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2002•Chinese Journal of ComputersRequires access

The Minimization of Axiom Groups of Rough Set

Sun Hui

Open publisher page 8 citations

Abstract

Rough set axiomatization is one aspect of rough set theory study, and the purpose is to get dependable and minimal axiom groups. Some papers reported the significative development about the research, and gave some rough set axiom groups. But the ideal goal isn't reached on the formal expressing, minimizing and reliability proving of rough set axiom groups. This paper discusses the minimization of axiom groups of rough set based on some literatures.First, two more essential axiom groups are derived and each reliability of the two axiom groups is proved respectively, after removing the connotative redundancy of existing axioms groups; second, the paper presents a new concept of minimal axiom group of rough set and proves that the two axiom groups are minimal; and third, a typical axiom group S5 of rough set is discussed and its reliability and minimization are proved.

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What this paper is about

Rough set axiomatization is one aspect of rough set theory study, and the purpose is to get dependable and minimal axiom groups. Some papers reported the significative development about the research, and gave some rough set axiom groups. But the ideal goal isn't reached on the formal expressing, minimizing and reliability proving of rough set axiom groups. This paper discusses the minimization of axiom groups of rough set based on some literatures.First, two more essential axiom groups are derived and each reliability of the two axiom groups is proved respectively, after removing the connotative redundancy of existing axioms groups; second, the paper presents a new concept of minimal axiom group of rough set and proves that the two axiom groups are minimal; and third, a typical axiom group S5 of rough set is discussed and its reliability and minimization are proved.

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Available abstract

Rough set axiomatization is one aspect of rough set theory study, and the purpose is to get dependable and minimal axiom groups. Some papers reported the significative development about the research, and gave some rough set axiom groups. But the ideal goal isn't reached on the formal expressing, minimizing and reliability proving of rough set axiom groups. This paper discusses the minimization of axiom groups of rough set based on some literatures.First, two more essential axiom groups are derived and each reliability of the two axiom groups is proved respectively, after removing the connotative redundancy of existing axioms groups; second, the paper presents a new concept of minimal axiom group of rough set and proves that the two axiom groups are minimal; and third, a typical axiom group S5 of rough set is discussed and its reliability and minimization are proved.

Key concepts: Zermelo–Fraenkel set theory, Axiom of choice, Urelement, Axiom, Constructive set theory, Mathematics, Rough set, Axiom independence

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