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Abstract Fuzzy objective relation systems are an important class of datasets that are generalizations of many types of decision tables. This paper proposes an approach, based on relation systems and fuzzy sets, to reduce data redundancy in fuzzy objective relation systems. We study lower and upper approximation reductions of a relation system for a given fuzzy set. As a generalization of such reductions, we consider lower and upper approximation reductions of fuzzy objective relation systems and give their corresponding reduction algorithms using methods based on the discernibility matrix. We note that the usual positive region reduction for a decision table can be considered a special case of our lower approximation reduction. Finally, we provide two examples from the UCI datasets to verify our theoretical results. These results can help in the decision making analysis of fuzzy objective relation systems. [ABSTRACT FROM AUTHOR]

Abstract Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision – even on finite underlying sample spaces – an infinite number of assessments is needed in general. Therefore, they are often only described approximately by some less general models, such as coherent lower probabilities or in terms of some other finite set of constraints. The magnitude of error induced by the approximations has often been neglected in the literature, despite the fact that it can be significant, with substantial impact on consequent decisions. An apparent reason is that no widely used general method for estimating the error seems to be available at the moment. This paper provides a practically applicable method that allows calculating an upper bound for the maximal error induced by approximating a coherent lower probability with its values on a finite set of gambles. An algorithm is also provided with an estimation of its computational complexity. [ABSTRACT FROM AUTHOR]

Abstract In covering-based rough sets, many basic issues are related to minimal and maximal descriptions. For a covering approximation space with a large cardinal, it would be tedious and complicated to use set representations to solve the issues about minimal and maximal descriptions. Therefore it is necessary to study matrix representations by which calculations will become algorithmic and can be easily implemented by computers. In this paper, we use matrix approaches to investigate some issues about minimal and maximal descriptions in covering-based rough sets. Firstly, several new matrices and matrix operations are defined by which one can compute the minimal description and the approximation operator about the minimal description. Inspired by this result, a matrix method is presented to judge whether a covering is unary. Secondly, the maximal description and the approximation operator about the maximal description are also computed by these new matrices and matrix operations. Finally, based on the above results, we propose a matrix method to efficiently compute reductions of coverings. Moreover, we propose two types of reducts of covering information systems via minimal and maximal descriptions respectively, and we use matrix approaches to compute them. In a word, these results show an interesting view to investigate the combination between matrices and covering-based rough sets. [ABSTRACT FROM AUTHOR]

In covering rough set theory, the basic problem is the calculation of lower and upper approximations for subsets of a covering approximation space. For a covering approximation space with a large cardinal, using definitions to calculate approximations would be tedious and complicated. So it is important to investigate matrix methods by which calculations will become algorithmic and can be easily implemented by computers. Since the covering in a covering approximation space can be represented by a Boolean matrix, every covering rough approximation operator must be closely related to this matrix. In this paper, we investigated 32 pairs of neighborhood-based dual lower and upper approximation operators and successfully obtained all the matrix representations of them. Some examples were presented in the manuscript to illustrate how to use matrix methods to compute lower and upper approximations and examples were also given to solve the inverse problem, i.e., finding all the subsets whose lower or upper approximation is a given subset. [ABSTRACT FROM AUTHOR]

The conditional independencies from a joint probability distribution constitute a model which is closed under the semi-graphoid properties of independency. These models typically are exponentially large in size and cannot be feasibly enumerated. For describing a semi-graphoid model therefore, researchers have proposed a more concise representation. This representation is composed of a representative subset of the independencies involved, called a basis, and lets all other independencies be implicitly defined by the semi-graphoid properties. An algorithm is available for computing such a basis for a semi-graphoid independency model. In this paper, we identify some new properties of a basis in general which can be exploited for arriving at an even more concise representation of a semi-graphoid model. Based upon these properties, we present an enhanced algorithm for basis construction which never returns a larger basis for a given independency model than currently existing algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The variable precision rough set model and graded rough set model are 2 important extended rough set models. This paper aims to make a comparative study of the 2 models. Rough set regions, primitive notions, are proposed first for the 2 models, which classify the universe more precisely. Then, both of their logical meanings related to quantitative indexes and their basic structure are investigated, and their precise descriptions are obtained as well. Furthermore, in the graded rough set model, macroscopic and microscopic algorithms are proposed and analyzed to calculate rough set regions; then, the conclusion is drawn that macroscopic and microscopic algorithms have advantages in time and space complexities, respectively, and a medical example is provided to illustrate the rough set regions and the 2 algorithms. In addition, 3 new properties of the 2 models are investigated, which are the results of extending the classical rough set model, i.e. the relationships between approximations and the basic set, the power actions of approximation operators, and the modifications of approximation operator actions on set operations. Finally, the classical rough set model is used to obtain many corresponding results, and moreover, the relationship and transformation between the 2 models is investigated. The study results of this paper have extended and enriched rough set theory from both operator-oriented and set-oriented points of view. [Copyright &y& Elsevier]

