A note on the core of fuzzy numbers

✍ Scribed by Dug Hun Hong; Eunho L. Moon; Jae Duck Kim

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 329 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2009.09.026

✦ Synopsis

of a sequence a b s t r a c t Recently, Aytar et al., The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems 159 ( ) 3369-3379 introduced the concept of the core for sequences of fuzzy numbers and gave a characterization for this concept. Aytar also introduced two different definitions of extreme limits (lim inf, lim sup and Lim inf, Lim sup) for a bounded sequence of fuzzy numbers. According to these definitions, Lim inf (Lim sup, resp.) of a sequence always exists even though lim inf (lim sup, resp.) may not exist. Thus we show that if lim inf and lim sup exist, then these two definitions are equivalent. We also characterize the core of a sequence in terms of Lim inf and Lim sup. It is analogous to the characterization of the core given by Aytar.