Program of Fuzzy Inference Based on Z-valuation of Uncertainty

<p>Report 40 p., 9 chapters, 18 fig., 5 tables, 4 append., 23 sources</p><p>Keywords: Z-number, Z-valuation, fuzzy set, fuzzy inference system</p><p>This graduation project is related to the studying and software implementation of methodology based on using Z-numbers as a formal representation of the information that is uncertain, inaccurate or incomplete by its nature in the fuzzy inference systems (Mamdani model).</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; In 2011&nbsp; Professor Lotfi A. Zadeh , University of California (Berkley), the founder of the Fuzzy Set Theory and Fuzzy Logic, proposed the concept of Z-number for capturing the sureness (reliability, degree of truth, etc.) in the information expressed in terms of natural language statements . According to this concept , Z-number is a 2-tuple (A,B), where A and B are both fuzzy numbers. &nbsp;. The first number (A) is a restriction on the values ​​of uncertain variable X. The second number (B)&ndash; is a restriction on a degree of confidence (reliability) of the first&nbsp; component, i.e. fuzzy number A. In most cases, the fuzzy numbers A and B are described by &nbsp;propositions in natural language, for example, (<em>about 80 degrees</em>, <em>absolutely sure</em>).</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Z-number theory is not mature yet, but a number of scientists have contributed to the development of Z-number theory , analyzed and proposed some approaches for their processing . Nevertheless, the use of Z-numbers in fuzzy inference systems remains a challenge.</p><p>The main purpose of the graduation project (presented report) is to study the methodology of using Z-numbers in fuzzy inference systems (FIS) and develop (write) &nbsp;a program based on the results of the study conducted.</p><p>The core tasks to be considered for achieving this goal are as follows:</p><p style="margin-left:71.4pt;">1.&nbsp;&nbsp;&nbsp;&nbsp; Examine existing approaches for dealing with Z-numbers,</p><p style="margin-left:71.4pt;">2.&nbsp;&nbsp;&nbsp;&nbsp; Develop the algorithm (scheme) of using transformed Z-numbers in FIS,</p><p style="margin-left:71.4pt;">3.&nbsp;&nbsp;&nbsp;&nbsp; Consider possibilities of direct utilization of Z-numbers in inference systems,</p><p style="margin-left:71.4pt;">4.&nbsp;&nbsp;&nbsp;&nbsp; Develop (write) a program that implements the constituents of the proposed methodology,</p><p style="margin-left:71.4pt;">5.&nbsp;&nbsp;&nbsp;&nbsp; Conduct experiments and analyze the results attained.</p><p>In the present report an approach based on using transformed Z-numbers (&ldquo;Z-number &reg; classical fuzzy number&rdquo;) in FIS is analyzed to&nbsp; . As a result of studying of this approach, a program that visualizes the work of the &nbsp;FIS is developed. Taking into account the fact that&nbsp; the analysis of the arithmetic operations on discrete Z-numbers was formalized by the &nbsp;time &nbsp;of project&rsquo;s active phase, the prospects of potential usage of arithmetics on Z-numbers in fuzzy inference systems are briefly considered in the report as well. Consequently, the problems arising in this case are &nbsp;highlighted.</p>