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Daneshpayeh, Roohallah, Jahanpanah, Sirous. (1404). Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures. فصلنامه علمی زیست فناوری گیاهان زراعی, (), -. doi: 10.30473/coam.2025.75088.1320
Roohallah Daneshpayeh; Sirous Jahanpanah. "Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures". فصلنامه علمی زیست فناوری گیاهان زراعی, , , 1404, -. doi: 10.30473/coam.2025.75088.1320
Daneshpayeh, Roohallah, Jahanpanah, Sirous. (1404). 'Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures', فصلنامه علمی زیست فناوری گیاهان زراعی, (), pp. -. doi: 10.30473/coam.2025.75088.1320
Daneshpayeh, Roohallah, Jahanpanah, Sirous. Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures. فصلنامه علمی زیست فناوری گیاهان زراعی, 1404; (): -. doi: 10.30473/coam.2025.75088.1320

Generalized (m,n)-Fuzzy BL-Subalgebras: Algebraic Foundations, Power-Implication Structures

Control and Optimization in Applied Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 آذر 1404    اصل مقاله (362.98 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2025.75088.1320
نویسندگان
Roohallah Daneshpayeh* ؛ Sirous Jahanpanah
Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎Iran.‎
چکیده
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.

تازه های تحقیق
  • Introduces the new notion of (anti) (m,n)-fuzzy BL-subalgebras, extending classical BL-algebras and unifying several existing fuzzy algebraic structures, including intuitionistic, Pythagorean, Fermatean, and q-rung orthopair fuzzy BL-subalgebras.
  • Establishes fundamental algebraic properties and equivalent characterizations of (m,n)-fuzzy BL-subalgebras through value-cut techniques, linking fuzzy semantics with crisp algebraic representations.
  • Develops the concept of power-implication preserving (PIP) BL-algebras, proving the existence of a PIP BL-algebra for every prime number and revealing a notable interaction between fuzzy algebra and number theory.
  • Demonstrates several closure properties of (m,n)-fuzzy BL-subalgebras under combination operations such as intersection and union, ensuring algebraic consistency within the proposed framework.
  • Introduces and analyzes (m,n)-fuzzy nil radical BL-subalgebras, with results showing stability of these structures under homomorphic images.
  • Provides a mathematical foundation suitable for applications in fuzzy control, optimization, and decision-making systems, particularly in environments involving uncertainty and graded information.
کلیدواژه‌ها
Fuzzy optimization؛ Fuzzy logic؛ PIP BL-algebra‎؛ (m,‎n)-fuzzy BL-subalgebra‎؛ ‎(m‎,‎n)-fuzzy nil radical
مراجع

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