Abstract
Near set theory supplies a major basis for the perception, differentiation, and classification of elements in classes that depend on their closeness, either spatially or descriptively. This study aims to introduce a lot of concepts; one of them is
μ
-clusters as the useful notion in the study of
μ
-proximity (or
μ
-nearness) spaces which recognize some of its features. Also, other types of
μ
-proximity, termed
R
μ
-proximity and
O
μ
-proximity, on
X
are defined. In a
μ
-proximity space
X
,
δ
μ
, for any subset
K
of
X
, one can find out nonempty collections
δ
μ
K
=
G
⊆
X
∣
K
δ
¯
μ
G
, which are hereditary classes on
X
. Currently, descriptive near sets were presented as a tool of solving classification and pattern recognition problems emerging from disjoint sets; hence, a new approach to basic
μ
-proximity structures, which depend on the realization of the structures in the theory of hereditary classes, is introduced. Also, regarding to specific options of hereditary class operators, various kinds of
μ
-proximities can be distinguished.