Knowledge-Based Systems

9.9 rough Set theory 267

The definition of a rough set is illustrated in Figure 9.15 (Akerkar & Lingras,

2008).

9.9.3 Rough Logic 

Rough set theory is based on a known equivalence relation. But the equiva-

lence relations are mostly unknown in applications. Therefore, the concept

of rough logic based on the notions of lower and upper approximations

without explicit equivalence relation was introduced. Rough logic (Lin,

1996) is an S

5

modal logic because the language structure is the same. The

model theory of rough logic has a similar possible-world model structure as

S

5

, but is different in its semantics.

A relational structure on E is a four-tuple:

E = (E, N, R, F )

where

E• is a set of entities {e, e1, ….}, the domain ...