## 3 DMAIR Description
### Assessment-Test Generation (TG)
#### 3.3.2 TG Component Structure  
Assessment Structures  
The main elements used in the generation process are the item (\(q\)), the sequence of items or the test (\(SI\)) and the requirements (\(R\)), described as follows:  
* \(q\): the item, a tuple \((id,nkw,kw,d,type)\), generated and stored in a database, where the elements of the tuple are as follows:
* \(id,id\in\mathbb{N}\): the unique identification particle of the item;
* \(stq\): the statement, which consists of a phrase or set of phrases that describes the initial data and item requests to be resolved;
* \(nkw,nkw\in\mathbb{N}\): the number of keywords that define an item;
* \(kw,kw=\{kw_{i}|i=\overline{1,nkw}\}\): the set of keywords, considered similar to a semantic tag, represents a collection of keywords defining an item. A keyword, denoted as \(kwi\), refers to a term or phrase that characterizes the subject matter of the item. These keywords can be acquired either manually by a human operator or automatically through Machine Learning (ML) powered Natural Language Processing (NLP) methodologies;
* \(d,d\in[0,1]\): the degree of difficulty of the item, determined through specific metrics (typically statistical, such as the ratio between the number of correct responses to the item and the total number of attempts or responses);
* \(type,type\in\{'m^{\prime},'e^{\prime},'s^{\prime}\}\): the item type, where m has the meaning of multiple-choice item, e essay item and s short-answer item;
* \(Vq\) (where necessary): a list of two or more possible answers when the item type is multiple or null or when the item type is short or essay;
* \(tp,tp\in\{0,1\}\): the theoretical or practical nature of the item, where 0 is theoretical and 1 is practical.
* SI: the sequence of items, a tuple \((id,m,Q,D,kwSI)\) that encodes an educational assessment test created according to specified criteria or requirements using genetic algorithms. The components of the tuple are as follows:
* \(id,id\in\mathbb{N}\): the unique identification particle of the test;
* \(m,m\in\mathbb{N}\): the test size (the number of questions);
* \(Q,Q=q_{i}|i\leq m\): the set of items that form the test;
* \(kw_{SI},kw_{SI}=\bigcup\limits_{i=1}^{m}kw_{i}\): the union of the sets of keywords of all the items \(q\) within the sequence;
* \(D,D\in[0,1]\): the degree of difficulty of the item, which is calculated as an average of the degrees of difficulty of all the items that form a test, as follows: \[D=\frac{1}{m}\sum\limits_{i=1}^{m}q_{i}(d)\] (10)
* TP being the proportion of practical questions;
* \(QT,QT=[qt_{m},qt_{s},qt_{e}]\): an array determining the predominant item type in SI. The values of the vector contain the number of items of each type in SI, \(qt_{m}\) being the number of multiple-choice items, \(qt_{s}\) being the number of short-type items, and \(qt_{e}\) being the number of essay-type items.
* \(R\): the set of requirements \(\{R_{1},R_{2},...,R_{k}\}\), where \(R_{i},i\leq k\) is a requirement for the test generation and \(k\) the total number of requirements. For this paper, \(k=3\) or \(k=4\) and the requirements are as follows:\(R_{1}\) represents the requirement associated with the topic of the items required in the sequence. This requirement is linked to the set of user-desired keywords, denoted as \(uKW\), where \(uKW=\{uKW_{i}|i=\{\overline{1,nKW}\}\}\) represents the list of user-defined keywords and \(nKW\) represents their total count;
* \(R_{2}\) is the requirement related to the degree of difficulty. \(R_{2}\) is related to the desired \(uD\) degree of difficulty, where \(uD\in[0,1]\), a value closer to zero means that the test is desired to be \"less difficult\" and closer to 1 being \"more difficult\";
* \(R_{3}\) is the requirement related to the predominant item type, which can take values from the type set; thus, \(uT\in\{^{\prime}m^{\prime},^{\prime}e^{\prime},^{\prime}s^{\prime}\}\);
* \(R_{4}\) is the requirement related to the desired theoretical/practical ratio (\(uTP\)).