# Fuzzy System for the Quality Assessment of Educational Multimedia Edition Design
## 4 Results  
Suppose the process of creating a design for a multimedia edition is a function \(Q=F(S_{1},S_{2},S_{3},S_{4},S_{5},S_{6},S_{7})\), the arguments of which are factors (linguistic variables) selected on the basis of expert evaluation. The value of this function is determined by the predicted edition integral quality indicator \(Q\), expressed through partial indicators. \[Q=F_{Q}(D,W,O) \tag{17}\]  
where \(D=F_{D}(d_{1},d_{2},d_{3})\)--characteristics of the quality of the edition output data; \(W=F_{w}(w_{1},w_{2})\)--the edition processing; \(O=F_{O}(o_{1},o_{2})\)--the quality of content representation. The quality of an educational multimedia edition is formed on the basis of three main parameters. The first parameter covers the characteristics of the output data, namely the structure and content of the edition. It takes into account the format, type and volume of the material, which affects the content filling and the information relevance. The second parameter concerns the quality of the material processing in terms of compliance of the text and graphic elements with the design standards. The third parameter determines the quality of content representation and determines the use of illustrations, multimedia elements and font solutions that affect the perception of the material and its visual appeal. The described parameters are interrelated and affect the design of educational editions. They are decisive for the quality formation. The identified linguistic variables are presented in Table 2. Their notation, names and values in conventional units (c. u.) are specified to standardize the values of linguistic terms. This allows for a high level of system adaptability to changes in requirements or analysis conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Linguistic Essence** & **Universal Set of Values** & \\
**of the Variable** & **(the Set \(V\))** & **Linguistic Terms (the Set \(L\))** \\ \hline \(d_{1}\) & Edition format & (1–3) c. u. & Small, medium, large \\ \(d_{2}\) & Edition type & (1–3) c. u. & Simple, complicated, complex \\ \(d_{3}\) & Edition volume & (1–3) c. u. & Small, medium, large \\ \(w_{1}\) & Page layout & (1–3) c. u. & Simple, complicated, complex \\ \(w_{2}\) & Proofreading & (1–3) c. u. & Simple, complicated, complex \\  & Illustrative and multimedia design & (1–3) c. u. & Small, medium, large \\  & (volume of illustrations and multimedia) & (1–3) c. u. & Small, medium, large \\ \(o_{2}\) & Typographic design (font size) & (1–3) c. u. & Small, medium, large \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Term-sets of values of linguistic variables. A logical inference model is constructed that represents the hierarchical dependency of the quality of a multimedia edition on the values of the linguistic terms of the factors (Figure 1). The developed model contributes to the consistent establishment of predictive quality of the multimedia edition design by accumulating knowledge from the lowest to the highest of its levels. Obtaining fuzzy sets is presented on the example of the factor \"edition format\". Calculations for other factors are carried out in a similar way. The matrix \(A\) is constructed for the linguistic variable \"edition format\". The universal set of values of the analyzed linguistic variable is \(V(d_{1})=[1;2;3]\) c. u. The corresponding term-set of values is \(L(d_{1})=\)small, medium, large\(>\). Matrices for the terms \"small\", \"medium\" and \"large\":  
\[A_{small}(d_{1})=\left[ \begin{array}{ccc}1&4/9&1/9\\ 9/4&1&1/4\\ 9&4&1\end{array} \right]\quad A_{medium}(d_{1})=\left[ \begin{array}{ccc}1&8&1 \\ 1/8&1/8\\ 1&8&1\end{array} \right]\quad A_{large}(d_{1})=\left[ \begin{array}{ccc}1&5&9 \\ 1/5&1&9/5\\ 1/9&5/9&1\end{array}