Rough implication operator based on strong topological rough algebras |
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Authors: | Xiaohong Zhang Yiyu Yao |
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Affiliation: | a Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang Province, PR China b Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 c Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China |
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Abstract: | The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are described, a uniform algebraic depiction of various rough set models are given. Secondly, based on interior and closure operators of a strong topological rough algebra, an implication operator (called rough implication) is introduced, and its important properties are proved. Thirdly, a rough set interpretation of classical logic is analyzed, and a new semantic interpretation of ?ukasiewicz continuous-valued logic system ?uk is constructed based on rough implication. Finally, strong topological rough implication algebra (STRI-algebra for short) is introduced. The connections among STRI-algebras, regular double Stone algebras and RSL-algebras are established, and the completeness theorem of rough logic system RSL is discussed based on STRI-algebras. |
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Keywords: | Rough implication Topological De Morgan algebra Strong topological rough algebra uk" target="_blank">?ukasiewicz logic system ?uk RSL" target="_blank">Rough logic system RSL |
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