On fuzzy probability theory
type: Item
instance of: scholarly article
title: On fuzzy probability theory
zbMATH Open document ID: 1021.81003
DOI: 10.1023/A:1015296814311
author: Eissa D. Habil
author: Taghreed Z. Nasr
published in: International Journal of Theoretical Physics
publication date: 2002-08-20T00:00:00Z
review text: The existence of a joint observable of a finite family of observables (with values in a space of fuzzy sets) was proved by \textit{S. Gudder} [Demonstr. Math. 31, 235--254 (1998; Zbl 0952.60002); Found. Phys. 30, 1663--1678 (2000)]. The authors generalize this result to infinite families of observables. Using it, they prove the weak law of large numbers and the central limit theorem. Special attention is paid to the interplay between observables and the less general notion of random variable.
reviewed by: Mirko Navara
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 47S40
zbMATH DE Number: 1784362
zbMATH Keywords: fuzzy set
zbMATH Keywords: fuzzy probability theory
zbMATH Keywords: observable
zbMATH Keywords: quantum mechanics
zbMATH Keywords: \(\sigma\)-morphism
zbMATH Keywords: joint observable
zbMATH Keywords: infinite families of observables
zbMATH Keywords: weak law of large numbers
zbMATH Keywords: central limit theorem
MaRDI profile type: Publication
full work available at URL: a:1015296814311
OpenAlex ID: W32397567
description: scientific article; zbMATH DE number 1784362