Variable-domain fuzzy sets - Part II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA2101W9U" target="_blank" >RIV/61988987:17610/20:A2101W9U - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.fss.2019.04.026" target="_blank" >https://doi.org/10.1016/j.fss.2019.04.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2019.04.026" target="_blank" >10.1016/j.fss.2019.04.026</a>

Result language
angličtina
Original language name
Variable-domain fuzzy sets - Part II
Original language description
This is the second part of a two-part paper on operations on fuzzy sets that may not share the same domain of definition. Part I described several ways of representing variable-domain fuzzy sets and introduced a few basic variable-domain fuzzy set operations. The present (largely self-contained) Part II further develops the theory of variable-domain fuzzy sets, based primarily on the representation of variable domains by a dummy membership degree that indicates the out-of-domain assignment error. We first describe several families of algebraic operations on the extended set of membership degrees; these are later employed in the investigation of basic notions of variable-domain fuzzy set theory. The fuzzy set operations studied in this paper include variable-domain variants of unions and intersections, kernels and supports, heights and plinths, equalities and inclusions, Cartesian products, and fuzzy relational compositions. Besides the initial examination of these variable-domain notions, our aim is to demonstrate the viability of variable-domain fuzzy set theory and highlight the similarity as well as differences between the fixed- and variable-domain treatments of fuzzy sets.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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