为了研究BL-代数的区间值滤子理论,分别引入了区间值直觉模糊滤子、格滤子、素滤子、布尔滤子、蕴涵滤子、正蕴含滤子、超滤子及固执滤子的概念,并研究它们的性质.在区间值直觉模糊集中,区间值直觉模糊滤子、布尔滤子和超滤子分别等价于格滤子、蕴含滤子和固执滤子.在BL-代数中,每个区间值直觉模糊布尔滤子都是一个正蕴含滤子,反之则不必然.给出了区间值直觉模糊正蕴含滤子成为区间值直觉模糊布尔滤子的条件,证明了在BL-代数中区间值直觉模糊超滤子等价于区间值直觉模糊固执滤子.
In order to study the interval-valued intuitionistic fuzzy filter theory of BL-algebras,the notions of interval-valued intuitionistic fuzzy filters,lattice filters,prime filters,Boolean filters,implicative filters,positive implicative filters,ultra filters and obstinate filters are introduced,respectively,and their properties are investigated.In interval-valued intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy filters,Boolean filters,ultra filters are proved to be equivalent to lattice filters,implicative filters,obstinate filters,respectively.Each interval-valued intuitionistic fuzzy Boolean filter is an interval-valued intuitionistic fuzzy positive implicative filter,but the converse may not be true in BL-algebras.The conditions under an interval-valued intuitionistic fuzzy positive implicative filter being an interval-valued intuitionistic fuzzy Boolean filter are constructed.Finally,the intervalvalued intuitionistic fuzzy ultra filter is proved to be equivalent to the interval-valued intuitionnistic fuzzy obstinate filter in BL-algebras.