Article:
On Inference Mechanisms of Fuzzy-Probabilistic Inference Systems

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dc.audienceResearchersen
dc.contributor.authorCao, Nhung
dc.contributor.authorHolčapek, Michal
dc.contributor.authorValášek, Radek
dc.date.accessioned2026-02-06T08:54:31Z
dc.date.available2026-02-06T08:54:31Z
dc.date.issued2026
dc.description.abstractThis work studies the inference mechanism of fuzzy--probabilistic inference systems (FPIS), a class of rule-based models where antecedents encode fuzzy information and consequents represent conditional probability distributions of the output variable. A system of m rules is considered: if the input belongs to a fuzzy set $A_k$, then the output follows a probability distribution described by an empirical quantile function. The antecedents form a covering fuzzy partition of the universe, ensuring that every input has positive membership in at least one fuzzy set. In practice, uniform or generalized partitions are typically employed.Local quantile functions are estimated from data as weighted quantiles, with weights given by membership degrees. The inference mechanism produces an empirical quantile function for any input as a linear combination of these local quantile functions, using normalized membership weights.Fuzzy rule-based systems capture input-output relationships in a rough manner, while the inference mechanism refines this into a complete mapping usable in practice. Previous studies compared the standard weighted average of quantile functions with several alternatives on synthetic and real datasets. However, a theoretical analysis of these mechanisms, including the original weighted average and related $L_1$-based minimization approaches, remains open. This gap motivates a deeper investigation of the foundations of the inference mechanism for FPIS.en
dc.description.sponsorshipThe study is supported by the project “Research of Excellence on Digital Technologies and Wellbeing CZ.02.01.01/00/22 008/0004583”, which is co-financed by the European Union.
dc.identifier.citationCAO, Nhung; HOLČAPEK, Michal and VALÁŠEK, Radek, 2026. On Inference Mechanisms of Fuzzy-Probabilistic Inference Systems. Online. In: STUPŇANOVÁ, Andrea; DYBA, Martin and PAVLISKA, Viktor (eds.). Proceedings of The Eighteenth International Conference on Fuzzy Set Theory and Applications. Ostrava: University of Ostrava, p. 41-45. ISBN 978-80-7599-515-5. Available at: https://doi.org/10.15452/978-80-7599-515-5.2026.06.en
dc.identifier.doi10.15452/978-80-7599-515-5.2026.06
dc.identifier.urihttps://eduo.osu.cz/handle/1/229
dc.language.isoen
dc.rights.licenseCC BY 4.0
dc.subjectfuzzy systemsen
dc.subjectmathematicsen
dc.subjectinformaticsen
dc.subjectfuzzy-probabilistic inference systemen
dc.subjectweighted quantile regressionen
dc.subjectinference mechanismen
dc.subjectlinear combinationen
dc.subjectWasserstein barycenteren
dc.subject.czenasfuzzy systémycz
dc.subject.czenasmatematikacz
dc.subject.czenasinformatikacz
dc.subject.konspekt519.1/.8 - Kombinatorika. Teorie grafů. Matematická statistika. Operační výzkum. Matematické modelovánícz
dc.titleOn Inference Mechanisms of Fuzzy-Probabilistic Inference Systemsen
dc.typeinfo:eu-repo/semantics/conferencePaper
dcterms.eventThe Eighteenth International Conference on Fuzzy Set Theory and Applications, Liptovský Ján, January 25 – 30, 2026
dspace.entity.typeArticle
oaire.resourceTypeconference paper
oaire.versioninfo:eu-repo/semantics/publishedVersion
relation.isPublicationOfArticle6afab15b-8c40-42f9-a7ec-39737fc00100
relation.isPublicationOfArticle.latestForDiscovery6afab15b-8c40-42f9-a7ec-39737fc00100
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