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Dempster–Shafer evidence theory (D–S theory) can effectively deal with uncertain information and it is one of the effective data fusion methods. However, Dempster's combination rule of D–S theory often produces counter-intuitive fusion results when the handled body of evidence (BOE) is highly conflicting with each other. Therefore, many new methods have been gradually proposed to optimize BOE to avoid the counter-intuitive fusion results. In this work, inspired by the complex network, a body of evidence is compared to a node, therefore multiple nodes composed of the BOEs constitute a complex network structure, and a correlation coefficient is adopted to measure the degree of correlation between two BOEs. The direct and indirect interaction weights of each node are determined through the direct and indirect interactions among the nodes to reflect their importance in the complex network. After that, the total weight of each BOE is calculated through using the direct and indirect weights. Finally, after modifying the original BOE with weight factor, the final result is obtained after information fusion by using Dempster's combination rule. This work analyses a practical application case based on the proposed evidential-weighting complex networks in D–S theory. The experiment result shows that the complex network optimization algorithm proposed in this work possesses a good convergence and has significantly improved the counter-intuitive fusion results brought about by the highly conflicting evidence with Dempster's combination rule. • Conflicting evidence fusion using a correlation coefficient method. • Conflicting evidence fusion from the perspective of complex network. • The correlation between bodies of evidence is modeled with correlation coefficient. • The interactions of complex networks are used to model the weight of evidence. • The new method can obtain correct fusion results for conflicting evidence. [ABSTRACT FROM AUTHOR]

This paper assumes that each proposition can be defined by a positive criterion together with a negative criterion. Then, within the framework of propositional logic, this paper proposes Belnap valuations as a truth model for bipolar propositions. The truth value of bipolar proposition is meant to be one of four values: absolutely true , absolutely false , borderline , and inconsistent . The borderline and inconsistent cases represent the truth-gap and truth-glut of a bipolar proposition, respectively. In order to reduce inconsistency two truth normalization methods, strong truth normalization and Kleene truth normalization, are proposed to approximate the original Belnap valuations. By integrating uncertainty of the true interpretations of bipolar propositions this paper introduces the following bipolar belief measures: positive and negative belief measures, lower and upper belief measures, and Kleene lower and upper belief measures. A mass function characterization of these bipolar belief measures are further explored. The relationship with Atanassov's intuitionistic fuzzy sets and interval fuzzy sets is also discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper, we mainly discuss the importance of distribution of nonzero elements in sparse representation. In feature space of low dimension, limited number of nonzero elements are needed to represent the target and therefore the representation is naturally sparse. Ideally, if most of nonzero elements assemble around samples of the same class as the target, the reconstruction error tends to be small and the result is more likely to be correct. Therefore, it is necessary to introduce some discriminative information into the objective function to adjust distribution of nonzero elements. We propose the Granular Locality-preserving Classification (GLC) algorithms within fine, intermediate and coarse granularity, which incorporate distance metric, class labels and clustering results of K -means on training data as discriminative information. Experiments conducted on several benchmark data sets show that GLC algorithms are comparable with state-of-the-art classification methods. [ABSTRACT FROM AUTHOR]

Abstract: We argue that vagueness is a multi-faceted phenomenon requiring a framework for concept representation incorporating aspects of typicality, semantic uncertainty and indeterminism. In this paper we propose a bipolar model for vague concepts within the framework of prototype theory where concepts are represented by prototypical regions of an underlying conceptual space, and in which the appropriateness of a concept label to describe a given instance is determined on the basis of both a lower and an upper threshold on the distance from the defining prototype. Essentially, the label is absolutely appropriate as a description, providing that the distance to the prototype is less than the lower threshold, and not absolutely inappropriate if it is less than the upper threshold. Hence, in effect a concept is defined by lower and upper neighbourhoods of the prototype within the conceptual space, and the borderline region between the neighbourhoods identifies those elements of the space for which the concept label is neither absolutely appropriate nor absolutely inappropriate to describe. Semantic uncertainty is then represented by a joint probability density function on the lower and upper thresholds so that the lower and upper neighbourhoods correspond to nested random sets. This naturally results in lower and upper appropriateness measures quantifying the belief that a concept label is absolutely appropriate and not absolutely inappropriate to describe a given element of the space. These measures can then be related to the random set interpretation of fuzzy sets and in particular to lower and upper membership functions in interval fuzzy set theory. [Copyright &y& Elsevier]

Abstract: The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label L has the form ‘about P’, where P is a set of prototypes of L and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function on . In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Density peaks clustering (DPC) algorithm is a succinct and efficient density-based clustering approach to data analysis. It computes the local density and the relative distance for objects to seek cluster centers and form clusters. However, it is difficult to estimate an appropriate local density by a rule of thumb; therefore, the performance of DPC may be poor on real datasets in practice. Thus, this study proposes a novel method for density peaks clustering based on fuzzy semantic cells. Specifically, each object is coarsened into a fuzzy point with the form of the fuzzy semantic cell model. Based on this model, a local density metric is defined and estimated via the principle of justifiable granularity. Our local density estimation can be converted into an optimization problem. In addition, a relative semantic distance is also introduced which concerns the distance between fuzzy semantic cells. The relative semantic distance is more informative for selecting cluster centers in the decision graph. The experimental results show that our method not only exhibits higher performance but also provides a clearer decision graph to select cluster centers. [ABSTRACT FROM AUTHOR]