Conditional states and independence in D-posets

Chovanec, Ferdinand; Eva, Drobná; Kōpka, František; Nánásiová, Olga

doi:10.1007/s00500-009-0487-0

Soft Comput

2009

DOI: 10.1007/s00500-009-0487-0

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Conditional states and independence in D-posets

Ferdinand Chovanec

Drobná Eva

František Kōpka

et al.

Abstract: In this paper a new approach to a conditional probability is studied in more general structure called a D-poset. The authors go into the inner structure of a conditional system which is a crucial notion for the existence of a conditional state. An independence of elements in a D-poset with respect to a state is defined.

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Cited by 2 publications

References 17 publications

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On Probability Domains II

Frič

Papčo

2011

Int J Theor Phys

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We continue our studies of the foundation of probability theory using elementary category theory. We propose a classification scheme of probability domains in terms of cogenerators and their algebraic and topological properties and use the scheme to describe the transition from classical to fuzzy probability. We show that Łukasiewicz tribes form a category of natural probability domains in which σ -fields of sets are "minimal" and measurable [0, 1]-valued functions are "maximal" objects. The maximal objects form an epireflective subcategory in which both the classical and fuzzy probability can be modelled. This leads to a better understanding of the transition.

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On Probability Domains II

Frič

Papčo

2011

Int J Theor Phys

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Real Functions in Stochastic Dependence

Babicová

Frič

2019

Tatra Mountains Mathematical Publications

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In a fuzzified probability theory, random events are modeled by measurable functions into [0,1] and probability measures are replaced with probability integrals. The transition from Boolean two-valued logic to Lukasiewicz multivalued logic results in an upgraded probability theory in which we define and study asymmetrical stochastic dependence/independence and conditional probability based on stochastic channels and joint experiments so that the classical constructions follow as particular cases. Elementary categorical methods enable us to put the two theories into a perspective.

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Conditional states and independence in D-posets

Cited by 2 publications

References 17 publications

On Probability Domains II

On Probability Domains II

Real Functions in Stochastic Dependence

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