Rough 3-valued algebras

  • Authors:

  • Jian-Hua Dai

  • Affiliations:

  • Institute of Artificial Intelligence, Zhejiang University, Hangzhou 310027, PR China and Center for the Study of Language and Cognition, Zhejiang University, Hangzhou 310028, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

Quantified Score

Hi-index 0.07

Visualization

Abstract

Rough set theory is an important tool for dealing with granularity and vagueness in information systems. This paper studies a kind of rough set algebra. The collection of all the rough sets of an approximation space can be made into a 3-valued Lukasiewicz algebra. We call the algebra a rough 3-valued Lukasiewicz algebra. In this paper, we focus on the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras. Firstly, we examine whether the rough 3-valued Lukasiewicz algebra is an axled 3-valued Lukasiewicz algebra. Secondly, we present the condition under which the rough 3-valued Lukasiewicz algebra is also a 3-valued Post algebra. Then we investigate the 3-valued Post subalgebra problem of the rough 3-valued Lukasiewicz algebra. Finally, this paper studies the relationship between the rough 3-valued Lukasiewicz algebra and the Boolean algebra constructed by all the exact sets of the corresponding approximation space.