Abstract: A new application of a genuinely six-qubit entangled state is studied for bidirectional quantum controlled remote state preparation. In this protocol, two distant parties can simultaneously and deterministically exchange their states under a third remote parties in such a way that it cannot succeed without permission of the controller. A genuinely six-qubit entangled state as the original non-local quantum resource is priori shared among the parties. Appling the hesitant fuzzy set to the filter and ideal theory of [BR0] algebras, the hesitant fuzzy filter and hesitant fuzzy ideal theory of [BR0] algebras are preliminary established. The concepts of hesitant fuzzy filters, hesitant fuzzy ideals and hesitant fuzzy prime ideals of [BR0] algebras are introduced, and their basic properties are studied. The sufficient and necessary conditions for hesitant fuzzy sets to be hesitant fuzzy filters （hesitant fuzzy ideals） are given. It is proven that hesitant fuzzy filters, hesitant fuzzy ideals and hesitant fuzzy prime ideals are closed for intersection. Finally, it is pointed out that hesitant fuzzy filters, hesitant fuzzy ideals and hesitant fuzzy prime ideals are invariant under [BR0] algebra isomorphism.

Key words: BR0 algebra, hesitant fuzzy filter, hesitant fuzzy ideal, hesitant fuzzy prime ideal

摘要： 将犹豫模糊集应用于[BR0]代数的滤子和理想理论中，初步建立[BR0]代数的犹豫模糊滤子与理想理论。引入了[BR0]代数的犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想的概念，研究它们的基本性质，给出了[BR0]代数的犹豫模糊集成为犹豫模糊滤子（犹豫模糊理想）的条件，证明了[BR0]代数的犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想关于交运算具有封闭性，指出了犹豫模糊滤子、犹豫模糊理想和犹豫模糊素理想在[BR0]代数同构下的不变性。

关键词: BR0代数, 犹豫模糊滤子, 犹豫模糊理想, 犹豫模糊素理想