MINIMAL INTUITIONISTIC GENERAL L-FUZZY AUTOMATA

Abstract

In this paper we present an intuitionistic general L-fuzzy automaton (IGLFA) based on lattice valued intuitionistic fuzzy sets [2].   In this note, we define (α, β)-language, (α, β)-complete, (α, β)-accessible, (α, β)-reduced for an IGLFA over a bounded complete lattice L, where α, β ∈ L and α ≤_L N (β).  In particular, we prove a theorem which is generalization of Myhill-Nerode theorem in ordinary deterministic automata.  In other words for any recognizable (α, β)-language over a bounded complete lattice L, there exist minimal (α, β)-complete and deterministic IGLFA, which preserve (α, β)-language, where α, β ∈ L and α ≤_L N (β).  Also, we show that for any given (α, β)-language \(\mathcal{L}\), the minimal (α, β)-complete and deterministic IGLFA recognizing \(\mathcal{L}\) is isomorphic with threshold (α, β) to any (α, β)-complete, (α, β)-accessible, deterministic, (α, β)-reduced IGLFA recognizing \(\mathcal{L}\).  Moreover, we give some examples to clarify these notions.  Finally, by using these notions, we give some theorems and obtain some results.