The problem of completeness for p-mean symmetric difference metric

✍ Scribed by Fachao Li; Jiqing Qiu; Jianren Zhai

• Book ID: 104293063
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 140 KB
• Volume: 116
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00331-5

✦ Synopsis

In this paper, by applying Lebesgue's measure on the symmetric di erence of sets, the p-mean symmetric di erence metric d p is established to measure the di erence between fuzzy numbers. The basic properties of Cauchy sequences of (E 1 ; d p ) are discussed, and we show (E 1 (K); d p ) is complete (where

), further, an example where the space (E 1 ; d p ) is not complete is given.