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

a theoretical framework for relaxation processes in pattern recognition application to robust nonparametric contour generalization while various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives the wider problem addressed here is to find the best suited relaxation process for a given assignment problem or better still to construct a task dependent relaxation process for this we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition the resulting structure enables 1 a description of all known relaxation processes in general terms and 2 the design of task dependent relaxation processes we show that the well known standard relaxation formulas verify our approach referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail important characteristics of the constructed task dependent relaxation process are 1 the independency of the segmentation from any parameters 2 the invariance to geometric transformations 3 the simplicity and 4 efficiency

a new belief based k nearest neighbor classification method the k nearest neighbor k nn classification method originally developed in the probabilistic framework has serious difficulties to classify correctly the close data points objects originating from different classes to cope with such difficult problem and make the classification result more robust to misclassification errors we propose a new belief based k nearest neighbor bk nn method that allows each object to belong both to the specific classes and to the sets of classes with different masses of belief bk nn is able to provide a hyper credal classification on the specific classes the rejection classes and the meta classes as well thus the objects hard to classify correctly are automatically committed to a meta class or to a rejection class which can reduce the misclassification errors the basic belief assignment bba of each object is defined from the distance between the object and its neighbors and from the acceptance and rejection thresholds the bba s are combined using a new combination method specially developed for the bk nn several experiments based on simulated and real data sets have been carried out to evaluate the performances of the bk nn method with respect to several classical k nn approaches

decision tree classifiers for evidential attribute values and class labels abstract decision trees are well known machine learning techniques for solving complex classification problems despite their great success the standard decision tree algorithms do not have the ability to process imperfect knowledge meaning uncertain imprecise and incomplete data in this paper we develop new decision tree approaches to cope with data that have uncertain attribute values and class labels more concretely we tackle the case where the uncertainty is represented and managed through the evidence theory

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

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

holomorphic isometries of mathbb b m into bounded symmetric domains arising from linear sections of minimal embeddings of their compact duals we study general properties of images of holomorphic isometric embeddings of complex unit balls mathbb b m into irreducible bounded symmetric domains varomega of rank at least 2 in particular we show that such holomorphic isometries with the minimal normalizing constant arise from linear sections varlambda of the compact dual x c of varomega the question naturally arises as to which linear sections z varlambda cap varomega are actually images of holomorphic isometries of complex unit balls we study the latter question in the case of bounded symmetric domains varomega of type iv alias lie balls i e bounded symmetric domains dual to hyperquadrics we completely classify images of all holomorphic isometric embeddings of complex unit balls into such bounded symmetric domains varomega especially we show that there exist holomorphic isometric embeddings of complex unit balls of codimension 1 incongruent to the examples constructed by mok proc am math soc 144 4515 4525 2016 from varieties of minimal rational tangents and that moreover any holomorphic isometric embedding f mathbb b m rightarrow varomega extends to a holomorphic isometric embedding f mathbb b n 1 rightarrow varomega dim varomega n the case of lie balls is particularly relevant because holomorphic isometric embeddings of complex unit balls of sufficiently large dimensions into an irreducible bounded symmetric domain other than a type iv domain are expected to be more rigid

polarized variation of hodge structures of calabi yau type and characteristic subvarieties over bounded symmetric domains in this paper we extend the construction of the canonical polarized variation of hodge structures over tube domain considered by gross math res lett 1 1 9 1994 to bounded symmetric domain and introduce a series of invariants of infinitesimal variation of hodge structures which we call characteristic subvarieties we prove that the characteristic subvariety of the canonical polarized variations of hodge structures over irreducible bounded symmetric domains are identified with the characteristic bundles defined by mok ann math 125 1 105 152 1987 we verified the generating property of gross for all irreducible bounded symmetric domains which was predicted in gross math res lett 1 1 9 1994

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

a novel combination method for conflicting evidence based on inconsistent measurements dempster shafer d s evidence theory is a kind of effective tool for uncertain information fusion however the counter intuitive results are often obtained when the conflicting pieces of evidence are fused with dempster s combination rule in order to solve the existing counter intuitive problem more effectively and less conservatively in this paper we propose an improved combination method for the conflicting evidence based on inconsistent measurements firstly a new approach is proposed for measuring the conflict between two pieces of evidence then the conflicting evidence is revised by selecting discount coefficients moreover dempster s combination rule is significantly improved by the new conflict coefficients and the fusion results are acquired by the improved combination rule finally examples are given to illustrate the effectiveness and potential of the developed new techniques

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

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

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

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

belief functions and default reasoning abstract we present a new approach to deal with default information based on the theory of belief functions our semantic structures inspired by adams epsilon semantics are epsilon belief assignments where mass values are either close to 0 or close to 1 in the first part of this paper we show that these structures can be used to give a uniform semantics to several popular non monotonic systems including kraus lehmann and magidor s system p pearl s system z brewka s preferred subtheories geffner s conditional entailment pinkas penalty logic possibilistic logic and the lexicographic approach in the second part we use epsilon belief assignments to build a new system called lcd and show that this system correctly addresses the well known problems of specificity irrelevance blocking of inheritance ambiguity and redundancy

regularity of mappings into classical domains we study the regularity and algebraicity for mappings into classical domains among other things we establish everywhere regularity and algebraicity results for c 2 cr maps into the set of smooth boundary points of a classical domain where the codimension can be arbitrarily large

