Conditional measures based on Archimedean semigroups
type: Item
instance of: scholarly article
title: Conditional measures based on Archimedean semigroups
zbMATH Open document ID: 0648.28015
DOI: 10.1016/0165-0114(88)90083-8
author: S. Weber
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: The starting point of our measure theory are \(\perp\)-decomposable measures m for crisp events, i.e. those characterized by the property \(m(A\dot\cup B)= m(A)\perp m(B)\) with respect to an Archimedean t-conorm \(\perp\). In the present paper we pay attention to the (NSA) case, i.e. where the measures can be transformed into probabilities. A generalized Bayesian model is presented based on inconditional and conditional decomposable measures (Section 1). Conditional measures as functions of the condition can be interpreted as fuzzy sets. Crisp and fuzzy valued measures for such fuzzy sets are discussed (Section 2). The model and the measures are applied to Sugeno's problem of buying residences (Section 3). The model is generalized (Section 4).
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 4057863
zbMATH Keywords: measure of fuzzy sets
zbMATH Keywords: quasi-inverse
zbMATH Keywords: decomposable measures
zbMATH Keywords: crisp events
zbMATH Keywords: Archimedean t-conorm
zbMATH Keywords: generalized Bayesian model
zbMATH Keywords: inconditional and conditional decomposable measures
zbMATH Keywords: Crisp and fuzzy valued measures
zbMATH Keywords: Sugeno's problem of buying residences
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90083-8
OpenAlex ID: W2038207178
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description: scientific article; zbMATH DE number 4057863