Idempotent Semiring Path Algebras and Fuzzy Dominance Automata for Multi-State Communication Reliability

Year : 2026 | Volume : 13 | Issue : 02 | Page : 07 14
By

Chethana N.S,

Mohammed Almakki,

Mohammed El Khider,

  1. Student, Department of Mathematics, Central University of Karnataka, Karnataka, India
  2. Assistant Professor, School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai International Academic City, Dubai, United Arab Emirates
  3. Assistant Professor, Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai, United Arab Emirates

Abstract

A semiring-based theory is proposed for multi-state communication reliability with fuzzy dominance constraints. Links are weighted in the max-product semiring, while nodes carry dominance coefficients and operating states that modulate admissible transitions in a weighted automaton. The paper derives semiring matrix products, Kleene closures, fixed point equations, congestion-regularized path scores, and reliability inequalities. A fuzzy dominance automaton is introduced so that route selection depends not only on link reliability but also on state compatibility and successor-node quality. The resulting recursion is monotone, bounded, and directly computable as a semiring closure. A stylized communication example shows that the dominance-aware automaton selects more robust routes than link-only rules, especially when state mismatch and congestion are relevant. The work contributes a discrete algebraic framework for uncertain communication systems that matches the scope of mathematical-structures research while drawing heavily on recent fuzzy graph and communication studies.

Keywords: Idempotent semiring, weighted automata, fuzzy dominance, communication reliability, path algebra, kleene closure

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article: Chethana N.S, Mohammed Almakki, Mohammed El Khider. Idempotent Semiring Path Algebras and Fuzzy Dominance Automata for Multi-State Communication Reliability. Research & Reviews: Discrete Mathematical Structures. 2026; 13(02):07-14.
How to cite this URL: Chethana N.S, Mohammed Almakki, Mohammed El Khider. Idempotent Semiring Path Algebras and Fuzzy Dominance Automata for Multi-State Communication Reliability. Research & Reviews: Discrete Mathematical Structures. 2026; 13(02):07-14. Available from: https://journals.stmjournals.com/rrdms/article=2026/view=250983

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Regular Issue Subscription Original Research
Volume 13
Issue 02
Received 13/04/2026
Accepted 19/05/2026
Published 30/05/2026
Publication Time 47 Days

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