TY  - JOUR
T1  - Lifts of $L$-valued powerset mapping systems
AU  - Zhou, Chang-jie
AU  - Yao, Wei
PY  - 2025
DA  - October
Y2  - 2024
DO  - 10.15672/hujms.1553887
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1730
EP  - 1736
VL  - 54
IS  - 5
LA  - en
AB  - Motivated by Zadeh's extension of mappings, this paper introduces a concept of lifts of powerset mapping systems. In this framework, $L$-subsets are lifts of ordinary subsets, $L$-Zadeh functions are lifts of ordinary mappings, $L$-fuzzy rough set operators are lifts of classical rough set operators, $L$-interior/closure operators of $L$-topology are lifts of interior/closure operators of level topologies. Consequently, lifts of powerset mapping systems can be considered as a useful fuzzy structures for future study.
KW  - completely distributive lattice
KW  - L-valued powerset mapping systems
KW  - lift
CR  - [1] N. Ajmal, Fuzzy group theory: a comparison of different notions of product of fuzzy
sets, Fuzzy Sets Syst. 110 (3), 437–446, 2000.
CR  - [2] R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic
Publishers, New York, 2002.
CR  - [3] Y.-M. Liu and D.X. Zhang, Lowen spaces, J. Math. Anal. Appl. 241, 30–38, 2000.
CR  - [4] F.-G. Shi, Theory of $L_\alpha$-nest sets and $L_\beta$-nest sets and their applications, Fuzzy Syst.
Math. 4 (in Chinese), 65–72, 1995.
CR  - [5] F.-G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets Syst. 160 (5),
696–705, 2009.
CR  - [6] Y. Sun and F.-G. Shi, Representations of L-fuzzy rough approximation operators, Inf.
Sci. 645, 119324, 2023.
CR  - [7] W.-Z. Wu, J.-S. Mi and W.-X. Zhang, Generalized fuzzy rough sets, Inf. Sci. 151,
263–282, 2003.
CR  - [8] L.A. Zadeh, Fuzzy sets, Inf. Control 8 (3), 338–353, 1965.
UR  - https://doi.org/10.15672/hujms.1553887
L1  - https://dergipark.org.tr/en/download/article-file/4231223
ER  -