L-upper Approximation Operators and Join Preserving Maps
Yong Chan Kim, Young Sun Kim · International Journal of Fuzzy Logic and Intelligent Systems · 2014
In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$ . They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.