DISSIMILIRATY ANALYSIS

Introduction

• In DISSIMILIRATY ANALYSIS we are going to discuss Knowledge Representation Systems in which neither condition nor decision attributes are distinguished.

• We are basically not interested in dependencies among attributes, but in description of some objects in terms of available attributes.

• We want to find essential differences between objects of interest.

Example 1

• Let us consider a real life example.• Objects in this example are:– 1 - Israel– 2 - Egypt– 3 - Palestinians– 4 - Jordan– 5 - Syria– 6 - Saudi Arabia

Example 1…• The attributes for the example are:

– a - autonomous Palestinian state on the West Bank and Gaza– b - return of the West Bank and Gaza to Arab rule– c - Israeli military outpost along the Jordan River– d - Israeli retains East Jerusalem– e - free access to all religious centers– f - return of Sinai to Egypt– g - dismantling Israeli Sinai settlements– h - return of Golan Heights to Syria– i - Israeli military outpost on the Golan Heights– j - Arab countries grant citizenship to Palestinians who chose to

remain within their borders

Example 1…

U a b c d e f g h I J

1 0 1 1 1 1 1 0 0 1 1

2 1 1 1 0 1 1 1 1 1 0

3 1 1 0 0 1 1 1 1 1 1

4 1 1 0 0 1 1 1 1 1 0

5 1 1 0 0 1 1 1 1 0 0

6 1 1 1 0 1 1 1 1 1 1

Example 1…

• Now we analyze the Middle East situation using table 1.

• The outcome of this analysis will give us the difference of the opinion between the participating countries.

Example 1…U a b c d e f g h I J

1 0 1 1 1 1 1 0 0 1 1

2 1 1 1 0 1 1 1 1 1 0

3 1 1 0 0 1 1 1 1 1 1

4 1 1 0 0 1 1 1 1 1 0

5 1 1 0 0 1 1 1 1 0 0

6 1 1 1 0 1 1 1 1 1 1

Example 1…

• Attributes a, g and h are equivalent, hence all of them are not necessary in the table and we can retain only one, say a.

• Also attributes b, e and f do not discern participants to the debate, since they have the same values for all negotiating partners, and therefore they are irrelevant in this specific situation, so they can be dropped from the table too.

Example 1…

U a c d i j

1 0 1 1 1 1

2 1 1 0 1 0

3 1 0 0 1 1

4 1 0 0 1 0

5 1 0 0 0 0

6 1 1 0 1 1

Example 1…

• Attribute a and d are dispensable, because dropping attributes a or d we get still consistent tables as shown below.

Table 3 Table 4

U a c i j

1 0 1 1 1

2 1 1 1 0

3 1 0 1 1

4 1 0 1 0

5 1 0 0 0

6 1 1 1 1

U c d i j

1 1 1 1 1

2 1 0 1 0

3 0 0 1 1

4 0 0 1 0

5 0 0 0 0

6 1 0 1 1

Example 1…• If we remove attribute c we get following table

Table 5

• Similarly if we remove i, j we get similar inconsistency.

• Set {c, i, j} is the core and there are two reducts in the table: {a, c, i, j} and {d, c, i, j}. Hence either of the reducts can be assumed as a basis for negotiations, for they provide two equivalent sets of issues for discussion.

Table 3 Table 4

U c d i j

1 1 1 1 1

2 1 0 1 0

3 0 0 1 1

4 0 0 1 0

5 0 0 0 0

6 1 0 1 1

U a c i j

1 0 1 1 1

2 1 1 1 0

3 1 0 1 1

4 1 0 1 0

5 1 0 0 0

6 1 1 1 1

Example 1…

• What we have achieved so far is the following. Not all issues are of equal importance in the debate. Some issues can be eliminated from the negotiations without affecting the position of the parties involved in the negotiation process, some can not be eliminated without changing the balance of opinion, (core issues c, i and j) and some issues can be mutually replaced, without changing essentially the views of the negotiating parties (issues a and d).

Example 1…

• Computing core values of attributes for Table 3 and Table 4 we obtain the following tables.

Table 3 Table 6

U c d i j

1 1 1 1 1

2 1 0 1 0

3 0 0 1 1

4 0 0 1 0

5 0 0 0 0

6 1 0 1 1

U c d i j

1 - 1 - -

2 1 - - 0

3 0 - - 1

4 0 - 1 0

5 - - 0 -

6 1 0 - 1

Example 1…

Table 4 Table 7

U a c i J

1 0 - - -

2 - 1 - 0

3 - 0 - 1

4 - 0 1 0

5 - - 0 -

6 1 1 - 1

U a c i j

1 0 1 1 1

2 1 1 1 0

3 1 0 1 1

4 1 0 1 0

5 1 0 0 0

6 1 1 1 1

Example 1…

• we might be interested in knowing how far apart the views of participant are. To this end, we can define a distance graph as follows:

• With each objects in the table we associate a node labeled by this object, and two nodes x and y are connected to the vertex labeled a if, removing the attribute a places objects x and y in the same equivalence class (i.e. they have the same description in terms of remaining attributes values).

Example 1…

•

•

• 2 Table 6

• Table 3 j c Table 6

• 1 d 6 4 i 5 c j

3 graph for table 6

U c d i j

1 - 1 - -

2 1 - - 0

3 0 - - 1

4 0 - 1 0

5 - - 0 -

6 1 0 - 1

U c d i j

1 1 1 1 1

2 1 0 1 0

3 0 0 1 1

4 0 0 1 0

5 0 0 0 0

6 1 0 1 1

Example 1…

• Also for table 7 we get

•

• 2

• j c

• 1 a 6 4 i 5 c j

3 graph for table 7

U a c i J

1 0 - - -

2 - 1 - 0

3 - 0 - 1

4 - 0 1 0

5 - - 0 -

6 1 1 - 1

Example 1…• Distance between two objects x and y is the length of the shortest

path between x and y in the distance graph, i.e. the smallest number of vertices which connect them.

• For example the distance between – Israel (1) and Syria (5) is 4– Israel (1) and Saudi Arabia (6) is 1– Saudi Arabia (6) and Jordan (4) is 2

• Distance between participants in this example has a quite clear intuitive explanation: it is the number of issues that separate then in their views. Removing of a specific issue would decrease the distance between some participants by 1, bringing their views closer.

• Thus the distance graph gives interesting insights in to the structure of the analyzed situation and enables us to better understand the nature of the conflict analyzed.

Thank You.