布尔代数的犹豫模糊理想

The Hesitant Fuzzy Ideals in Boolean Algebra

将犹豫模糊集的思想和方法应用于布尔代数,提出了犹豫模糊理想的概念,给出了一些性质和若干等价刻画;定义了犹豫模糊集下直积和投影的概念,研究了布尔代数犹豫模糊理想与直积布尔代数犹豫模糊理想之间的关系,得到了HR×R′的犹豫模糊理想可分解为R,R′犹豫模糊理想直积的充分必要条件;最后定义R/HA上的三种运算,证明了当HA是布尔代数R的犹豫模糊真理想时,则R/HA是布尔代数。

In this paper, by applying the idea and method hesitant fuzzy set theory to Boolean algebra, we propose the concept of hesitant fuzzy ideal of Boolean algebra. And some properties of hesitant fuzzy ideal are discussed and several equivalent characterization of hesitant fuzzy ideal are given. We also introduce the nation of direct product and projection under the hesitating fuzzy set. The relationships between hesitant fuzzy ideals of Boolean algebra and hesitant fuzzy ideals of direct product Boolean algebra are discussed. And we obtain the sufficient and necessary conditions, which hesitant fuzzy ideals of HR×R′ can be decomposed as direct product of hesitant fuzzy ideals in R and R′. Finally, the three operations is defined in R/HA, and we prove R/HA also be Boolean algebra as HA is hesitant fuzzy real ideals of Boolean algebra.