Quotient space model based on algebraic structure |
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Institution: | 1. School of Information Science and Engineering, Central South University, Changsha 410083, P.R.China;School of Computer Science and Engineering, Hunan University of Science and Technology, Xiangtan 411201, P.R.China;2. School of Information Science and Engineering, Central South University, Changsha 410083, P.R.China;3. Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, P.R.China |
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Abstract: | 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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Keywords: | granular computing quotient space congruence closure quotient operation upper (lower) quotient |
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