# Gurbanov F.M., Masimov E.D. MATHEMATICAL MODEL AND EXPERT SYSTEM OF DIAGNOSTICS AND CURING OF ILLNESSES

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## Gurbanov F.M., Masimov E.D. MATHEMATICAL MODEL AND EXPERT SYSTEM OF DIAGNOSTICS AND CURING OF ILLNESSES

Organizm of human being can be considered as dynamic system which is described by variables of two sets X and Y, where

X = x1, x2, ... , xn , Y =  y1, y2, ... yk ,

xi = xi (t) for 1  i  n, yj = yj (t) for 1  j  k.

According to medical terminology, the elements of the set Y are named as symptoms of the illnesses, and elements of the set X are named as parameters of human’s organism like temperature, pressure, weight and so on. Variables of the set Y take values from the segment 0,1 in conformity with the degree of symptoms. Variables xi take values from the set pi, where pi may be a segment, an interval, isolated points or any finite, measurable subset of axis of R.

We consider the m-dimensional Euckleed’s space Rm, where m = n + k. In the space Rm we consider a subset Q which is decartian product of the following sets

Q = p1 p2  ...  pn, where c =  0,1 .

A state of a human being at the time t can be described by movement of point S(t, x, y) inside the set Q of space Rm. Let the medicine know the number of L illnesses z1, z2, ... , zL.

For each illness Zi one can construct the corresponding it fuzzy subset inside Q with function of belonging i according to it can be constructed.

By the help of software DELPHI an expert system is developed, the base of knowledge of which is filled in conformity with shown mathematical model. At the beginning, an user enters the known parameters of organism and symptoms of illnesses. By doing that the degree of each symptom is entered by additional menu. Program displays the list and degree of illnesses in accordance to entered data. There is a special section in the expert system named as “Teaching” where an expert (doctor) has a possibility to add, remove or renew the rules of the system on the basis of private experience.

After determination of diagnosis the program displays known methods of curing by the help of traditional and nontraditional medicine noting the sources of information.

## V.E. Zolotovsky INTERACTIVE DESIGNING AND MODELING SYSTEMS

During the computing technics facilities design the main difficulty lies onto the developer, who must take into account and check a wide range of parameters. Frequently, to make sure that designed facilities are runnable it is necessary to completely or partly realize them in practice and spend a time for testing. Such approach is not always suitable and can bring appreciable expenses else before a moment of computing systems installation in the usage. The going out from this situation is a creation and use of interactive designing software programs. During making the multiprocessor modeling systems and information - computing networks (ICN), used for these purposes, the difficulties repeatedly increase. There exists the ensembles of methods, which allow to design the ICN, however many of them do not allow to conduct the ISN design with plural restrictions taken into account and are limited only by making a topology of minimum cost, reducing the complex many-sided process to the classical problem. The strategy allowing to design the ICN with the ensembles of parameters influencing upon its work is considered in this report.

In this case the ICN is presented in the manner of layered hierarchical model. Such presentation allows to easy going from the mathematical description to the program presentation of ICN model in the manner of the objects set. It was conducted the categorization of different devices functioning in network, on this base the layered model was received. The network is presented as a collection of models of devices functioning in this network (computers, hubs, routers, repeaters and etc.) from which it is possible to select the three main levels:

- The level of sources and consumers of information flows;

- The level of devices ensuring physical connection into ICN;

- The level of devices ensuring ICN operation in the logical level.

Founding on described above suggestions, the base model of such ICN was designed (fig. 1).
The base ICN model

Fig. 1
The computers, printers, scanners and etc are the devices of first level.

The devices providing the network join (hubs, routers, repeaters, bridges and etc.) are located at the second level.

The third level consists of devices checking the network operation as well as realizing different facilities - the servers of different type.

The level amount of network model can vary depending on its difficulty (fig. 2).

Fig. 2
In this case the increasing an amount of levels occurs thanks to appearance of new network management link (switch).

At present the macrooperations are developing with the help of which it will be possible to manipulate ICN models, for instance: association, rearrangement and etc.

The offered system ensures an interactive approach to ICN designing, as follows, it affords to user at any time the possibility of free access to any ICN level and supports the suitable designing facilities and etc.

This strategy allows to begin the ICN designing from most simple network models, gradually raising its difficulty, ensures a possibility of different parameters analysis, on each stage, founding on preceding analysis results.