The bag model in language statistics
type: Item
instance of: scholarly article
title: The bag model in language statistics
zbMATH Open document ID: 1036.91050
DOI: 10.1016/S0020-0255(02)00201-3
author: F. Criado
author: T. Gachechiladze
author: H. V. Meladze
author: G. Tsertsradze
published in: Information Sciences
publication date: 2003-02-11T00:00:00Z
review text: Fuzzy quantitative models of language statistics are constructed. All suggested models are based on an assumption about a superposition of two kinds of uncertainties: probabilistic and possibilistic. The new approach has been applied to the representation of fuzzy sets as a result of the set splitting procedure into usual subsets of some universal set, which is convenient for describing possibilistic and probabilistic superpositions. Let \(\Omega \) be a finite set and \(A\) be any subset, \(A \subseteq \Omega \). Consider a correspondence \( I_{A} \rightarrow (I_{ \widetilde {A}}, I_{ \widetilde {{A}^{D}}}), \) where \(I_{A}\) is the indicator of the subset \( A,I_{ \widetilde {A}},I _{ \widetilde {{A}^{D}}} \in [0;1]^{\Omega} \) and \( I_{A}(\omega)= I_{\widetilde {A}}(\omega)+I_{\widetilde {{A}^{D}}}(\omega)\) \(\forall \in \Omega. \) \(A\) is the support of the mappings \( I_{ \widetilde {A}} \) and \(I_{ \widetilde {{A}^{D}}} \). According to Zadeh, the splitting components \(I _{\widetilde {A}}\) and \(I_{ \widetilde {{A}^{D}}}\) are fuzzy subsets of \(\Omega\). Call \(I_{ \widetilde {{A}^{D}}}\) the dual subset with respect to \(I_{ \widetilde {{A}^{\cdot}}}\) The procedure in which the indicator \(I_{A}\) is compared with the pair \((I_{ \widetilde{A}}, I_{ \widetilde{{A}^{D}}})\) is called ``splitting of indicator \(I_{A}\) (subset \(A\))''. The splitting procedure of some subsets \(A,B \subseteq \Omega\) induces the corresponding splitting of the union and intersection of these two subsets. For split indicators \(I_{ \widetilde {A \cap B}}\) and \(I_{ \widetilde {A \cup B}}\) it is essential to fulfill the natural conditions (as for non-split ones) \( I_{ \widetilde {A}}( \omega ),I_{ \widetilde{B}}( \omega ) \geq I_{ \widetilde {{A} \cap {B}}}( \omega), \) \( I_{ \widetilde{A}}( \omega ),I_{ \widetilde {B}}( \omega ) \leq I_{\widetilde {A \cup B}}( \omega), \omega \in \Omega.\) Then, as can be easyly seen for intersection and union indicators, the followi…
reviewed by: Fatima T. Adylova
Mathematics Subject Classification ID: 91F20
Mathematics Subject Classification ID: 68T50
zbMATH DE Number: 1866950
zbMATH Keywords: fuzzy sets
zbMATH Keywords: membership functions
zbMATH Keywords: probability theory
zbMATH Keywords: linguistic modeling
MaRDI profile type: Publication
cites work: Q3322155
cites work: Q4371981
cites work: Q5824570
cites work: Q5529067
cites work: ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval
cites work: Fuzzy sets
cites work: The concept of a linguistic variable and its application to approximate reasoning. I
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description: scientific article; zbMATH DE number 1866950