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

  • Authors:

  • Zhengjiang Wu;Tianrui Li;Keyun Qin;Da Ruan

  • Affiliations:

  • (Correspd.) (Also working: School of Computer Science and Technology, Henan Polytechnic Unviersity, Jiaozuo 454001, China) School of Information Science and Technology, Southwest Jiaotong Universi ...;School of Computer Science and Technology, Southwest Jiaotong University, Chengdu 610031, China. trli@swjtu.edu.cn;College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China. qinkeyun@swjtu.edu.cn;(Also working: Department of Applied Mathematics & Computer Science, Ghent University, 9000 Gent, Belgium) Belgian Nuclear Research Centre (SCK••CEN), Boeretang 200, 2400 Mol, Belgium. ...

  • Venue:
  • Fundamenta Informaticae - Knowledge Technology
  • Year:
  • 2011

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Abstract

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.