessimistic multigranulation fusion functions they are used to aggregate multiple granular structures from a set theoretic standpoint however the two combination rules seem to lack robustness because one is too relaxed and the other too restrictive to solve some practical problems dempster s combination rule in the evidence theory has been employed to aggregate information coming from multiple sources however it fails to deal with conflict evidence to overcome these limitations we focus on the combination of granular structures with both reliability and conflict from multiple sources which has been a challenging task in the field of granular computing we first address the connection between multigranulation rough set theory and the evidence theory then a two grade fusion approach involved in the evidence theory and multigranulation rough set theory is proposed which is based on a well defined distance function among granulation structures finally an illustrative example is given to show the effectiveness of the proposed fusion method the results of this study will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing