关键词: 区间集, 正常蕴涵算子, 剩余格, 弱S-蕴涵

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