Abstract
Using the notion of bipolar-valued fuzzy soft set, the concepts of bipolar-valued fuzzy soft (weak, [Formula: see text]-weak, strong) hyper BCK ideal are introduced, and related properties and relations are investigated. Characterizations of bipolar-valued fuzzy soft (weak) hyper BCK ideal are considered. Conditions for a bipolar-valued fuzzy soft weak hyper BCK ideal to be a bipolar-valued fuzzy soft [Formula: see text]-weak hyper BCK ideal are provided. Conditions for a bipolar-valued fuzzy soft set to be a bipolar-valued fuzzy soft strong hyper BCK ideal are displayed.
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