Necessary and Sufficient Conditions for Generalized Uniform Fuzzy Partitions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F15%3AA16017UB" target="_blank" >RIV/61988987:17610/15:A16017UB - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Necessary and Sufficient Conditions for Generalized Uniform Fuzzy Partitions
Original language description
The fundamental concept in the theory of fuzzy transform (F-transform) is the fuzzy partition, which is a generalization of the classical concept of partition. The original definition assumes that every two normal fuzzy subsets in a partition overlap insuch a way that the sum of the membership degrees at each point is equal to 1. This condition can be generalized by relaxing the assumption of normality for fuzzy sets. The result is a denser fuzzy partition that may improve the approximation propertiesand the smoothness of the inverse F-transform. A fuzzy partition with this property will be referred to as general. The problem is how a general fuzzy partition can be effectively constructed. If we use a generating function with special properties, thenit is not immediately clear whether it defines a general fuzzy partition. In this paper, we find a necessary and sufficient condition that will enable the optimal generalized fuzzy partition to be designed more easily.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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