The Limit Theory Of Fuzzy Complex Variables

This paper mainly deals with the limit theory of fuzzy complex number. As the grounded theory, we discusses the characters of convergence in uniform, convergence in level sets and convergence in graphs of sequences of the complex fuzzy number and this three convergence's correlations, based on the convergence of the fuzzy sets. Firstly, we obtain the good result on the convergence in graphs, and prove that above three convergences are equivalent in some suitable condition. Our result is not intersecting or containing in the result of the paper [10,12]. During the proof, we make good use of the properties of the continuous fuzzy complex number, which is innovating in some extent. Secondly, the convergence of the fuzzy complex series and the fixed point theorem of fuzzy mappings are studied. On the other hand, the necessary and sufficient conditions for fuzzy complex series are discussed, for example, the criterion of the judgment and the corrective principle. After that, by introducing the partial ordering of the fuzzy complex number, we prove that there exists one fixed point at least if it satisfies some conditions. And also this paper gives the conditions for thefuzzy complex mapping which existing the maximal and the minimal fixed point, generalizing the result of the [16]. It can be seen that the method has been improved in compared with the method of paper [16].