Abstract
This paper deals with the study of the special lattices of rough algebras. We discussed the basic properties such as the rough distributive lattice; the rough modular lattice and the rough semi-modular lattice etc., some results of lattice are generalized in this paper. The modular lattice of rough algebraic structure can provide academic base and proofs to analyze the coverage question and the reduction question in information system.
Highlights
It is generally known that the order and the partial order set theory were widely applied in the discrete mathematics and fuzzy mathematics
This paper deals with the study of the special lattices of rough algebras
We discussed the basic properties such as the rough distributive lattice; the rough modular lattice and the rough semi-modular lattice etc., some results of lattice are generalized in this paper
Summary
It is generally known that the order and the partial order set theory were widely applied in the discrete mathematics and fuzzy mathematics. The modular lattice of rough algebraic structure can provide academic base and proofs to analyze the coverage question and the reduction question in information system. We give several special lattices of rough algebras that we discuss in this article; for instance, we prove that a lattice is necessary and sufficient condition of the rough semi-modular lattice. We will describe a lattice definition and we introduce rough approximation spaces.
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