粗糙集是一个近似集合区间,在对粗糙集代数结构研究中考虑到它与信任函数和似然函数、可能性和必然性测度相关, 它们之间存在一个通用的代数框架-区间结构.文章在分配BZ-格上建立了区间结构,定义了分配BZ-格上的一对对偶映射,并讨论了该映射的性质,最后分析了基本分配函数和区间代数的关系.研究成果进一步拓展了区间代数、粗糙集和分配BZ-格理论.

Rough set is an interval of approximate sets in the study of its algebra structure. It is related to belief and plausibility function, possibility and necessity measurement among which a common algebras framework called interval structure exist. In this paper, interval structure is established based on the distributive BZ lattice. A couple of dual mapping is defined on the distributive BZ lattice, and the natures of the mapping are discussed in detail. Meanwhile, the relationship between the basic distribution function and interval algebra is analyzed. The research results broadened the theories of the interval algebra, rough set and the distributive BZ lattice.