TY - GEN
T1 - Bipolar Fuzzy Extension of Topological Structures on Fuzzy Powersets
AU - Šostak, Alexander
AU - Uļjane, Ingrīda
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - We present a model allowing to extend an L-topology τ on a set X (i.e. τ⊆LX) to a bipolar L-fuzzy topology T on this set (i.e. T:LX→L). This model is based on the use of a residuated-type structure on a lattice L, and the derived lattice L obtained by “bipolarizing” the original lattice L. The properties of the obtained bipolar L-fuzzy topology are studied. We specially consider the case when the original lattice L is enriched with a monoid Girard structure. In this case, the results obtained become especially transparent.
AB - We present a model allowing to extend an L-topology τ on a set X (i.e. τ⊆LX) to a bipolar L-fuzzy topology T on this set (i.e. T:LX→L). This model is based on the use of a residuated-type structure on a lattice L, and the derived lattice L obtained by “bipolarizing” the original lattice L. The properties of the obtained bipolar L-fuzzy topology are studied. We specially consider the case when the original lattice L is enriched with a monoid Girard structure. In this case, the results obtained become especially transparent.
KW - (L,M)-fuzzy topologies
KW - bipolar lattices
KW - Complete infinitely distributive lattices
KW - fuzzy topologies
UR - https://link.springer.com/chapter/10.1007/978-3-031-74000-8_29
UR - https://www.scopus.com/pages/publications/105004638685
U2 - 10.1007/978-3-031-74000-8_29
DO - 10.1007/978-3-031-74000-8_29
M3 - Conference paper
AN - SCOPUS:105004638685
SN - 9783031739996
VL - 2
T3 - Lecture Notes in Networks and Systems
SP - 349
EP - 361
BT - Information Processing and Management of Uncertainty in Knowledge-Based Systems - 20th International Conference, IPMU 2024, Proceedings
A2 - Lesot, Marie-Jeanne
A2 - Vieira, Susana
A2 - Reformat, Marek Z.
A2 - Carvalho, João Paulo
A2 - Batista, Fernando
A2 - Bouchon-Meunier, Bernadette
A2 - Yager, Ronald R.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 20th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2024
Y2 - 22 July 2024 through 26 July 2024
ER -