EECS 839
Fall 2008 Homework Assignment # 2
due: October 7, 2008
40 pts. 1. For the following decision table
Attributes Decision
Wind Humidity Temperature Trip
1 low high low no
2 low high low yes
3 low low high yes
4 low high high yes
5high high low no
6high low high no
7high low high no
using lower and upper approximations and the LEM2 algorithm determine
(a) a set of certain rules,
(b) a set of possible rules
for both concepts: (Trip, no) and (Trip, yes).
20 pts. 2. Show an example of a decision table with four examples, with one attribute
a and two subsets X and Y of the set U of all examples such that _
AX ∩ _
AY ≠
_
A(X ∩ Y), where A = {a}. Show your work.
3. For the following decision table
Attributes Decision
Wind Humidity Temperature Trip
1 ? high low no
2 low * – yes
3 * low ? yes
4 low – high yes
5high high low no
6 – low ? no
7high low high no
compute
10 pts. (a) all blocks of attribute-value pairs,
5 pts. (b) characteristic sets for A = {Wind, Humidity, Temperature},
15 pts. (c) all singleton A-lower and A-upper approximations, check whether all
singleton A-lower and A-upper approximations are locally A-definable,
5 pts. (d) all subset A-lower and A-upper approximations,
5 pts. (e) all concept A-lower and A-upper approximations.