In this paper, we apply the rough set theory to pseudo-BCK-algebras. As a generalization of pseudo-BCK-algebras, the notions of rough pseudo-BCK-algebras, rough subalgebras and rough pseudo-filters are introduced and ...In this paper, we apply the rough set theory to pseudo-BCK-algebras. As a generalization of pseudo-BCK-algebras, the notions of rough pseudo-BCK-algebras, rough subalgebras and rough pseudo-filters are introduced and some of their properties are discussed in an algebra-like approximation space. Furthermore, we investigate rough subalgebras and rough pseudo-filters in a pseudo-BCK-algebra approximation space. Finally, we give several verification programs of pseudo-BCK-algebras, pseudo-filters and subalgebra.展开更多
The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras...The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra.In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.展开更多
基金Supported by Ningbo Natural Science Foundation Project(Grant No.2013A610100)the Twelfth Five-Year Plan of Zhejiang Province Key Discipline-Computer Application Technology(Grant No.20121114)the Science Foundation Project of Ningbo University(Grant No.XYL13004)
文摘In this paper, we apply the rough set theory to pseudo-BCK-algebras. As a generalization of pseudo-BCK-algebras, the notions of rough pseudo-BCK-algebras, rough subalgebras and rough pseudo-filters are introduced and some of their properties are discussed in an algebra-like approximation space. Furthermore, we investigate rough subalgebras and rough pseudo-filters in a pseudo-BCK-algebra approximation space. Finally, we give several verification programs of pseudo-BCK-algebras, pseudo-filters and subalgebra.
基金The 973 NationalKey BasicResearchand Development Program of China (No .2002CB312106 ) theChinaPostdoctoralScience Foundation (N o.2004035715)+1 种基金 the Science & Technology Program of Zhejiang Province in C hina(N o.2004C31098 )thePostdoctoraSlcienceFoundationofZhejiangProvinceinChina (No .2004-bsh-023).
文摘The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra.In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.
