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Spectral clustering is one of the most effective methods of data mining, in which the adjacency matrix is constructed by using the similarity matrix. In this paper, to extend spectral clustering method for uncertain data clustering, we propose a new spectral clustering method based on JS-divergence. In the proposed method, the JS-divergence is used to construct the adjacency matrix in the spectral...
One of the essences of fuzzy logic is how fuzzy variables and fuzzy expressions may be transformed into precise quantities and rigorous models in fuzzy inferences. This paper presents a denotational mathematical structure and methodology for modeling fuzzy qualifications and quantifications in cognitive informatics, soft computing, and computational intelligence. Fuzzy qualifications and quantifications...
A fuzzy inference is an extended form of formal inferences that enables symbolic and rigorous evaluation of the degree of a confidential level for a given causality on the basis of fuzzy expressions constructed with fuzzy sets and fuzzy logic operations. Fuzzy inferences are powerful denotational mathematical means for rigorously dealing with degrees of matters, uncertainties, and vague semantics...
Granular computing provides a new perspective on computing architectures and behaviors. This paper presents a recent development in denotational mathematics known as granular algebra, which enables a rigorous treatment of computing granules as a generic abstract mathematical structure and granular behaviors as a set of algebraic operations. An abstract granule is modeled as a mathematical entity that...
A formal theory for abstract concepts and knowledge manipulation is created by Wang recently known as concept algebra. Concept algebra is an abstract mathematical structure for the formal treatment of concepts and their algebraic relations, operations, and associative rules for composing complex concepts, which provides a denotational mathematic means for knowledge system representation and manipulation...
On-line knowledge discovery is an important area of knowledge engineering. This paper develops a visualized concept network explorer and a semantic analyzer to locate, capture, and refine queries based on concept algebra. A graphical interface is built using concept and semantic models to refine users' query structures. This tool kit can generate a structured XML query package that accurately express...
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