Lesson6

Hi again,

today we are going to learn a few more rules to start our job. So we have to explain about acceptable clusters.

Clusters should fulfill 2 main rules and 2 main property to be an acceptable clusters in fuzzy logics:

Rules:

1. Being NORMAL.
2. Just increasing or decreasing before reaching to the top point (so called: Being convex).

Rule 1:

Being a normal cluster is just a function of having at least one member with the membership degree of 1. That means, a normal cluster's diagram should reach to the line of grade 1 at least at one point.

(figure1&2)

Rule 2:

As a matter of fact, using the word convexity may not always satisfy the main idea but it is very common to here this term between academics. Like wise, a hunch shape may occur due to some special cases.

The property of having an increasing or decreasing diagram before reaching to the available top, is needed to fulfill the main property of fuzzy clusters. remember that this property should continue after reaching to the top point. (eg: a cluster has a rising diagram before reaching to the top, after reaching to the top the line continues during the membership line and then decreases up to the 0).

(figure1&2)

figure 1

figure 2

Properties:

1. None including member's value is 0, in that cluster.
2. the whole set, should cover the numbers that are not included in the clusters.

Property 1:

The members which are not included in a cluster, have the degree of membership equal to zero in that cluster. But that is not exactly means that they have the same degree of membership in other clusters of the set. (figure3)

figure 3

 Property 2:

As show in (figure 4), we have to clarify the situation of none including numbers. (eg: In the case study of age classification, in Lesson 4 we have to clarify the situation of ages under 0 and bigger than 80).

As show in the figure, red diagrams shows the property 1 for the values out of the limits of the whole set.

figure 4

There fore, fulfilling this rules have a vital importance for acceptable fuzzy clusters and this is the beginning for using this clusters in fuzzy cases. In next article we will analyze a document, including some fuzzy words and this will help us to be more sensitive about this issue. 

sincerely yours.

Babak. Vaheddoost.[p]