BL-代数的反犹豫模糊子代数

The Anti-Hesitant Fuzzy Subalgebras in BL-Algebras

初步将犹豫模糊集应用于BL-代数中,引入了BL-代数中反犹豫模糊子代数的概念,讨论它的基本性质,得到若干等价刻画;根据犹豫模糊集的反扩张定理,讨论反犹豫模糊子代数的像与原像的关系;最后根据犹豫模糊集反直积的定义,研究反犹豫模糊子代数与直积BL代数的反犹豫模糊子代数之间的关系,证明了乘积BL代数的犹豫模糊子集是反犹豫模糊子代数的必要条件.

The hesitant fuzzy set was initially applied to the BL-algebras and the concept of anti-hesitant fuzzy subalgebras was introduced and some properties and equivalent characterizations of anti-hesitant fuzzy sub-algebras were obtained.Based on the anti-expansion principle in anti-hesitant fuzzy set,some properties between homomorphic image and homomorphic inverse image of anti-hesitant fuzzy sub-algebras were investigated;Finally,based on the concept of anti-direct product in the hesitant fuzzy set,the relationships between anti-hesitant fuzzy sub-algebras in direct product BL-algebras and anti-hesitant fuzzy sub-algebras in BL-algebras were studied.The necessary condition of the hesitant fuzzy subset of the product BL algebra being a anti-hesitant fuzzy sub-algebras is proved.