on the combination and normalization of interval valued belief structures this paper investigates the issues of combination and normalization of interval valued belief structures within the framework of dempster shafer theory dst of evidence existing approaches are reviewed examined and critically analysed they either ignore the normalization or separate it from the combination process leading to irrational or suboptimal interval valued belief structures a new logically correct optimality approach is developed where the combination and the normalization are optimised together rather than separately numerical examples are provided throughout the paper

handling possibilistic labels in pattern classification using evidential reasoning abstract a category of learning problems in which the class membership of training patterns is assessed by an expert and encoded in the form of a possibility distribution is considered each example i thus consists in a feature vector x i and a possibilistic label u 1 i u c i where u k i denotes the possibility of that example belonging to class k this problem is tackled in the framework of evidence theory the evidential distance based classifier previously introduced by one of the authors is extended to handle possibilistic labeling of training data two approaches are proposed based either on the transformation of each possibility distribution into a consonant belief function or on the use of generalized belief structures with fuzzy focal elements in each case a belief function modeling the expert s beliefs concerning the class membership of each new pattern is obtained this information may then be either interpreted by a human operator to support decision making or automatically processed to yield a final class assignment through the computation of pignistic probabilities experiments with synthetic and real data demonstrate the ability of both classification schemes to make effective use of possibilistic labels as training information

inverse halftoning and kernel estimation for error diffusion two different approaches in the inverse halftoning of error diffused images are considered the first approach uses linear filtering and statistical smoothing that reconstructs a gray scale image from a given error diffused image the second approach can be viewed as a projection operation where one assumes the error diffusion kernel is known and finds a gray scale image that will be halftoned into the same binary image two projection algorithms viz minimum mean square error mmse projection and maximum a posteriori probability map projection that differ on the way an inverse quantization step is performed are developed among the filtering and the two projection algorithms map projection provides the best performance for inverse halftoning using techniques from adaptive signal processing we suggest a method for estimating the error diffusion kernel from the given halftone this means that the projection algorithms can be applied in the inverse halftoning of any error diffused image without requiring any a priori information on the error diffusion kernel it is shown that the kernel estimation algorithm combined with map projection provide the same performance in inverse halftoning compared to the case where the error diffusion kernel is known

a linear time combinatorial algorithm to find the orthogonal hull of an object on the digital plane a combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper the resolution and complexity of the orthogonal hull can be controlled by varying the grid size which may be used for a multiresolution analysis of a given object existing algorithms on finding the convex hull are based on divide and conquer strategy sweepline approach etc whereas the proposed algorithm is combinatorial in nature whose time complexity is linear on the object perimeter instead of the object area for a larger grid size the perimeter of an object decreases in length in terms of grid units and hence the runtime of the algorithm reduces significantly the algorithm uses only comparison and addition in the integer domain thereby making it amenable to usage in real world applications where speed is a prime factor experimental results including the cpu time demonstrate the elegance and efficacy of the proposed algorithm

an alternative approach to the handling of subnormal possibility distributions abstract in this short note a definition of the necessity measure in case of a subnormal possibility distribution already proposed by the authors is recalled this definition both satisfies the axiomatics of necessity measures and preserves the desirable inequality between possibility and necessity measures the handling of subnormal basic probability assignments in the more general framework of shafer s belief functions is also discussed

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

restoration of error diffused images using projection onto convex sets a novel inverse halftoning method is proposed to restore a continuous tone image from a given half tone image a set theoretic formulation is used where three sets are defined using the prior information about the problem a new space domain projection is introduced assuming the halftoning is performed using error diffusion and the error diffusion filter kernel is known the space domain frequency domain and space scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution

completeness of arbitrarily sampled discrete time wavelet transforms an arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible i e if the underlying signal can be uniquely recovered from the available samples of the wavelet transform we develop easy to compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal in particular we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z 1 we present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros we also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform all the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank they can easily be checked without explicitly computing of the rank of a matrix finally we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete

viability for delay evolution equations with nonlocal initial conditions abstract we prove a sufficient condition for a time dependent closed set to be viable with respect to a delay evolution inclusion subjected to an implicit nonlocal initial condition an application to a comparison problem is also included

viability for stochastic functional differential equations in hilbert spaces driven by fractional brownian motion abstract in this paper we consider a class of stochastic functional differential equations in hilbert spaces driven by a fractional brownian motion with hurst parameter 1 2

