# Effect of COVID-19 on Selected Characteristics of Life Satisfaction Reflected in a Fuzzy Model
## 2 Materials and Methods
### Computational Methods  
The main goal of the research was to adopt linguistic models of psychological questionnaires in an evaluation algorithm. Therefore, for its construction, the fuzzy system was used as the basic tool for the computation of linguistically defined rules.To design the evaluation process, where the different sources of data are proposed, we need a system with multiple inputs and one output, which will be the final assessment. As part of the research, three fuzzy systems were defined. Since the assumptions of the evaluation are based on questionnaires whose principles and interpretation are described linguistically, we rely on fuzzy systems of the Mamdani type. During previous research [9; 10; 11; 12; 13], the configuration below was efficient:  
* aggregation of premises in the rules--PROD;
* implication--MIN;
* aggregation of results from the rules (accumulation)--MAX;
* defuzzification--center of gravity (COG). The aforementioned parameters were used also in all of the models proposed in this paper. By using fuzzy systems in the models of evaluation, we obtain a flexible tool for scaling the results. We use this advantage to make the results scale as an interval [0;1]. We use mainly normal trapezoidal fuzzy sets (they can also be called fuzzy intervals); therefore, to describe them, we use a similar notation as in LR fuzzy sets (see [PERSON], 1980 [38]). However, we change the order of the values. For example, a trapezoidal fuzzy set T can be described as below:  
\[\text{T}=(\text{l},\text{k}_{1},\text{k}_{2},\text{r})\]  
where l--the beginning of the support of T, r--end of the support, k\({}_{1}\),k\({}_{2}\)--define the kernel interval of trapezoidal fuzzy set T.  
Such description of a fuzzy set is a standard in many popular scientific tools such as Mathlab, Octave, or Scilab. For the research in this paper, the six inputs of data were separated as follows. * PSS10--Perceived Stress Score
* range of values XPSS = (0;40);
* general interpretation: the higher value means the worse situation;
* specificity of the interpretation suggests three potential output states. * SWLS
* range of values XSWLS = (5;35);
* general interpretation: a lower value means a worse situation;
* specificity of the interpretation suggests six potential output states; however, as the numerical interval is narrow, we paired the context of the outputs, obtaining finally three potential output states. * NMQ--Nordic Musculoskeletal Questionnaire
* range of values XNMQ = (0;40);
* general interpretation: ahigher value means aworse situation;
* there is no specific number of output interpretations. Although the Maslach Burnout Inventory (MBI) is one questionnaire, it represents three quite different factors, so it is reasonable to treat them separately. Additionally, each of them has its own scale and interpretation. * \"Emotional exhaustion\" \(X_{\text{em}}\)
* range of values \(X_{\text{em}}\) = (0,54);
* general interpretation: a higher value means a worse psychological condition. * \"Deppersonalization\" \(X_{\text{dep}}\)
* range of values \(X_{\text{dep}}\) = (0,30);
* general interpretation: a higher value means a worse psychological condition. * \"Lack of personal achievements\" \(X_{\text{achiev}}\)
* range of values \(X_{\text{achiev}}\) = (0,48);
* general interpretation: a lower value means a worse psychological condition-- note that it is opposite to the other MBI factors. All three factors have three specific potential interpretations of output states. These above input data belong to three different concepts of life quality evaluation. * PSS10 and SWLS--the respondent's general opinion about their own life. * NMQ--physical state. * MBI factors--job burnout. **Proposition 0**  
The very first trivial attempt of the design of the evaluation proposition was a simple fuzzy system. The input variables PSS10 and SWLS were described by three linguistic values (derived from the specificity of questionnaire interpretation) and the rest by two.