FUZZY MEASURABLE FUNCTIONS

Authors
MESIAR R
Citation
R. Mesiar, FUZZY MEASURABLE FUNCTIONS, Fuzzy sets and systems, 59(1), 1993, pp. 35-41
Citations number
13
Categorie Soggetti
Computer Sciences, Special Topics","System Science",Mathematics,"Computer Applications & Cybernetics","Statistic & Probability",Mathematics
Journal title
Fuzzy sets and systems → ACNP
ISSN journal
01650114
Volume
59
Issue
1
Year of publication
1993
Pages
35 - 41
Database
ISI
SICI code
0165-0114(1993)59:1<35:FMF>2.0.ZU;2-F
Abstract
A generated fuzzy sigma-algebra equipped by Giles fuzzy connectives is considered as a basis of this paper. Starting from a simple fuzzy mea surable function, we introduce the notion of a fuzzy measurable functi on. A one-to-one correspondence between the fuzzy measurable functions and the random variables with values in the fuzzy real line is shown. An inverse of a fuzzy measurable function is proved to be an extended T(infinity)-fuzzy observable and vice versa. Linear operations on fuz zy measurable functions are introduced.