Sharp and fuzzy observables on effect algebras

TL;DR

This paper explores the relationship between sharp and fuzzy observables on effect algebras, establishing conditions for fuzzy versions and analyzing their ordering and minimality, with applications to classical experiment theory.

Contribution

It introduces a framework for constructing fuzzy observables from sharp ones on effect algebras with the (E)-property and studies their ordering and minimality conditions.

Findings

Existence of fuzzy versions of observables on effect algebras with the (E)-property.

Definition of an ordering of observables based on fuzzy properties.

Identification of minimality conditions within this ordering.

Abstract

Observables on effect algebras and their fuzzy versions obtained by means of confidence measures (Markov kernels) are studied. It is shown that, on effect algebras with the (E)-property, given an observable and a confidence measure, there exists a fuzzy version of the observable. Ordering of observables according to their fuzzy properties is introduced, and some minimality conditions with respect to this ordering are found. Applications of some results of classical theory of experiments are considered.