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On Fuzzy Probability Theory

Name: On Fuzzy Probability Theory
Keywords: fuzzy set, Complemented lattices, orthocomplemented lattices and posets, \(\sigma\)-morphism, fuzzy probability theory, Fuzzy measure theory, Fuzzy real analysis, quantum mechanics, central limit theorem, Fuzzy functional analysis, Fuzzy operator theory

On fuzzy probability theory

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2002 Palestinian-administered areas Publisher:Springer Science and Business Media LLCJournal:International Journal of Theoretical Physics, volume 41, pages 791-810 (issn: 0020-7748, eissn: 1572-9575,

Authors: Habil, Eissa D.; Nasr, Taghreed Z;

doi: 10.1023/a:1015296814311

handle: 20.500.12358/26164

On Fuzzy Probability Theory

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Abstract

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.

Country

Palestinian-administered areas

Related Organizations

Islamic University of Gaza
Palestinian-administered areas

Keywords

fuzzy set, Complemented lattices, orthocomplemented lattices and posets, \(\sigma\)-morphism, fuzzy probability theory, Fuzzy measure theory, Fuzzy real analysis, quantum mechanics, central limit theorem, Fuzzy functional analysis, Fuzzy operator theory, weak law of large numbers, joint observable, Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects), Limit theorems for vector-valued random variables (infinite-dimensional case), observable, infinite families of observables

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