Efficient Minimization of BL-General Fuzzy Automata via Fuzzy Ideals

We address the problem of minimizing BL-general fuzzy automata (BL-GFA) with respect to a given fuzzy ideal [Formula: see text]. We formalize the notion of [Formula: see text]-equivalence between states, prove that the coarsest [Formula: see text]-stable partition yields a canonical quotient automaton preserving the accepted fuzzy language, and design a partition-refinement algorithm to compute this quotient efficiently. The algorithm runs in time [Formula: see text] and space [Formula: see text], where [Formula: see text] is the number of nonzero fuzzy transitions and [Formula: see text] is the number of states. By integrating fuzzy ideals into a refinement framework, our approach bridges the theoretical foundations of BL-GFA with their practical minimization, providing the first complete and complexity-accurate method for [Formula: see text]-aware state space reduction.