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This article establishes and explores bipolar fuzzy dot β-subalgebras, suggesting new connections and insights.
In this article, we present the concepts of bipolar fuzzy dot β ‐subalgebras (BFD β ‐SAs) within the context of β ‐algebra and explore their associated characteristics. We establish the connections between a BF β ‐SA and a BFD β ‐SA. We examine the homomorphic and inverse images of BFD β ‐SAs and prominent results. Furthermore, we provide insights into the Cartesian product of BFD β ‐SAs and derive some related results. Finally, we consider the bipolar fuzzy dot relations on β ‐subalgebras and explore their related characteristics.
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Derseh et al. (2026) studied this question.
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