## Intelligent System to Support the Decision-Making Process in Lean Maintenance Management
### The Theory of Rough Sets to Support the Lean Maintenance Assessment
In order to generate decision rules on the basis of the rough set theory, Rough Set Exploration System (RSES) software was used. The software was developed at the Institute of Mathematics of Warsaw University. RSES software allows one to generate decision rules with the means of four algorithms: exhaustive algorithm, genetic algorithm, covering algorithm, and learning from examples module version 2 (LEM2). They were described in the works [57; 58]. Furthermore, the software contains a number of other options, which, e.g., assign reductions for a given computer system. A reduct is a set of R attributes, where R \(\subset\) A, which allows to differentiate pairs of objects in a computer system, and at the same time, no other R proper subset possesses this property. Reductions are calculated with an exhaustive or genetic algorithm. On the basis of the assigned reductions, it is possible to create decision rules as well. For each of decision classes, RSES software calculates three indicators, which indicate classification quality:  
* Accuracy--the ratio of properly classified objects of a given class to all objects belonging to this class;
* Coverage--the ratio of the objects classified to a given class with decision rules to all objects belonging to this class;
* True positive rate--the ratio of the properly classified objects of a given class to all objects that were classified to this class. Accuracy and coverage are also calculated jointly for all decision classes (for the whole set of rules). Decision rules for the described variable \"an average OEE value\" were generated by means of all four algorithms available in RSES. The scheme of the conducted study is shown in Figure 7. The OEE symbol designates a decision table which contains 34 studied objects (enterprises). Each object is described by 17 explanatory variables: an enterprise size, production type, industry, ownership type, capital, actions undertaken to prevent unplanned downtimes (NPA number--MSI indicator), machine category, spare parts category, actions in the TPM implementation (NTPMA indicator), and mean time to repair. The described variable \"an average OEE value\" played in the study the role of a decision attribute. The remaining symbols in the scheme are described in Table 11.  
While formulating the decision rules, the parameters of genetic and covering algorithms were chosen in such a way that the accuracy and coverage of the created set were equal to 1. Table 12 includes the information on a number of rules in each of the four sets of rules. For each of the rules, a rule match is calculated. It is equal to the number of objects from the learning set and matching the forerunner of the rule. Each of the four rule sets was used for the classification of the data from the OEE decision table. The classification was accomplished by a standard voting method. The manner of such voting is as follows: each of the generated rules determines the value of a variable described for the considered object (an enterprise). The calculated match value of particular rules is treated during the voting as an importance--the higher the match of a given rule, the more important is its vote. That is why it is more influential on a final voting result than the vote of the rule with a lower match. Eventually, the object is assigned such a value of an explanatory variable that won the weighted voting. The result of the classification was presented in the form of a confusion matrix. The confusion matrix that includes the results of the classification accomplished by the rule set generated by an exhaustive algorithm was presented in Figure 8. Matrix rows correspond to the real decision classes (the values of the variable described). However, matrix columns are the results of the classification that was accomplished by the generated rules. All 34 objects that are in the decision board were classified properly. It is reflected in the values located only on the main diagonal of the confusion matrix. The last