Abstract: The equivalent characterizations of bipolar-value fuzzy soft subgroup are investigated. The concept of bipolar-value fuzzy normal soft subgroup based on the bipolar-value fuzzy soft subgroup is introduced and in the meantime, some of its properties and equivalent characterizations are discussed. Furthermore, the theorems of soft homomorphic image and pre-image of bipolar-value fuzzy normal soft subgroup are given.

Key words: bipolar-value fuzzy soft set, bipolar-value fuzzy soft subgroup, bipolar-value fuzzy normal soft subgroup, bipolar-value fuzzy soft homomorphism

摘要： 研究了双极值模糊软子群的等价刻画。在双极值模糊软子群的基础上定义了双极值模糊正规软子群，得到了它的一些性质及等价刻画，进一步还研究了在双极值模糊软同态下，双极值模糊正规软子群的像与原像一些性质。

关键词: 双极值模糊软集, 双极值模糊软子群, 双极值模糊正规软子群, 双极值模糊软同态