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Properties of cluster points of sequences of fuzzy real numbers are investigated in the paper. It is shown that some similar theorems like in the case of real sequences hold. On the other hand, some differences from real case are discussed.Keywords Fuzzy real numbers Á Cluster point of sequence of fuzzy numbers PreliminariesThere are two standard ways how to understand the concept of fuzzy real numbers. The first one goes back to Zadeh's pioneering paper see Zadeh (1965) and it is still widely used, see Klement et al. (2000). In this concept fuzzy real numbers are represented as special functions from the set R of all real numbers to the interval ½0; 1 (see Definition 1.2) and crisp real numbers are identified with characteristic functions of corresponding singletons. Ten years later Hutton (1975) introduced another way how to understand fuzzy real line, generalizing the representation of real numbers by Dedekind's cuts. This idea was further developed in many papers and the algebraic and topological structures of the fuzzy real line were investigated by several authors, among others by Lowen (1983Lowen ( , 1984, , , Wang (1988) and Wang and Xiaoyong (2002). In the present paper, we define the concept of cluster point of a sequence of fuzzy real numbers in the Zadeh's sense and we prove some properties similar to that of cluster points of sequences of crisp real numbers.As usual, in the whole paper we will denote by N and R the sets of all positive integers and all real numbers, respectively.Definition 1.1 Let f : R ! ½0; 1: The kernel kerðf Þ of f is given by kerðf Þ ¼ fx 2 Rjf ðxÞ ¼ 1g:The support suppðf Þ of f is given by suppðf Þ ¼ fx 2 Rjf ðxÞ [ 0g:For each a 2 ½0; 1 the a À cut½f a of f is given by ½f a ¼ fx 2 Rjf ðxÞ ! ag: Definition 1.2 By fuzzy (real) number we mean any function f : R ! ½0; 1 with bounded nonempty kernel and such that for each a 2 ½0; 1 the aÀcut½f a is a nonempty convex subset of R:For a fuzzy real number f we will denote by ½f À a and ½f þ a the left and the right bound of ½f a ; respectively. Notice that every fuzzy real number, as piecewise monotone function, has at most countably many points of discontinuity. Cluster points of sequences of fuzzy real numbersThere are several ways how to introduce convergence of sequences of fuzzy real numbers. From the point of view of Supported by the grant MSM6198898701.

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