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