This paper defines (fq, hq)-derivations and explores their algebraic properties in BP-algebras, highlighting their implications for information systems.
This paper introduces and investigates the concept of (fq, hq)-derivations in BP-algebras, extending the existing framework of fq-derivations by incorporating two endomorphisms and a fixed element. We formally define inside and outside (fq, hq)-derivations, as well as left-right and right-left variants, and establish several algebraic properties characterizing their behavior. Illustrative examples are provided to demonstrate their validity and distinguish them from classical derivations. Fundamental theorems are proved, including regularity conditions, identity behavior, and commutative properties of the involved endomorphisms. These results not only generalize previous findings but also enhance the theoretical understanding of non-classical derivations in algebraic structures, with potential implications for logic, fuzzy computation, and information systems.
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Muangkarn et al. (2025) studied this question.
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