Rough logic system RSL and fuzzy logic system Luk

Xiao-hong Zhang, Feng Zhu
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引用次数: 6

Abstract

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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粗糙逻辑系统RSL和模糊逻辑系统Luk
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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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
自引率
0.00%
发文量
7228
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