Journal of Frontiers of Computer Science and Technology ›› 2013, Vol. 7 ›› Issue (3): 282-288.DOI: 10.3778/j.issn.1673-9418.1206050

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A Weak S-Implication on Interval Sets

XUE Zhan'ao1+, CHENG Huiru1, HUANG Haisong2, LI Yuejun1   

  1. 1. College of Computer and Information Technology, Henan Normal University, Xinxiang, Henan 453007, China
    2. Public Basic Course Education Department, Wanfang College of Science and Technology, Henan Polytechnic University, Zhengzhou 451400, China
  • Online:2013-03-01 Published:2013-03-05

区间集上的弱S-蕴涵

薛占熬1+,程惠茹1,黄海松2,李跃军1   

  1. 1. 河南师范大学 计算机与信息技术学院,河南 新乡 453007
    2. 河南理工大学 万方科技学院 公共基础课教学部,郑州 451400

Abstract: The theory of interval sets provides an effective method for expressing fuzzy information. Researching implication operators is a key step for fuzzy logic system. Thus it is very important to construct implication operators on interval sets. This paper constructs a new implication operator of interval sets, named as weak S-implication. Meanwhile, it proves the regularity, monotonicity and other important properties of weak S-implication. Finally, it proves that the residuated lattice is constituted under the S-implication operator on interval sets. This research provides a theoretical foundation for the logic system of interval sets.

Key words: interval sets, normal implication operators, residuated lattice, weak S-implication

摘要: 区间集是表达模糊信息的一种有效方法,蕴涵算子的研究是逻辑研究的关键,在区间集上构造蕴涵具有重要的研究价值。在区间集上构造了一个新的区间集弱S-蕴涵,证明了其正则性、单调性以及其他一些重要性质。最后证明了由它可构造剩余格,这为区间集的逻辑系统的建立提供了理论基础。

关键词: 区间集, 正常蕴涵算子, 剩余格, 弱S-蕴涵