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OPTIMIZATION OF HARD FORMALIZED PROCESSES USING FUZZY NEURAL MODEL

Natalia G. Levchenko

The proposed modeling method of hard formalized processes regards not only qualitative data, but attribute (descriptive) as well as fuzzy defined non-formalized criterion & their connections. The model is developed for further process exploration with its behavioral forecasting and operational optimization. The method is based on fuzzy neuron nets technology. The operational optimization method is shown with factor analysis.

Keywords: intellectual controlling systems, data system, modeling, neural network technologies, fuzzy logic.

Currently, the decision-making administrators need powerful intellectual tool that would process data from information systems and produce targeted (selective) analysis, i.e. a range of possible management solutions and authorities to various officials such as:

• Real time analysis of the situation and the behavior of the system interacting elements.

• Providing dynamical monitoring and diagnostic of management decisions.

• Real events and processes modeling.• Critical situations prediction and prevention.Often there are poorly formalized tasks that can not be solved by

classical deterministic methods. We are talking about the analysis, planning and economic decision-making tasks in conditions of uncertainty as well as the initial information incompleteness and

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fuzziness i.e. the data that is fuzzy, vague, dim, uncertain, undefined or imprecise in nature.

Most appropriate and effective way to solve these problems is the method of modeling using fuzzy neural techniques. The main advantage of this method lies in the ability of the algorithm to adjust the structure of the network under the new observations or factors and to identify complex non-linear relationship between the input and output data. [1] This hybrid intelligent systems (HIS) taking advantage of traditional means and methods of artificial intelligence, and at the same time overcoming some of its drawbacks, can solve problems usually unsolvable by individual methods of artificial intelligence. [2]

Hybrid intelligent systems allow more efficient approach to integrate formalized and non-formalized values. They combine the advantages of neural networks and fuzzy inference systems. They allow developing and presenting visual and informative model systems in the forms of fuzzy production rules, using the techniques of neural networks, which is more convenient and less time-consuming process for systems analysts. [3]

Urgency of the control system model development by such business process as a learning process is stipulated by both scientific expansion of theoretical ideas about the knowledge transmission-acquisition processes and practical goals to create more efficient management, implementation of which should help to ensure the required quality of education.

An institution of higher education as an object of modelling is characterized as a complex system with a high level of uncertainty of the initial information and environment. Systematic approach to quality management of educational services considers it as a set of interrelated factors that affects the system of educational services in all cycles of young professionals formation. Enhancing the quality of student education is associated with the improvement of a material and technical base of the educational institutions as well as its educational standards and programs quality growth and introduction of advanced educational technologies and modern infoware.

Since most of the factors relates to the subjective category, the experimental results can not be fully processed using classical

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mathematics capabilities. In this case, we must use the assistance of the fuzzy information processing. In order to formalize acquired knowledges without destroying properties of fuzziness and inaccuracy it is necessary to apply the formal fuzzy algebra and fuzzy logic capabilities.

When considering various views, during the experiments we have to introduce the quality assessment factor reflecting the subjective confidence of the expert.

To build the model following the theory of fuzzy identification we should first:

- Identify the factors that evaluate the education process and affect it as well as their interrelationships. Typically the total number of the influencing factors is unknown and not all of them are evident. Therefore a set of criteria is selected, which, during the model enhancement, can be supplemented without affecting the system itself, so called the method of solution, but qualitatively improving the “portrait” of the object of research or study.

- Identify fuzzy “if - then” rules of interaction of all defined factors.- Form experimental data samples to train the neural network.- Create a learning process model using the MATLAB computing

environment i.e. Fuzzy Logic Toolbox package, a method of identification by fuzzy knowledge bases.

- Form real data test samples and compare the results using well-known mathematical methods, e.g. SRME - method of least squares.

On the system entrance as the input data there are a lot of parameters evaluating an entrant (xi), which can be divided into two groups:Academic achievements (xij – the results of a student i on the subject j, which are defined in the linguistic form of “excellent”, “good” or

“satisfactory” and further marks for each subject from course to course).Psychological profile (soi – will for learning, koi - ability to live and work in a team - sociability, uoi - equilibrity (resistance to stress), etc. They are also given in the linguistic form of “excellent”, “good” or “satisfactory”).

The whole set of characteristics of the future student is unknown and can not be known for objective reasons. However, some data can be extracted from the results of the tests that applicants pass before entering the navigational specialties.

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Later in the educational process these parameters will change under the influence factors. They are also divided into several groups such as educational, financial, social, education support, etc.

Educational groupkvj – teacher qualification in the discipline j defined linguistically

(“high”, “medium”, “low”).The teacher can be an assistant, senior lecturer, associate professor

and professor.Str_pj - will to improve skills and efficiency in the teacher training

in the discipline j defined linguistically (“high”, “medium”, “low-something”). It depends on the age of the teacher (agej).

Agej - the age of the teacher in the discipline j, which is divided into 3 periods and defined by a fuzzy variable.

The teacher willingness to participate in the education process also depends on salary (zpj), which is included in the financial group.

Str_kij - willingness of the student xij to acquire knowledge in the discipline j defined linguistically (“high”, “medium”, “low”). It depends on the prestige of the profession (presti from the social group) according to the student, as he is interested to get an education that will allow him to find a job at a high-payed job. Student opinion may vary from course to course.

