Epsilon-removal constructions of fuzzy finite automata based on fuzzy matrices

Abstract The equivalence of different forms of automata provides a lot of convenience for us to solve practical problems. Sometimes, for efficient use of a fuzzy finite automaton, it is preferable to remove all ε-transitions since in general they induce a delay in their using, that is, to create an equivalent fuzzy finite automaton with no ε-transition. An epsilon-removal construction method with fuzzy ε-closure of fuzzy finite automata with ε-transitions over lattice-ordered monoids is proposed in Li et al.(2006). In this paper, we define the fuzzy languages accepted by fuzzy fifinite automata with ε-transitions by fuzzy matrices, fuzzy matrices yield the very compact and intuitive representations of fuzzy finite automata with ε-transitions and often very concise proofs about their languages. Next, based on fuzzy matrices, we propose four epsilon-removal constructions of fuzzy finite automata with ε-transitions over lattice-ordered monoids. Furthermore, the conditions of applications for the four epsilon-removal constructions are discussed and compared in detail, then we study the four epsilon-removal constructions of fuzzy finite automata over more general algebraic structures, such as semirings, and we give some examples to illustrate the applications of the four epsilon-removal constructions.