Fuzzy sets (in)equations with a complete codomain lattice

Vanja Stepanović; Andreja Tepavčević

Kybernetika (2022)

  • Volume: 58, Issue: 2, page 145-162
  • ISSN: 0023-5954

Abstract

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The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.

How to cite

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Stepanović, Vanja, and Tepavčević, Andreja. "Fuzzy sets (in)equations with a complete codomain lattice." Kybernetika 58.2 (2022): 145-162. <http://eudml.org/doc/298879>.

@article{Stepanović2022,
abstract = {The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.},
author = {Stepanović, Vanja, Tepavčević, Andreja},
journal = {Kybernetika},
keywords = {fuzzy relations; fuzzy set equations; fuzzy set inequations; monotonous operator; upper continuous lattice},
language = {eng},
number = {2},
pages = {145-162},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fuzzy sets (in)equations with a complete codomain lattice},
url = {http://eudml.org/doc/298879},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Stepanović, Vanja
AU - Tepavčević, Andreja
TI - Fuzzy sets (in)equations with a complete codomain lattice
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 2
SP - 145
EP - 162
AB - The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.
LA - eng
KW - fuzzy relations; fuzzy set equations; fuzzy set inequations; monotonous operator; upper continuous lattice
UR - http://eudml.org/doc/298879
ER -

References

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