Some Properties Of I-convergence On The Sequence

The convergence theory of fuzzy numbers is an important part of fuzzy anal-ysis. According to the practical requirement, the researchers have proposed the D-convergence, level convergence, statistical convergence and I-convergence. The main purpose of this paper is to study I-convergence and display some im-portant properties. More precisely,Firstly, by giving the definition of I-monotonicity and I-boundness of the fuzzy number sequence, we give the decomposition theorem of I-mono-tonicity sequence and I-oundness sequence. Meanwhile, we prove that the I-monotonicity bounded fuzzy number sequence is I-level convergent.Secondly, we introduce the notions of I-limit inferior, I-limit superior and I-cluster point of fuzzy number sequence and discuss the relationship between them. Under the suitable conditions, the conclusions which the I-superior limit is the maximal I-cluster point and I-inferior limit is the minimal I-cluster point are proved.Thirdly, we shall show that the I-onvergence of the fuzzy number se-quence is equivalent to the uniform I-onvergence of the real function sequences, which consists of the left and right endpoints of level sets of the same fuzzy num-ber sequence. We also show the consistency between the level I-onvergence of the fuzzy number sequence and the I-onvergence of real function sequence which is defined by the left and right endpoints of α-evel set of the same fuzzy number sequence. At the end, we get the conclusion that the fuzzy number se-quence is level I-auchy sequence if and only if it is level I-onvergence.