CAJ | 학술논문

格蕴涵代数是一种处理不确定或不精确信息的格值逻辑系统，区间集是在近似推理、模糊控制等领域中有着广泛应用的重要研究方向。本文是在区间集上，给出了区间补、区间伪补和区间蕴涵三个运算的概念，证明了<I (2U )，?，?， c ，*>是有余格。与此同时，我们在区间集上重新构造了格蕴涵代数<I (2U )，?，?， c ，*，?>，且讨论了该格蕴涵代数的一些特性，如等价性质，等于全集的性质，不等式性质和条件性质等等。
격온함대수시일충처리불학정혹불정학신식적격치라집계통，구간집시재근사추리、모호공제등영역중유착엄범응용적중요연구방향。본문시재구간집상，급출료구간보、구간위보화구간온함삼개운산적개념，증명료<I (2U )，?，?， c ，*>시유여격。여차동시，아문재구간집상중신구조료격온함대수<I (2U )，?，?， c ，*，?>，차토론료해격온함대수적일사특성，여등개성질，등우전집적성질，불등식성질화조건성질등등。
Lattice implication algebra is a kind of lattice-valued logic systems to deal with uncertain or imprecise information, and interval set is an important research direction, which has been widely applied in approximate reasoning, fuzzy control, and so on. In this paper, the operations are redefined on the interval sets, which are the interval complement, the interval pseudo-complement and the interval implication. Furthermore, algebras system <I(2U),?,?,c,*> is proved complemented lattice. At the same time, the Lattice Implication Algebras <I(2U),?,?,c,*,?> is reconstructed on the internal sets, and some features are discussed, such as equivalent, equal to complete corks, inequality and conditions properties.