On compositions of (L-fuzzy) automata: A categorical approach

Abstract

This paper studies different compositions of (L-fuzzy) automata by using the notions from category theory, where L is a complete residuated lattice. Specifically, we introduce four different categories of (L-fuzzy) automata with morphisms as crisp relations and L-fuzzy relations, and show that each category is a symmetric monoidal with a product, coproduct, internal monoid, and comonoid. Such categorical study advances the existing categories because of the choice of morphisms. Also, among these compositions, the monoidal description of these categories further enriches the more established fuzzy automata theory.