Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616931" target="_blank" >RIV/61989592:15310/22:73616931 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S016501142200063X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016501142200063X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2022.02.013" target="_blank" >10.1016/j.fss.2022.02.013</a>
Alternative languages
Result language
angličtina
Original language name
Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval
Original language description
In numerous generalizations of the original theory of fuzzy sets proposed by Zadeh, the considered membership degrees are often taken from lattices isomorphic to the lattice LI of closed subintervals of the unit interval [0, 1]. This is, for example, the case of intuitionistic values, Pythagorean values or q-rung orthopair values. The mentioned isomorphisms allow to transfer the results obtained for the lattice LI directly to the other mentioned lattices. In particular, basic connectives in Zadeh's fuzzy set theory, i.e., special functions on the lattice [0, 1], can be extended to the interval-valued connectives, i.e., to special functions on the lattice LI , and then to the connectives on the lattices L* of intuitionistic values, P of Pythagorean values, and also on the lattice L tau q of q-rung orthopair values. We give several examples of such connectives, in particular, of those which are related to strict t-norms. For all these connectives we show their link to an additive generator f of the considered strict t-norm T. Based on our approach, many results discussed in numerous papers can be treated in a unique framework, and the same is valid for possible newly proposed types of connectives based on strict t-norms. Due to this approach, a lot of tedious proofs of the properties of the proposed connectives could be avoided, which gives researchers more space for presented applications.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
1872-6801
Volume of the periodical
441
Issue of the periodical within the volume
AUG
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
17
Pages from-to
262-278
UT code for WoS article
000812960300012
EID of the result in the Scopus database
2-s2.0-85125501716