Rough 3-Valued Łukasiewicz Agebras and MV-Algebras

  • Authors:

  • Jianhua Dai;Xiaochun Liu

  • Affiliations:

  • School of Computer Science and Technology, Zhejiang University, Hangzhou, P.R. China 310027 and Center for the Study of Language and Cognition, Zhejiang University, Hangzhou, P.R. China 310028 and ...;School of Computer Science and Technology, Zhejiang University, Hangzhou, P.R. China 310027 and Qiushi Academy of Advanced Studies, Zhejiang University, Hangzhou, P.R. China 310027

  • Venue:
  • RSKT '09 Proceedings of the 4th International Conference on Rough Sets and Knowledge Technology
  • Year:
  • 2009

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Abstract

Many researchers study rough sets from the point of view of description of the rough set pairs(a rough set pair is also called a rough set), i.e. "lower approximation set, upper approximation set". Dai [4] showed that all the rough sets in an approximation space constructs a 3-valued Łukasiewicz algebra. The constructed algebra is called the rough 3-valued Łukasiewicz algebra. It is shown that a rough 3-valued Łukasiewicz algebra is an MV-algbra in this paper. The direct relation between rough set theory and MV-algebras is constructed. The definition of rough MV-algebras is also given.