Abstract: The concepts of disturbing fuzzy finite switchboard state machines and（strong） homomor-phisms of disturbing fuzzy finite-state machines are introduced, and related properties are investigated. After two congruence relations on the set of all words of elements of [Σ] of finite length are given, the quotient structures are discussed. It is showed that the families of corresponding equivalence classes are finite semigroups with identity, and they are homomorphic as semigroups. Eventually, the notions of admissible relations on [Q] and kernels of strong homomorphisms are introduced, and their related properties are studied.

Key words: disturbing fuzzy finite（switchboard） state machine, （strong） homomorphism, congruence relation, admissible relation, kernel

摘要： 引入了扰动模糊有限转换状态机和扰动模糊有限状态机的（强）同态的概念，研究了它们的相关性质。给出了[Σ]的元素构成所有长度有限的词集上的两种同余关系，讨论商结构问题，证明了相应的所有等价类构成具有单位元的有限半群，并且这两个有限半群是同态的。给出了[Q]上容许关系及强同态的核的概念，研究了它们的相关性质。

关键词: 扰动模糊有限（转换）状态机, （强）同态, 同余关系, 容许关系, 核