Financial groupzpj – teacher’s salary in the discipline j defined linguistically

(“high”, “medium”, “low”). It depends on the skills and the university administration ability to pay an appropriate salary.

fes_ki – the scholarship of the student xi defined linguistically (“high”, “medium”, “low”).

fes_libj –funds for new textbook purchase for the discipline j.fes_equipj – funds for new educational equipment purchase for the

discipline j.Education support grouplibj – provision with the literature defined linguistically (“high”,

“medium”, “low”). It depends on the funds for the new textbooks purchase.equipj – provision with the educational equipment defined

linguistically (“high”, “medium”, “low”). It depends on the funds for the new educational equipment purchase.

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Social group comfort_pj – workplace comfort of the teacher of the discipline j (in

the department, at the lecturer laboratory environment, relationship with the team). It depends on the age and qualifications of the teachers etc.

comfort_ki – comfort of the student xi in the studying process, in a hostel, relationship with the group of students, team of teachers, administration staff.

com_ki – participation of the student xi in the university social life (clothes, amateur performances, sports, conferences).

The model is built on the real data of the university graduates, provided by the dean of the Navigation Department of the Naval Academy of Adm. G.I. Nevelskoy Maritime State University. The information concerning the results in all disciplines from first to fifth year of the students from Company 12 of the Navigation Department (admission year 2002) was selected as training samples. The information about the teaching personnel was also real of those years according to the Curriculum database. Verification and adequacy of this model was tested on the second part of the same company.

Figure 1. Settings of membership functions

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The control and configuration of the parameters of membership functions of input variables was performed using MATLAB graphic tools. To perform such operations the editor of membership functions was applied (Figure 1).

After completing the hybrid network training the analysis of training error graph was performed (Figure 2). Verification of the constructed fuzzy model adequacy was made by the test sample.

Left side of the table in Figure 3 contains a set of pre-known initial data on teaching staff (qualifications and age), laboratory and methodological support and real learning results of the student taken from the gradebook (totally 7 factors). The right side of the table shows the test results of the hybrid intelligent systems.

Comparing the results from the system with the corresponding ones of the tested student from course to course, we can say almost the exact coincidence of these values and, if rounding them to integer, a perfect

Figure 2. Training error graph of the neural network

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match (in reality the teacher puts rounded learning marks). Received average square error of the arithmetic mean is 0.04 and shows that the proposed model accurately describes the real processes occurring in the system (Figure 4).

Presence of the model allows conducting factor analysis for maximum efficiency of the process (Figure 5).

The factor analysis I:1. Within the available values we rearranged the highly qualified

teacher factors of the graduation year and low skills ones of the freshman year. As a result, the student achievements improved (see increased average value from 3.59 to 3.90)

2. A reverse process was conducted only with the teachers. The student achievements deteriorated up to the average value of 3.53. The results of the analysis are shown on the Graph (Figure 6).

Figure 3. Fragment of the table with the original data and verification results

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The factor analysis II:1. Within the available values we rearranged the factors of laboratory equipment and literature which support the education process in better

Figure 5. Fragment of the table with the factor analysis results

Figure 4. Graph of the model test results

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way of the graduation year and low cost obsolete supporting means of the freshman year. As a result, the student achievements improved (see increased average value from 3.59 to 3.69).

2. During the reverse equipment and literature change the student achievements deteriorated to average value 3.43. The results of the analysis are shown on the Graph (Figure 7).

Figure 6. The graph of the teacher qualification factor analysis

Figure 7. The graph of the factor analysis of education supporting equipment and literature

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The factor analysis III: 1. Within the available values we rearranged the factors of the

highly qualified teachers and the laboratory equipment and literature which support the education process in better way of the graduation year and low skills teachers and low cost obsolete supporting means of the freshman year. As a result, the student achievements improved (see increased average value from 3.59 to 3.95).

2. During reverse change of the factors the student achievements deteriorated to average value 3.37. The results of the analysis are shown on the Graph (Figure 8).

Thus, the article presents one of the methods for modeling the weakly formalized process using the fuzzy neural techniques. The example of the model construction is given, in which the educational process in the university was selected as the weakly formalized process. Several examples of the factor analysis were proposed. The factor analysis in this fuzzy neural model showed that if the freshman course was provided with high qualified teachers, modern equipment and new literature, despite the poor ability to ensure the same education support to the graduate course, the overall students performance increased by about half a point. And vice versa, no matter how improved the learning environment of the graduation course, if the basic disciplines were poorly mastered during the first year, then the overall academic performance of students would be low.

Figure 8. The graph of both factor analysis

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REFERENCES

1. Круглов В.В., Дли М.И. Интеллектуальные информационные системы: компьютерная поддержка систем нечеткой логики и нечеткого вывода. М.: Издательство Физико-математической литературы, 2002. (Russian). [Kruglov V.V., Dli M.I. Intellektualniye informatsionniye sistemy: kompyuternaya podderzhka sistem nechetkoy logiki i nechetkogo vyvoda. Moskva: Izdatelstvo Fiziko-matematicheskoy literatury, 2002]. Kruglov, V.V. & Dli, M.I. (2002) Intelligent information systems: computer support for fuzzy logic and fuzzy inference systems. Moscow: Publishing House of physical and mathematical literature.

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3. Штовба С.Д. Проектирование нечетких систем средствами MATLAB // С.Д. Штовба, М.: Горячая линия–Телеком, 2007. (Russian). [Shtovba S.D. Proyektirovaniye nechetkikh sistem sredstvami MATLAB // S.D. Shtovba, M.: Goryachaya liniya–Telekom, 2007]. Shtovba, S.D. (2007). Fuzzy systems projecting by means of MATLAB. Moscow: Hotline-Telecom.

Optimization of Hard Formalized Processes Using Fuzzy Neural Model