.png){kind=icon}
.png){kind=icon}
Return
Lifting filters in residuated lattices and their applications in multi-valued decision-making
.png){kind=icon}
PRE
AI
S
DOI：10.1007/s00500-025-11054-4.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This paper investigates lifting filters in residuated lattices, extending techniques from ring theory to this algebraic framework and linking them to decision-making under uncertainty. We introduce and study pseudo-irreducible and lifting filters, showing that a proper filter is pseudo-irreducible if and only if it is local. Lifting filters are characterized both algebraically and geometrically, through clopen sets in the prime spectrum and via Pierce stalks, and we prove that every Stone filter is a lifting filter. A key result settles an open problem by characterizing residuated lattices whose radical is a lifting filter. We further establish the lifting comaximal factorization property, providing equivalent formulations in terms of partitions of closed spectral subsets. Finally, we examine how lifting filters facilitate the transition from graded truth values to Boolean approximations, thereby enhancing logical consistency in decision-making frameworks. Applications illustrate how lifting filters improve logical consistency in multi-valued decision-making, with examples drawn from robotic navigation, smart home systems, and agriculture.
Keywords:
Residuated lattice
Comaximal factorization
Pseudo-irreducible filter
Lifting filter
Lifting comaximal factorization
Decision-making
Journal
IF:
2.5
Papers:
1.0W
Citations:
2.1W
Organization
Cited Papers