A Rough Set Based Total Quality Management Approach in Higher Education - Complex System Modelling and Control Through Intelligent Soft Computations - page 393

A reduct can be thought of as a suf cient, that is, to

represent the category structure and no attribute can be removed from reduct set
without changing the equivalence classes. There may be 2 n

cient set of features suf

− 1 reducts of a

decision table and it is not always feasible to find all the reducts of a set (Pawlak

and Skowron 2007c ). Therefore the reduct of an information system is not unique.
Reducts of Table 3 as discover by Rose2 s/w are

R 1 = {a, b, c, e, f, h}
R 2 = {a, c, e, h, i}
R 3 = {a, c, d, e, i}
R 4 = {a, b, d, e, g, i}
R 5 = {a, c, e, f, g, i}
R 6 = {a, b, c, d, g, h}
R 7 = {a, b, c, e, g, h}
R 8 = {a, b, c, f, g, h}
R 9 = {a, b, d, g, h, i}
R 10 = {a, b, d, g, h, i}
The set of attributes which is common to all reducts is called the core. The core
is the set of attributes which is possessed by every legitimate reduct, and therefore
core consists of attributes which cannot be removed from the information system
without causing collapse of the equivalence class structure. RST considers that the
core is the set of necessary attributes and it is the set of most important attributes of
the dataset and if any of the core attribute is eliminated from the dataset then it
shoddily affect the classi cation (Pawlak and Skowron 2007b ). It is pertinent here

to mention that the core set may be empty for some datasets.

Core ¼\ Reduct

where Reduct is the set of all the reducts.

Core ¼ R 1 \ R 2 \ R 3 \ R 4 \ R 5 \ R 6 \ R 7 \ R 8 \ R 9 \ R 10

Therefore core of Table 3 is:

Core ¼ fg¼ a f Effective learning and teachingf g

cant attribute of Table 3 .
The lower and upper approximation of the table is given by the Fig. 2 . The
accuracy of approximation is given by

This is the most signi

Þ¼ j

Þj
j P ð X Þj

P ð X

a P ð X

where |X| denotes the cardinality of X ≠ φ and Obviously 0 ≤ α ≤ 1.