This research introduces fuzzy neutrosophic prime ideals in BCK-algebras, highlighting their uniqueness.
In this research paper, we introduce and analyze the notion of fuzzy neutrosophic prime ideals (FNPIs) in a commutative BCK-algebra K. It represents a further extension of prime ideals in the context of fuzzy neutrosophic sets. We provide an example that shows that not every fuzzy neutrosophic ideal of a commutative BCK-algebra K is a FNPI of K. We also prove that a fuzzy neutrosophic set of K is a FNPI of K if, for all a,b,c ∈ [0,1], the upper (a,b)-level cut and lower c-level cut are prime ideals of K.
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Satyanarayana et al. (2025) studied this question.
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