Though the section Introduction has been improved a lot,
still the draft of the newest version resists to be
easily understood.

As the Chapter 1. Artificial Neural Network (ANN) is a general
explanation of what is ANN, and most part of the description
has no direct relation of the theme of this dissertation 
--- Devide and Conquer Approach, I start my comments with 
the Chapter 2.

As for English, the author starts with:

     Apart from explicit solution of problem by specialized 
     "one-piece" algorithm, there exist a number of solutions, 
     which have modular structure. In modular structure modules
     could have some defined and regularized structure or be
     more or less randomly connected, ending up at completely
     independent and individual modules.

Let me try to paraphrase, or I might say one possible 
interpretation is:

     Besides an explicit solution usually obtained when we solve 
     a problem by a so-called one-piece-algorithm, sometimes 
     there exists a number of implicit solutions which have 
     a modular structure in which each of the modules can be some
     of those already defiened and usually completely independent 
     with each other, is connected to some of the other modules 
     at random, more or less, and constructs a whole regularized 
     structure.

Still long long one sentence though.

However, I assume this english version of the dissertation is
a complementary one which compliments the original French version.
So let us now forget the issue of English representation, for 
the time being. We are running out of time, are we not?

Well, Devide and Conquer approach is, essencially made up of the 
following three procedures.

1) Divide the target problem into some sub-problems of similar structure.
2) Solve each of the sub-problems
3) Combine the results to create the solution to the original problem.

Though author descirbe the a couple of previous devide and conquer
approach in the research field of ANN. Those are 

* Mixture of Expert (no reference)
* Multi-modelling
* Hybridization
as a general approach, and 
* Intelligent Hybrids Systems
* Neural Network Ensemble Concept
* Models of experts Mixture,
* Dynamic Cell Structure Architecture; and
* Active learning.
as the one particularly based on ANN.

Although the purpose is described like it is to reduce 
the complexity and run-time of the algorithm, description of 
each method is not given and remain totally unclear. 
As it is difficult to guess what does each of these methods 
look like from the name of the method, summary, and hopefully
example of applying it to a problemm, from one method to the
next is more inportant than a very general detailed expalanation
of ANN in the chapter 1.


Then author gives a formula to estimate time-complexity


this section is followed by two alternatives of the divide and conquer
approach, i.e., Committee Machines and Malti agent System (MAS).
What I cannnot understand is that author says those two alternatives
are less important than the Devide & Conquer and despite of that
each of these two less important are given much more detailed 
explanation, including pseud-code for the algorithm.

Then section goes to "Clustering" which has not even been explained 
so far in this chapter. 

     Decomposition modules could be based on any efficient clustering 
     algorithm. We have chosen to use for decomposition ANN structures 
     similar in activity to well-known k-means clustering algorithm,


     Clustering is described in details in the section 2.4 of this work
     in connection with modular algorithms.

And in fact, there is a description of "Clustering" in the section 2.4
but the method --- How an ANN could be used to "decompose" the problem.

Chapter 3 is for "Complexity Estimation" As author writes at the 
beginning of the chapter

     Complexity estimation is a supportive tool for classification

the task of decomposision of a problem starts with estimating
the complesity of the problem.


3.5 Presentation of selected methods
3.5.1 Indirect Bayes error estimation

After the preparation with 6 subsections in 3.5.7
Shannon's entropy is given. but is this a measure of complexity?

3.5.2 Non-Parametric Bayes error estimation and bounds
In the last subsection of this subsection
the formula of "overlap-sum". But again it's not the explist
measure of complexity.

3.5.3 Measures related to space partitioning
Class Discriminability Measures
Purity measure
Neighborhood Separability
Collective entropy]

3.5.4 Other Measures
3.5.4.1 Correlation-based approach
3.5.4.2 Fisher discriminant ratio
3.5.4.3 Interclass distance measures (scatter matrices)
3.5.4.4 Volume of the overlap region
3.5.4.5 Feature efficiency
3.5.4.6 Minimum Spanning Tree (MST)
3.5.4.7 Inter-intra cluster distance
3.5.4.8 Space covered by epsilon neighborhoods


After a series of sub-sub-sub-sections, in the last sub-section 3.5.5 
Ensemble of estimators, the author write

     The computation of several methods at once is potentially 
     more difficult than one, but using several simple methods 
     could be faster than one complex method.

According to this each of them above a method of complex estimation
and author seems to propose "pick up som simple methods and 
combine them somehow." 

However, in my humble opinion none of the 7 methods is not
a method for extimate complexity.

3.6 Complexity Estimation Conclusion

This section start with
   
     Classification complexity estimation methods present great variability. 

Hence, we now know what has so far called Complexity Estimation is 
classification complexity.  No wonder colmogorof --- the most popular
complexity mesure --- was not referred to.

Then this section was concluded

Not every method
is suitable to estimate a complexity of multi-class classification problem - some are
designed only to two-class problems, and as such they need special procedures to
accommodate them to multi-class problem (like counting the average of complexi-ties
of all two-class combinations) what usually result in combinatorial increase in
computational complexity.

That's it. My guess seems to be correct.


This is the end of Part I and we could expect 
How the author estimate classification complexity in the Part II.

Finally, Chapter 5. Let's expect a concrete implementation of T-DTS.

As before it is needed to be paraphrase the original text.

Decomposition Unit is for the purpose of dividing the database into several sub-databases.
The unit is constructed using Kohonen's Self-Organizing Maps.

......

Finally, all the su-databases are feeded to any of Processing Unit.

either of LVQ, MLP, LN, Perceptrons, GRNN or Probabilistic Networks 
The selection of which is by "assignment rules". The author introduces
here a couple of diferent rules, but which one is used is remain unclear.

The trained model is used later in processing of
the data patterns assigned to the Processing Unit by assignment rules, as specified in
the previous section. Processing Unit models used in this work are: LVQ, MLP, LN,
Perceptrons, GRNN, and Probabilistic Networks.

Here the author gives examples from two categories
(1) model identification and (2) data classification.
2 from the 1st category 3 from the 2nd category.
The first one is ...
The problem is