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

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

on generalized fuzzy belief functions in infinite spaces determined by a fuzzy implication operator a general type of fuzzy belief structure and its induced dual pair of fuzzy belief and plausibility functions in infinite universes of discourse are first defined relationship between the belief structure based and the belief space based fuzzy dempster shafer models is then established it is shown that the lower and upper fuzzy probabilities induced by the fuzzy belief space yield a dual pair of fuzzy belief and plausibility functions for any fuzzy belief structure there must exist a fuzzy belief space such that the fuzzy belief and plausibility functions defined by the given fuzzy belief structure are just the lower and upper fuzzy probabilities induced by the fuzzy belief space respectively essential properties of the fuzzy belief and plausibility functions are also examined the fuzzy belief and plausibility functions are respectively a fuzzy monotone choquet capacity and a fuzzy alternating choquet capacity of infinite order

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

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

a new combination of evidence based on compromise dempster rule of combination is the standard way of combining multiple pieces of evidence given by independent sources of information however it aroused many controversies about its validity and many alternatives have been proposed the paper examines the model of combination in dempster s original paper and indicates that handling of the independence required among multiple pieces of evidence is strange from the viewpoint of semantics where the independence among occurrences of multiple pieces of information might be confused with the consistency among contents of the information the paper then proposes a new model of combination and a new rule of combination called combination by compromise as a consensus generator the properties of the proposed combination as well as several alternative combination methods proposed so far are discussed in the light of the drawbacks and advantages of dempster rule several numerical examples which demonstrate the properties are also shown the discussion and the examples suggest that the proposed combination produces the most preferable results among them from the viewpoints of consensus generation

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

conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence dempster s rule plays a central role in the theory of belief functions however it assumes the combined bodies of evidence to be distinct an assumption which is not always verified in practice in this paper a new operator the cautious rule of combination is introduced this operator is commutative associative and idempotent this latter property makes it suitable to combine belief functions induced by reliable but possibly overlapping bodies of evidence a dual operator the bold disjunctive rule is also introduced this operator is also commutative associative and idempotent and can be used to combine belief functions issues from possibly overlapping and unreliable sources finally the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms

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

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

ecm an evidential version of the fuzzy c means algorithm a new clustering method for object data called ecm evidential c means is introduced in the theoretical framework of belief functions it is based on the concept of credal partition extending those of hard fuzzy and possibilistic ones to derive such a structure a suitable objective function is minimized using an fcm like algorithm a validity index allowing the determination of the proper number of clusters is also proposed experiments with synthetic and real data sets show that the proposed algorithm can be considered as a promising tool in the field of exploratory statistics

the location of noncrossed products in brauer groups of laurent series fields over global fields since amitsur s discovery of noncrossed product division algebras in 1972 their existence over more familiar fields has been an object of investigation brussel s work was a culmination of this effort exhibiting noncrossed products over the rational function field k t and the laurent series field k t over any global field k the smallest possible centers of noncrossed products witt s theorem gives a transparent description of the brauer group of k t as the direct sum of the brauer group of k and the character group of the absolute galois group of k we classify the brauer classes over k t containing noncrossed products by analyzing the fiber over for each character in witt s theorem in this way a picture of the partition of the brauer group into crossed products noncrossed products is obtained which is in principle ruled by a relation between index and number of roots of unity as a side consequence of the result there are crossed products that have a noncrossed product primary component

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

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

uniqueness theorems of hermitian metrics of seminegative curvature on quotients of bounded symmetric domains in the theory of locally symmetric spaces of negative ricci curvature it has been a classical problem to study the extent to which the topology of the manifold determines the geometry and in the hermitian case the complex structure the rigidity theorem of mostow 26 asserts that for a compact locally symmetric riemannian manifold of negative ricci curvature the manifold is determined up to isometry and normalizing constants by its fundamental group among the class of such manifolds with the obvious exceptions involving compact riemann surfaces the same theorem for locally symmetric riemannian manifolds of finite volume and negative ricci curvature was proved by prasad 27 in case of rank 1 and included in the super rigidity theorem of margulis 13 in the case of rank 2 in the class of compact locally symmetric hermitian manifolds of negative ricci curvature calabi vesentini 5 and borel 3 proved vanishing theorems of certain cohomology groups which imply in particular that for x locally irreducible of complex dimension 2 there exists no non trivial deformation of x as a complex manifold in this direction siu 32 33 proved the strong rigidity of the kdhler manifold x in the sense that any compact kkhler manifold m homotopic to x is necessarily biholomorphic or conjugate biholomorphic to x if m is also locally symmetric by assumption then it follows from the uniqueness of kihler einstein metrics of negative ricci curvature yau 37 that the conjugate biholomorphism is in fact an isometry up to a normalizing constant it is thus natural to ask

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