A granularity-based framework of deduction, induction, and abduction

AbstractIn this paper, we propose a granularity-based framework of deduction, induction, and abduction using variable precision rough set models proposed by Ziarko and measure-based semantics for modal logic proposed by Murai et al. The proposed framework is based on α-level fuzzy measure models on the basis of background knowledge, as described in the paper. In the proposed framework, deduction, induction, and abduction are characterized as reasoning processes based on typical situations about the facts and rules used in these processes. Using variable precision rough set models, we consider β-lower approximation of truth sets of nonmodal sentences as typical situations of the given facts and rules, instead of the truth sets of the sentences as correct representations of the facts and rules. Moreover, we represent deduction, induction, and abduction as relationships between typical situations

Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems

Matroidal structure of generalized rough sets based on symmetric and transitive relations

Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.Comment: 5 page

Fuzzy-rough set and fuzzy ID3 decision approaches to knowledge discovery in datasets

Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets mainly concentrate on the construction of approximation operators. Less effort has been put on the knowledge discovery in datasets with fuzzy rough sets. This paper mainly focuses on knowledge discovery in datasets with fuzzy rough sets. After analyzing the previous works on knowledge discovery with fuzzy rough sets, we introduce formal concepts of attribute reduction with fuzzy rough sets and completely study the structure of attribute reduction

Three-valued logics, uncertainty management and rough sets

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets

Uncertainty Management of Intelligent Feature Selection in Wireless Sensor Networks

Wireless sensor networks (WSN) are envisioned to revolutionize the paradigm of monitoring complex real-world systems at a very high resolution. However, the deployment of a large number of unattended sensor nodes in hostile environments, frequent changes of environment dynamics, and severe resource constraints pose uncertainties and limit the potential use of WSN in complex real-world applications. Although uncertainty management in Artificial Intelligence (AI) is well developed and well investigated, its implications in wireless sensor environments are inadequately addressed. This dissertation addresses uncertainty management issues of spatio-temporal patterns generated from sensor data. It provides a framework for characterizing spatio-temporal pattern in WSN. Using rough set theory and temporal reasoning a novel formalism has been developed to characterize and quantify the uncertainties in predicting spatio-temporal patterns from sensor data. This research also uncovers the trade-off among the uncertainty measures, which can be used to develop a multi-objective optimization model for real-time decision making in sensor data aggregation and samplin