Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 Articles in Press 2025 12 01 Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures 12478 10.30473/coam.2025.75088.1320 EN Roohallah Daneshpayeh Department of Mathematics‎, ‎Payame Noor University (PNU)‎, Tehran, ‎Iran Sirous Jahanpanah Department of Mathematics‎, ‎Payame Noor University (PNU)‎, Tehran, ‎Iran Journal Article 2025 07 07 This paper offers the idea of (anti) (m‎, ‎n)-fuzzy BL-subalgebras as a novel extension of classical BL-algebras within the fuzzy mathematical framework. ‎The proposed structures generalize various types of fuzzy subalgebras, including (anti) intuitionistic, (anti) Pythagorean, (anti) Fermatean, and (anti) q-rung orthopair fuzzy BL-subalgebras for q >= 1. Fundamental algebraic properties and equivalent characterizations of (m,n)-fuzzy BL-subalgebras are established through the notion of value-cuts. Furthermore, the concept of power-implication preserving (PIP) BL-algebras is introduced, and it is shown that a PIP BL-algebra exists for every prime number. Several closure properties of (m,n)-fuzzy BL-subalgebras under combination operations are also derived within this framework. From an applied perspective, the developed theoretical results can serve as a mathematical foundation for modeling and reasoning in fuzzy control systems and optimization processes, particularly in decision-making environments characterized by uncertainty and graded information. https://mathco.journals.pnu.ac.ir/article_12478_5a67698f3cb54c89612a8d90bd1507ab.pdf