区间集上的格蕴涵代数、FI-代数、MV-代数的研究

计算机科学 ›› 2010, Vol. 37 ›› Issue (12): 218-223.

区间集上的格蕴涵代数、FI-代数、MV-代数的研究

薛占熬,杜浩翠,尹昊喆，肖运花

(河南师范大学计算机与信息技术学院新乡453007)

出版日期:2018-12-01 发布日期:2018-12-01
基金资助:
本文受河南省重点科技攻关项目(No. 092102210149) ,河南省教育厅自然科学研究计划项目(No. 2009B520015)资助.

Lattice Implication Algebras, FI-algebras, and MV-algebras Based on the Interval Sets

XUE Zhan-ao,DU Hao-cui,YIN Hacr-zhe,XIAO Yun-hua

Online:2018-12-01 Published:2018-12-01

摘要/Abstract

摘要： 区间集是一个新的重要的研究方向，在近似推理、模糊控制等领域中有着广泛的应用。在区间集上，重新定义了区间蕴涵今，构造了格蕴涵代数，讨论了格蕴涵代数的一系列性质。同时在区间集上也重新定义了可换FI-代数和MV-代数，证明了格蕴涵代数、FI-代数和MV-代数3种不同的代数系统是等价的。

关键词: 区间集，格蕴涵代数，可换FI-代数，MV-代数

Abstract: The interval sets arc new important direction of the research, which have been widely applied in approximate reasoning,fuzzy control, and so on. In the interval sets, the new interval implication (→) was redefined, the lattice implication algebras was reconstructed and its properties were discussed. Meanwhile, commutative FI-algebras and MV-algebras also were redefined in the interval sets. Three different algebraic systems were proved to equivalence, which are lattice implication algebras, commutative FI-algebras and MV-algebras.

Key words: Interval sets,Lattice implication algebras,FI-algebras,MV-algebras

薛占熬,杜浩翠,尹昊喆，肖运花. 区间集上的格蕴涵代数、FI-代数、MV-代数的研究[J]. 计算机科学, 2010, 37(12): 218-223. https://doi.org/

XUE Zhan-ao,DU Hao-cui,YIN Hacr-zhe,XIAO Yun-hua. Lattice Implication Algebras, FI-algebras, and MV-algebras Based on the Interval Sets[J]. Computer Science, 2010, 37(12): 218-223. https://doi.org/

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