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This paper presents the application of abstraction methods in creating concepts that allow to describe and solve more complex problems of knowledge representation in semantic networks. In the Semantic Web, knowledge is represented by the attributive language AL. There are many information granules theories formulated in different theories such as set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy set theory, and rough set theory. In order to equally interpret AL language expressions in different information granules theories within the Semantic Web, it is assumed that AL language expressions are interpreted in the chosen relational system called a granule system. This paper formally describes information granule system and shows the example how to formulate such granule system in the theory of the contextual rough sets [14] which describes inclusions of fuzzy context relations with some error. Defined granule system allows to interpret AL languages. It is shown that there is such subsystem of this granule system that is adequate i.e. it is homomorphic within some ordered set algebra. [ABSTRACT FROM AUTHOR]

Probabilistic rough set approximations are proposed based on a conditional probability to describe the desired levels of precision between the equivalence classes and an approximated set. This definition shows the detailed information on individuals satisfying some conditions but ignores the structural information. In this paper, applying the structured granules in a coarsened-grained universe, we introduce structured probabilistic rough set approximations between the power sets of the original universe and the coarsened-grained universe. By using the zooming-in and structured probabilistic rough approximation operators, two pairs of probabilistic rough lower and upper approximations on the same universe are investigated. Related properties and relationships of them are investigated. Furthermore, applying the Bayesian decision procedure, conditional probability and loss functions, three-way classifications in structured probabilistic rough set approximations are then proposed to classify the structured granules of the coarsened-grained universe into three disjoint structured probabilistic regions. This method gives the values of the pair of thresholds. Meanwhile, by using the minimum-risk decision rules, we also can construct the structured probabilistic rough lower and upper approximations. Finally, we discuss the monotonicity of structured probabilistic positive and negative regions. [ABSTRACT FROM AUTHOR]

Probabilistic Argumentation (PA) is a recent line of research in AI aiming to combine the strengths of argumentation and probabilistic reasoning. Though several models of PA have been proposed, the development of practical applications is still hindered by the lack of inference procedures and reasoning engines. In this paper, we present a reduction method to compute a recently proposed model of PA called PABA. Using the method we design inference procedures to compute the credulous semantics, the ideal semantics and the grounded semantics for a general class of PABA frameworks, that we refer to as Bayesian PABA frameworks. We also show that, though restricting to Bayesian PABA frameworks, the inference procedures can be used to compute other PA models thanks to simple translations. Finally, we implement the inference procedures to obtain a multi-semantics engine for probabilistic argumentation and demonstrate its usage. [ABSTRACT FROM AUTHOR]

In order to use fuzzy sets in real-world applications, an interpretation for the values of membership functions is needed. The history of fuzzy set theory shows that the interpretation in terms of statistical likelihood is very natural, although the connection between likelihood and probability can be misleading. In this paper, the likelihood interpretation of fuzzy sets is reviewed: it makes fuzzy data and fuzzy inferences perfectly compatible with standard statistical analyses, and sheds some light on the central role played by extension principle and α -cuts in fuzzy set theory. Furthermore, the likelihood interpretation justifies some of the combination rules of fuzzy set theory, including the product and minimum rules for the conjunction of fuzzy sets, as well as the probabilistic-sum and bounded-sum rules for the disjunction of fuzzy sets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method called 2-probabilities focused combination for combining information about user preferences on products or services in recommender systems based on Dempster–Shafer theory. Regarding this method, in focal sets of mass functions representing user preferences, focal elements with probabilities in top two highest ones are retained and the remaining focal elements are considered as noise and then transferred to the whole set element. To demonstrate the advantages of the new method, a baseline known as 2-points focused combination is selected for performance comparison in a range of experiments using Movielens and Flixster data sets. According to the results of experiments, the new method is more effective in accuracy of recommendations and comparable in computational time. Also, the new method is capable of overcoming the weakness of the baseline because of the ability to generate stable results. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak rough set model, decision-theoretic rough set model (DTRS) adopts the Bayesian decision theory to compute the required thresholds in probabilistic rough set models. It gives a new semantic interpretation of the positive, boundary and negative regions by using three-way decisions. DTRS has been widely discussed and applied in data mining and decision making. However, one limitation of DTRS is its lack of ability to deal with numerical data directly. In order to overcome this disadvantage and extend the theory of DTRS, this paper proposes a neighborhood based decision-theoretic rough set model (NDTRS) under the framework of DTRS. Basic concepts of NDTRS are introduced. A positive region related attribute reduct and a minimum cost attribute reduct in the proposed model are defined and analyzed. Experimental results show that our methods can get a short reduct. Furthermore, a new neighborhood classifier based on three-way decisions is constructed and compared with other classifiers. Comparison experiments show that the proposed classifier can get a high accuracy and a low misclassification cost. [ABSTRACT FROM AUTHOR]

This paper considers the problem of learning multinomial distributions from a sample of independent observations. The Bayesian approach usually assumes a prior Dirichlet distribution about the probabilities of the different possible values. However, there is no consensus on the parameters of this Dirichlet distribution. Here, it will be shown that this is not a simple problem, providing examples in which different selection criteria are reasonable. To solve it the Imprecise Dirichlet Model (IDM) was introduced. But this model has important drawbacks, as the problems associated to learning from indirect observations. As an alternative approach, the Imprecise Sample Size Dirichlet Model (ISSDM) is introduced and its properties are studied. The prior distribution over the parameters of a multinomial distribution is the basis to learn Bayesian networks using Bayesian scores. Here, we will show that the ISSDM can be used to learn imprecise Bayesian networks, also called credal networks when all the distributions share a common graphical structure. Some experiments are reported on the use of the ISSDM to learn the structure of a graphical model and to build supervised classifiers. [ABSTRACT FROM AUTHOR]