粗糙逻辑系统RSL和模糊逻辑系统Luk

Xiao-hong Zhang, Feng Zhu
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引用次数: 6

摘要

从粗糙集对(低逼近、上逼近)的描述出发,通过对Ref.[1]方法的改进,引入了一种新的粗糙蕴涵算子,研究了该粗糙蕴涵算子的一些代数性质,并将这些结果推广到正则双Stone代数上,证明了以下重要结果:具有新粗糙蕴涵算子的正则双Stone代数是mv -代数。进一步构造了一个粗糙逻辑系统RSL,其示意图为粗糙集和扩展正则双Stone代数。引入RSL-代数的概念,证明了RSL的完备性定理。最后讨论了粗糙逻辑RSL与模糊逻辑Luk(连续值tukasiewicz逻辑系统)之间的关系。
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Rough logic system RSL and fuzzy logic system Luk
From the description of the pairs (low approximation,upper approximation) of rough sets,a new rough implication operator is introduced by modifying the method by Ref.[1],some algebraic properties of this rough implication operator are investigated,and these results are generalized to regular double Stone algebras and the following important result is proved: the regular double Stone algebra with the new rough implication operator is an MV-algebra.Further more a rough logic system RSL is constructed,its schematic is rough sets and extensional regular double Stone algebras.The completeness theorem of RSL is proved by introducing the notion of RSL-algebra.Finally,the relationship between rough logic RSL and fuzzy logic Luk(continuous-valued tukasiewicz logic system) is discussed.
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来源期刊
电子科技大学学报
电子科技大学学报 Engineering-Electrical and Electronic Engineering
CiteScore
1.40
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0.00%
发文量
7228
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