a novel classification method of halftone image via statistics matrices existing classification methods tend not to work well on various error diffusion patterns thus a novel classification method for halftone image via statistics matrices is proposed the statistics matrix descriptor of halftone image is constructed according to the characteristic of error diffusion filters on this basis an extraction algorithm is developed based on halftone image patches the feature modeling is formulated as an optimization problem and then a gradient descent method is used to seek optimum class feature matrices by minimizing the total square error a maximum likelihood method is proposed according to priori knowledge of training samples in experiments the performance evaluation method is provided and comparisons of performance between our method and seven similar methods are made then the influence of parameters performance under various attacks computational time complexity and the limitations are discussed from our experimental study it is observed that our method has lower classification error rate when compared with other similar methods in addition it is robust against usual attacks

maximal confidence intervals of the interval valued belief structure and applications an unsolved problem in the interval valued belief structure is the existence of maximal confidence intervals referring to the credible and maximal interval valued beliefs assigned to focal elements in which every point can be reached by a combination rule in this study the existence of maximal confidence intervals of the interval valued belief structure was investigated and validated in addition some applications of the maximal confidence interval in constructing valid and normalized interval valued belief structures are discussed a numerical experiment was conducted to illustrate the existence of maximal confidence intervals several propositions and a theorem were further proposed to demonstrate the validity of the maximal confidence interval by using the concept of the maximal confidence interval a procedure was proposed to construct valid and normalized interval valued belief structures and some meaningful guidance for assigning interval valued beliefs was also suggested to the experts finally a series of well designed examples was presented as applications of the maximal confidence interval the proposed procedure and the suggestions they indicated that valid and normalized interval valued belief structures can be achieved accurately and efficiently in practical applications with the proposed procedure and guidance on the basis of the concept of the maximal confidence interval

flow invariance for nonlinear partial differential delay equations several fundamental results on existence flow invariance regularity and linearized stability of solutions to the nonlinear partial differential delay equation u t bu t f u t t 0 uo with b c x x x w accretive are developed for a general banach space x in contrast to existing results with the history response f globally defined and at least lipschitz on bounded sets the results are tailored for situations with f defined on possibly thin subsets of the initial history space e only and are applied to place several classes of population models in their natural l 1 setting the main result solves the open problem of a subtangential condition for flow invariance of solutions in the fully nonlinear case paralleling those known for the cases of a no delay b ordinary delay equations with b 0 and c the semilinear case

generalized k nearest neighbor rules abstract this paper discusses a suitable framework for generalizing the k nearest neighbor k nnr algorithms to cases where the design labels are not necessarily crisp i e not binary valued the proposed framework imbeds all crisp k nnr s into a larger structure of fuzzy k nnr s the resultant model enables neighborhood voting to be a continuous function of local labels at a point to be classified we emphasize that the decision itself may be crisp even when a fuzzy k nnr is utilized the usefulness of this extension of the conventional technique is illustrated by comparing the observed error rates of four classifiers the hard k nnr two fuzzy k nnr s and a fuzzy 1 nearest prototype rule 1 npr on three data sets anderson s iris data and samples from synthetic univariate and bivariate normal mixtures our conclusions all four designs yield comparable usually within 4 error rates the fuzzy c means fcm based k nnr is usually the best design the fcm 1 npr is the most efficient and perhaps most useful of the four designs and finally that generalized nnr s are an important and useful extension of the conventional ones

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

naive possibilistic classifiers for imprecise or uncertain numerical data in real world problems input data may be pervaded with uncertainty in this paper we investigate the behavior of naive possibilistic classifiers as a counterpart to naive bayesian ones for dealing with classification tasks in the presence of uncertainty for this purpose we extend possibilistic classifiers which have been recently adapted to numerical data in order to cope with uncertainty in data representation here the possibility distributions that are used are supposed to encode the family of gaussian probabilistic distributions that are compatible with the considered dataset we consider two types of uncertainty i the uncertainty associated with the class in the training set which is modeled by a possibility distribution over class labels and ii the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data moreover the approach takes into account the uncertainty about the estimation of the gaussian distribution parameters due to the limited amount of data available we first adapt the possibilistic classification model previously proposed for the certain case in order to accommodate the uncertainty about class labels then we propose an algorithm based on the extension principle to deal with imprecise attribute values the experiments reported show the interest of possibilistic classifiers for handling uncertainty in data in particular the probability to possibility transform based classifier shows a robust behavior when dealing with imperfect data

signal recovery from wavelet transform maxima the paper presents an iterative algorithm for signal recovery from discrete time wavelet transform maxima the signal recovery algorithm is developed by using the method of projections onto convex sets convergence of the algorithm is assured

generalized probabilities of fuzzy events from fuzzy belief structures abstract we extend shafer s theory of evidence to include the ability to have belief structures involving fuzzy sets we then obtain under the condition of bayesian belief structure a whole family of possible definitions for the probability of fuzzy sets we also suggest a procedure for including belief qualification in pruf

