| Chen Linshu (陈林书),Wang Jiayang,Li Li,Yang Zhenghua.[J].高技术通讯(英文),2016,22(2):160~169 |
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| Quotient space model based on algebraic structure |
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| DOI：10.3772/j.issn.1006-6748.2016.02.007 |
| 中文关键词: |
| 英文关键词: granular computing, quotient space, congruence closure, quotient operation, upper ( lower ) quotient |
| 基金项目: |
| Author Name | Affiliation | | Chen Linshu (陈林书) | | | Wang Jiayang | | | Li Li | | | Yang Zhenghua | |
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| 中文摘要: |
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| 英文摘要: |
| In the quotient space theory of granular computing, the universe structure is assumed to be a topology, therefore, its application is still limited. In this study, based on the quotient space model, the universe structure is assumed as an algebra instead of a topology. As to obtain the algebraic quotient operator, the granulation must be uniquely determined by a congruence relation, and all the congruence relations form a complete semi-order lattice, which is the theoretical basis of granularities’ completeness. When the given equivalence relation is not a congruence relation, it defines the concepts of upper quotient and lower quotient, and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid. Finally, it presents the algorithms and example of upper quotient and lower quotient. The work extends the quotient space theory from structure, and provides theoretical basis for the combination of the quotient space theory and the algebra theory. |
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