Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms Group Theory; but some much deeper, Complete Ordered Fields with which Real Analysis starts. Groups abound in sciences, while by Dedekind's theorem there exists only one complete ordered field, up to isomorphism. Cayley's Abstract Alge...

In [She82], it is shown that four of its basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that ...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...