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1

Relational Operations and Uncertainty Measure in Rough Relational Database

Jiang F., Sui Y., Cao C., Wan X., Du J.

Fundamenta Informaticae

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2013

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Vol. 123, nr 4

401--416

EN

The traditional relational database model (RDM) is not effective for dealing with imprecise and uncertain data as it deals with precise and unambiguous data. Hence, Beaubouef et al. proposed the rough relational database model (RRDM) for the management of uncertainty in relational databases. Beaubouef et al. defined the corresponding rough relational operators in rough relational databases as in ordinary relational databases. And to give an effective measure of uncertainty in rough relational databases, they defined the rough relation entropy. In this paper, we further discuss the issues of relational operations and uncertainty measure in rough relational databases. We give some new definitions for rough relational operators and rough relation entropy in rough relational databases. Furthermore, we discuss the basic properties of rough relational operators and rough relation entropy, as well as the connections between rough relational operators and rough relation entropy.

2

A new hybrid finite element approach for three-dimensional elastic problems

Cao C., Qin Q. H., Yu A.

Archives of Mechanics

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2012

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Vol. 64, nr 3

261-261

EN

A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.

3

Relational Contexts and Relational Concepts

Jiang F., Sui Y., Cao C.

Fundamenta Informaticae

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2010

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Vol. 99, nr 3

293-314

EN

Formal concept analysis (FCA) is a mathematical description and theory of concepts implied in formal contexts. And the current formal contexts of FCA aim to model the binary relations between individuals (objects) and attributes in the real world. In the real world we usually describe each individual by some attributes, which induces the relations between individuals and attributes. But there also exist many relations between individuals, for instance, the parent-children relation in a family. In this paper, to model the relations between individuals in the real world, we propose a new context - relational context for FCA, which contains a set U of objects and a binary relation r on U. Corresponding to the formal concepts in formal contexts, we present different kinds of relational concepts in relational contexts, which are the pairs of sets of objects. First we define the standard relational concepts in relational contexts. Moreover, we discuss the indirect relational concepts and negative relational concepts in relational contexts, which aim to concern the indirection and negativity of the relations in relational contexts, respectively. Finally, we define the hybrid relational concepts in relational contexts, which are the combinations of any two different kinds of relational concepts. In addition, we also discuss the application of relational contexts and relational concepts in the supply chain management field.

4

Normalized-scale Relations and Their Concept Lattices in Relational Databases

Lei Y., Sui Y., Cao C.

Fundamenta Informaticae

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2009

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Vol. 93, nr 4

393-409

EN

Formal Concept Analysis (FCA) is a valid tool for data mining and knowledge discovery, which identifies conceptual structures from (formal) contexts. As many practical applications involve non-binary data, non-binary attributes are introduced via a many-valued context in FCA. In FCA, conceptual scaling provides a complete framework for transforming any many-valued context into a context, in which each non-binary attribute is given a scale, and the scale is a context. Each relation in relational databases is a many-valued context of FCA. In this paper, we provide an approach toward normalizing scales, i.e., each scale can be represented by a nominal scale and/or a set of statements. One advantage of normalizing scales is to avoid generating huge (binary) derived relations. By the normalization, the concept lattice of a derived relation is reduced to a combination of the concept lattice of a derived nominal relation and a set of statements. Hence, without transforming a relation into a derived relation, one can not only determine concepts of the derived relation from concepts of given scales, but also determine concepts of the derived relation from concepts of a derived nominal relation and a set of statements. The connection between the concept lattice of a derived nominal relation and the concept lattice of a derived relation is also considered.

5

Formal Concept Analysis in Relational Database and Rough Relational Database

Jiang F., Sui Y., Cao C.

Fundamenta Informaticae

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2007

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Vol. 80, nr 4

435-451

EN

Since its foundation in the early 1980's, Formal Concept Analysis (FCA) has been used in many applications in data analysis, information retrieval, and knowledge discovery. In this paper, we suggest to exploit the framework of relational database model (RDM) and rough relational database model (RRDM) for Formal Concept Analysis. The basic idea is as follows. We firstly treat any relation (R,A) of RDM as a many-valued context of FCA. But for the rough relations of RRDM, we define a special kind of many-valued context - rough-relational context in FCA (In this kind of context, every attribute value is a subset, but not an element, of the corresponding attribute domain), and treat any rough relation (R,A) of RRDM as a rough-relational context of FCA. Correspondingly, the definitions for concepts or rough concepts in context or rough-relational context (R,A) are given. The basic properties about these concepts or rough concepts in (R,A) are also discussed.