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Research & Reviews: Discrete Mathematical Structures Original Research

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

  1. Chethana N.S Department of Mathematics, Central University of Karnataka
  2. Mohammed Almakki School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai International Academic City
  3. Mohammed El Khider Department of General Undergraduate Curriculum Requirements, University of Dubai

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

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