CAJ | 학술논문

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.
구간집시표체모호신식적일충유효방법,온함산자적연구시라집연구적관건,재구간집상구조온함구유중요적연구개치.재구간집상구조료일개신적구간집약S-온함,증명료기정칙성、단조성이급기타일사중요성질.최후증명료유타가구조잉여격,저위구간집적라집계통적건립제공료이론기출.
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.