Lifts of $L$-valued powerset mapping systems

Abstract

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.

Keywords

• completely distributive lattice
• L-valued powerset mapping systems
• lift

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