  Given a raw knowledge in the form of a data table/a decision system, one is
facing two possible venues. One, to treat the system as closed, i.e., its
universe does not admit new objects, or, to the contrary, its universe is open
on admittance of new objects. In particular, one may obtain new objects whose
sets of values of features are new to the system. In this case the problem is
to assign a decision value to any such new object. This problem is somehow
resolved in the rough set theory, e.g., on the basis of similarity of the value
set of a new object to value sets of objects already assigned a decision value.
It is crucial for online learning when each new object must have a predicted
decision value.\ There is a vast literature on various methods for decision
prediction for new yet unseen object.
  The approach we propose is founded in the theory of rough mereology and it
requires a theory of sets/concepts, and, we root our theory in classical set
theory of Syllogistic within which we recall the theory of parts known as
Mereology. Then, we recall our theory of Rough Mereology along with the theory
of weight assignment to the Tarski algebra of Mereology.\ This allows us to
introduce the notion of a part to a degree. Once we have defined basics of
Mereology and rough Mereology, we recall our theory of weight assignment to
elements of the Boolean algebra within Mereology and this allows us to define
the relation of parts to the degree and we apply this notion in a procedure to
select a decision for new yet unseen objects.\ In selecting a plausible
candidate which would pass its decision value to the new object, we employ the
notion of Vapnik - Chervonenkis dimension in order to select at the first stage
the candidate with the largest VC-dimension of the family of its
$\varepsilon$-components for some choice of $\varepsilon$.
