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Algorithms of Fuzzy Structural System’s Analysis (Q-Analysis)

Student: Levshenkova Elizaveta

Supervisor: Konstantin Y. Degtyarev

Faculty: School of Software Engineering

Educational Programme: Master

Year of Graduation: 2014

<p>The theme of the master&rsquo;s thesis is &ldquo;Algorithms of Fuzzy Structural System&rsquo;s Analysis (Q-Analysis)&rdquo;.</p><p>Master&rsquo;s thesis contains 157 of text, 35 figures, 36 tables, 54 formulas, 15 definitions. When writing the thesis 24 sources of information were used (books, articles and various internet-resources).</p><p>Keywords: system, system analysis, Q-Analysis, simplex, simplicial complex, linguistic variable, fuzzy set, membership function, term set, interval computation, interval with fuzzy boundaries, <em>a</em>-cut, defuzzification.</p><p>The thesis consists of an introduction, main part (3 chapters), conclusion and reference list.</p><p>In the introduction the topic of the research is revealed, its relevance is described, an object and tasks, which have to be addressed to achieve this object, are defined.</p><p>The object of this master&rsquo;s thesis is the development of algorithms for fuzzy structural system&rsquo;s analysis (Q-Analysis).</p><p>The main tasks of this thesis are:</p><p>1) Studying and presentation of the basic concepts and methods associated with different approaches of representation of the strength of links between system&rsquo;s model elements in the framework of system&rsquo;s structural analysis (the so-called Q-Analysis),</p><p>2) analysis of the nature of uncertainty to be considered at the stage of system&rsquo;s model construction; description of suggested approaches focused on the account of this uncertainty, as well as those operations that are performed while implementing the procedure of fuzzy Q-Analysis,</p><p>3) description and analysis of the Q-analysis algorithm&rsquo;s variant(-s) in case of fuzzy-defined strength of links between system&rsquo;s model elements.</p><p>The first chapter of the thesis is devoted to the description of system&rsquo;s structural analysis, namely Q-Analysis. There are basic definitions related to the procedure of Q-Analysis (simplex, simplicial complex, q-connectivity, eccentricity) and also the algorithm of classic Q-Analysis in the form proposed by an English mathematician Ronald Atkin.</p><p>The second chapter of the thesis is devoted to analysis of possible usage of fuzzy sets in the procedure of Q-Analysis. Particularly, there are basic definitions of the fuzzy set&rsquo;s theory. The first section of the second chapter includes a description of the algorithm of fuzzy Q-Analysis, in case of giving the strength of links between system&rsquo;s model elements in the form of intervals. There is also an example, which illustrates the details of the proposed algorithm. At the end of this section obtained results are analyzed and also subsequent phases of the studying are described.</p><p>The second section of the second chapter contains a description of two proposed algorithms of fuzzy Q-Analysis, in case of giving the strength of links between system&rsquo;s model elements in the form of intervals with fuzzy boundaries. Also there are two examples which illustrate the implementation of proposed algorithms. At the end of this section there is a comparison of the algorithms based on the obtained results and also there are main conclusions regarding the strengths and weaknesses of these algorithms.</p><p>The third section of the second chapter contain a description of the possible prospects for further studying in the topic under consideration, namely the application of Type-2 Fuzzy Sets for the description of linguistic uncertainty, which is typical for representation (of verbal characteristics) of the strength of links between system&rsquo;s model elements.</p><p>The third and the final chapter of the main part of the thesis is devoted to the description of the software implementation of the algorithms proposed in the second chapter. There is the description of used means of implementation, the screenshots of the program, the necessary explanations. This chapter also provides a brief user&rsquo;s guide.</p><p>The conclusion is devoted to the summary and comparison of the results, obtained during the studying of the topic. There are the main conclusions formulated and the prospects for further research are outlined.</p>

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