
## 3. Original Operators Of Alm

Flowchart of ALM is shown in Fig.3.1. Two operators are used to diffuse and fuse data in the space, IDS and COG respectively. IDS spreads the information in the problem space and COG extracts the behavior of diffused data. These operators act as a fuzzy curve fitting method [1]. They search for possible continuous paths by interpolating data points on data planes using a fuzzy method.

2 And Max is an S-norm, because:
Max(x, y) = Max(y, x)
If x<y => Max(x, z) < Max(y, z)
Max(x, Max(y, z)) = Max (Max(x, y), z)
Max (0, x) = x for x in [0, 1]

![0_image_1.png](0_image_1.png)

Saving the model in the form of its behavior if the 

![0_image_3.png](0_image_3.png)

error is less than the threshold Dividing the data domain and decreasing the change threshold of the linear prediction coder
-Figure 3.1: proposed algorithm for Active Learning Method
[1]
In the following both operators, IDS and COG, are described.

## 3.1.Ids

IDS considers each data point on a data plane as a light source with a cone-shaped illumination pattern. This concept is illustrated in Fig.3.2, where we have used pyramids instead of cones. The projection of process on the plane is called Ink Drop Spread. Pyramids can be considered as 2-dimensional fuzzy membership functions which are centered on each data point and show the degree of belief we have in the value of that data point and its neighbors.

![0_image_0.png](0_image_0.png)

functions.
Applying the algorithm on the data used by Takagi and 

![0_image_2.png](0_image_2.png)

Sugeno [23], results in Fig.3.3 for spread radiuses equal to 0.3 and 1.

IDS satisfies fuzzy S-norm conditions. We considered each data point on a data plane is a light source which has a pyramid shape illumination pattern. Let us assume that A and B are data points in a plane. As shown in Fig.3.4, IA is the area of diffused point A and IB is the area of diffused point B using IDS.