Fuzzy random measure and its extension theorem

✍ Scribed by Liu Dsosu; Cheng Shaozhong

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 703 KB
• Volume: 11
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(83)80074-8

✦ Synopsis

The goal of this paper is to introduce random measures into fuzzy u-algebras. The structure of random measures of fuzzy sets is studied. Extension theorems of random measure on fuzzy algebras to the generated u-algebras are founded. It shows that Bochner integrals with respect to measures of fuzzy sets can be used to express random measures of fuzzy sets. If it turns out that random measures have their fuzzy meanings then this paper presents a way to deal with fuzzy measures of fuzzy sets by use of a classical mathematical method, such as measure theory, functional analysis and topology.