the normative representation of quantified beliefs by belief functions abstract the use of belief functions has recently been advocated as an alternative to the use of probability functions in order to represent quantified beliefs such a proposal lacked justification we present a set of requirements that justify the use of belief functions the assessment of the validity of these requirements provides a tool for assessing the relative value of normative models of subjective behaviors

paper evidence measures based on fuzzy information an organized body of results pertaining to the analysis of evidence when the available knowledge is pervaded with imprecision is provided the evidence theory of dempster and shafer is extended to the case of fuzzy observations and fuzzy events upper and lower possibilities of such events are derived by iterating the generation process of upper and lower probabilities as done by dempster both probabilistic and possibilistic models are developed in parallel these evidence measures are used for decision evaluation when the available knowledge is poor the classical model of decision making under uncertainty is thus extended to the case when the consequences of a decision are only roughly described and their probabilities of occurrence modeled by intervals or fuzzy numbers

upper probabilities based only on the likelihood function summary in the problem of parametric statistical inference with a finite parameter space we propose some simple rules for defining posterior upper and lower probabilities directly from the observed likelihood function without using any prior information the rules satisfy the likelihood principle and a basic consistency principle avoiding sure loss they produce vacuous inferences when the likelihood function is constant and they have other symmetry monotonicity and continuity properties one of the rules also satisfies fundamental frequentist principles the rules can be used to eliminate nuisance parameters and to interpret the likelihood function and to use it in making decisions to compare the rules they are applied to the problem of sampling from a finite population our results indicate that there are objective statistical methods which can reconcile three general approaches to statistical inference likelihood inference coherent inference and frequentist inference

halftone image classification using lms algorithm and naive bayes former research on inverse halftoning most focus on developing a general purpose method for all types of halftone patterns such as error diffusion ordered dithering etc while fail to consider the natural discrepancies among various halftoning methods to achieve optimal image quality for each halftoning method the classification of halftone images is highly demanded this study employed the least mean square filter for improving the robustness of the extracted features and employed the naive bayes classifier to verify all the extracted features for classification nine of the most well known halftoning methods were involved for testing the experimental results demonstrated that the classification performance can achieve a 100 accuracy rate and the number of distinguishable halftoning methods is more than that of a former method established by chang and yu

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

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

inverse halftoning via map estimation there has been a tremendous amount of research in the area of image halftoning where the goal has been to find the most visually accurate representation given a limited palette of gray levels often just two black and white this paper focuses on the inverse problem that of finding efficient techniques for reconstructing high quality continuous tone images from their halftoned versions the proposed algorithms are based on a maximum a posteriori map estimation criteria using a markov random field mrf model for the prior image distribution image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along image edges algorithms are developed and example gray level reconstructions are presented generated from both dithered and error diffused halftone originals application of the technique to the problems of rescreening and the processing of halftone images are shown

halftone to continuous tone conversion of error diffusion coded images considers the problem of reconstructing a continuous tone contone image from its halftoned version where the halftoning process is done by error diffusion the authors present an iterative nonlinear decoding algorithm for halftone to contone conversion and show simulation results that compare the performance of the algorithm to that of conventional linear low pass filtering they find that the new technique results in subjectively superior reconstruction as there is a natural relationship between error diffusion and spl sigma spl delta modulation the reconstruction algorithm can also be applied to the decoding problem for spl sigma spl delta modulators

image restoration by the method of convex projections part 2 applications and numerical results the image restoration theory discussed in a previous paper by youla and webb 1 is applied to a simulated image and the results compared with the well known method known as the gerchberg papoulis algorithm the results show that the method of image restoration by projection onto convex sets by providing a convenient technique for utilizing a priori information performs significantly better than the gerchberg papoulis method

the evidential reasoning approach for multiple attribute decision analysis using interval belief degrees abstract multiple attribute decision analysis mada problems having both quantitative and qualitative attributes under uncertainty can be modeled using the evidential reasoning er approach several types of uncertainties such as ignorance and fuzziness can be modeled in the er framework in this paper the er approach will be extended to model new types of uncertainties including interval belief degrees and interval data that could be incurred in decision situations such as group decision making the dempster shafer d s theory of evidence is first extended which is one of the bases of the er approach the analytical er algorithm is used to combine all evidence simultaneously two pairs of nonlinear optimization models are constructed to estimate the upper and lower bounds of the combined belief degrees and to compute the maximum and the minimum expected utilities of each alternative respectively interval data are equivalently transformed to interval belief degrees and are incorporated into the nonlinear optimization models a cargo ship selection problem is examined to show the implementation process of the proposed approach

viability for stochastic functional differential equations with infinite memory driven by a fractional brownian motion abstract in this paper we prove a viability result for stochastic functional differential equation with infinite memory driven by a fractional brownian motion with hurst parameter 1 2 h 1 using pathwise approach