Abstract: This paper derives a particle filter algorithm within the Dempster–Shafer framework. Particle filtering is a well-established Bayesian Monte Carlo technique for estimating the current state of a hidden Markov process using a fixed number of samples. When dealing with incomplete information or qualitative assessments of uncertainty, however, Dempster–Shafer models with their explicit representation of ignorance often turn out to be more appropriate than Bayesian models. The contribution of this paper is twofold. First, the Dempster–Shafer formalism is applied to the problem of maintaining a belief distribution over the state space of a hidden Markov process by deriving the corresponding recursive update equations, which turn out to be a strict generalization of Bayesian filtering. Second, it is shown how the solution of these equations can be efficiently approximated via particle filtering based on importance sampling, which makes the Dempster–Shafer approach tractable even for large state spaces. The performance of the resulting algorithm is compared to exact evidential as well as Bayesian inference. [Copyright &y& Elsevier]

When arbitrary sets are approximated by more structured sets, it may not be possible to obtain an exact approximation that is equivalent to a given set. Presented here, is a new proposal for a ‘metric’ approach to Rough Sets. We assume some finite measure space is defined on a given universe, and then use it to define various similarity indexes . A set of axioms and the concept of consistency for similarity indexes are also proposed. The core of the paper is a definition of the ‘ optimal ’ or ‘ best ’ approximation with respect to any particular similarity index, and an algorithm to find this optimal approximation by using the Marczewski–Steinhaus Index. This algorithm is also shown to hold for a class of similarity indexes that are consistent with the Marczewski–Steinhaus Index. [ABSTRACT FROM AUTHOR]

Abstract: Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids. [Copyright &y& Elsevier]

Abstract: In this paper, we address the problem of complex object tracking using the particle filter framework, which essentially amounts to estimate high-dimensional distributions by a sequential Monte Carlo algorithm. For this purpose, we first exploit Dynamic Bayesian Networks to determine conditionally independent subspaces of the object’s state space, which allows us to independently perform the particle filter’s propagations and corrections over small spaces. Second, we propose a swapping process to transform the weighted particle set provided by the update step of the particle filter into a “new particle set” better focusing on high peaks of the posterior distribution. This new methodology, called Swapping-Based Partitioned Sampling, is proved to be mathematically sound and is successfully tested and validated on synthetic video sequences for single or multiple articulated object tracking. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the flexible inference method with parameters, that is the parametric triple I method by the combination of Schweizer–Sklar operators and triple I principles for fuzzy reasoning. Because the Schweizer–Sklar parameter m reflects the interaction between propositions in reasoning processes, the new parameterized triple I algorithms are closer to human reasoning in daily life. Also some properties of the new algorithms such as the reductivity, continuity and approximation are discussed. It is shown that some existing results are special cases of the new algorithms given here and in view of the variability of the parameter m the new algorithms have excellent flexibility in reasoning processes. [Copyright &y& Elsevier]

Abstract: A Recursive Probability Tree (RPT) is a data structure for representing the potentials involved in Probabilistic Graphical Models (PGMs). This structure is developed with the aim of capturing some types of independencies that cannot be represented with previous structures. This capability leads to improvements in memory space and computation time during inference. This paper describes a learning algorithm for building RPTs from probability distributions. The experimental analysis shows the proper behavior of the algorithm: it produces RPTs encoding good approximations of the original probability distributions. [Copyright &y& Elsevier]

Abstract: In this paper a novel approach for recognizing actions in video sequences is presented, where the information obtained from the segmentation and tracking algorithms is used as input data. First of all, the fuzzification of input data is done and this process allows to successfully manage the uncertainty inherent to the information obtained from low-level and medium-level vision tasks, to unify the information obtained from different vision algorithms into a homogeneous representation and to aggregate the characteristics of the analyzed scenario and the objects in motion. Another contribution is the novelty of representing actions by means of an automaton and the generation of input symbols for the finite automaton depending on the comparison process between objects and actions, i.e., the main reasoning process is based on the operation of automata with capability to manage fuzzy representations of all video data. The experiments on several real traffic video sequences demonstrate encouraging results, especially when no training algorithms to obtain predefined actions to be identified are required. [Copyright &y& Elsevier]

Abstract: The goal of designing optimal nearest neighbor classifiers is to maximize classification accuracy while minimizing the sizes of both reference and feature sets. A usual way is to adaptively weight the three objectives as an objective function and then use a single-objective optimization method for achieving this goal. This paper proposes a multi-objective approach to cope with the weight tuning problem for practitioners. A novel intelligent multi-objective evolutionary algorithm IMOEA is utilized to simultaneously edit compact reference and feature sets for nearest neighbor classification. Three comparison studies are designed to evaluate performance of the proposed approach. It is shown empirically that the IMOEA-designed classifiers have high classification accuracy and small sizes of reference and feature sets. Moreover, IMOEA can provide a set of good solutions for practitioners to choose from in a single run. The simulation results indicate that the IMOEA-based approach is an expedient method to design nearest neighbor classifiers, compared with an existing single-objective approach. [Copyright &y& Elsevier]

The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resource-bounded anytime algorithms, where the maximal time of computation is determined by the user. [Copyright &y& Elsevier]