✦ LIBER ✦

The recurrence of dynamic fuzzy systems

✍ Scribed by Yuji Yoshida

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 827 KB
Volume: 95
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(96)00252-7

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✦ Synopsis

This paper analyses a recurrent behavior of dynamic fuzzy systems defined by fuzzy relations on a Euclidean space. By introducing a recurrence for crisp sets, we prove probability-theoretical properties for the fuzzy systems. In the contractive case in Kurano et al. [Fuzzy Sets and Systems 51 (1992) 83-88], the existence of the maximum recurrent set is proved. As another case, we introduce a monotonicity for fuzzy relations, which is extended from the linear structure in Yoshida et al. [Fuzzy Sets and Systems 66 (1994) 83-95]. In the monotone case we prove the existence of the arcwise connected maximal recurrent sets. @

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