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Approximation Operators, Binary Relation and Basis Algebra in L-fuzzy Rough Sets

Wu Z., Li T., Qin K., Ruan D.

Fundamenta Informaticae

2011

Vol. 111, nr 1

47-63

Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations.

Synthesis and Evaluation Analysis of the Indicator Information in Nuclear Safeguards Applications by Computing With Words

Liu J., Ruan D., Carchon R.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 3

449-462

This paper aims at the handling and treatment of nuclear safeguard relevant information by using a linguistic assessment approach. This is based on a hierarchical analysis of a State's nuclear activities in a multi-layer structure of the evaluation model. After a hierarchical analysis of the State's nuclear activities on the basis of the IAEA Physical Model, the addressed objective is divided into several less complex levels. The overall evaluation can be obtained step by step from those lower levels. Special emphasis is put on the synthesis and evaluation analysis of the Physical Model indicator information. Accordingly, the aggregation process with the consideration of the different kinds of qualitative criteria is in focus. Especially, the symbolic approach is considered by the direct computation on linguistic values instead of the approximation approach using the associated membership function. In this framework, several kinds of ordinal linguistic aggregation operators are presented and analyzed. The application of these linguistic aggregation operators to the combination of the Physical Model indicator information is provided. An example is given to support and clarify the mathematical formalism.