# Bayes Conditional Probability of Fuzzy Damage and Technical Wear of Residential Buildings
## 1 Introduction
### Research Sample  
The research sample, which included 102 technically assessed residential buildings from the \"Srodmiesce\" district of Wroclaw, was selected from a group of 160 examined objects [39]. The overriding criterion for sampling involved the obtaining of a comparable group of objects. Mutual comparability of the downtown tenement houses meant:  
* age coherence, i.e., a similar period of erection, maintenance, and use with regards to historical and social aspects;
* compactness of the building development in the urban layout that remained unchanged for years;
* similar location along downtown street routes with an urban, but not representative, character;
* construction and material homogeneity, especially with regards to the load-bearing structure of buildings;identical functional solutions, understood as the standard of apartment amenities and furnishings (for that time), and a defined standard of living for residents.  
The method of selecting the research sample at the level of greater detail was based on the mutual similarity of all the technical solutions of the downtown tenement houses. The selected research sample, according to the criteria presented above, is a representative sample with regards to the concept of representativeness that is specific to the adopted purpose of the study [40; 41]. It contains all the values of the variables that could be recreated from the research carried out earlier using a different objective function than the one adopted in the study.  
These values and variables were then compiled and processed in such a way that it was possible to make conclusions about the cause-effect relationships between them in the general population.  
Therefore, it can be considered as a typologically representative sample that includes the desired types of homogeneous variables. Due to the fact that the structure of the population and its properties were previously well recognized, such a selection of the research sample can also be seen as a deliberate selection. It should be noted that the sample may not be representative in terms of the distributions of the studied variables, which may--for the adopted level of significance--not correspond to analogous distributions in the general population. It is also not known--at this stage of the research--whether the selected sample is representative due to the relationship between its variables and the identically defined variables in the entire set of downtown residential buildings. Therefore, at the very beginning of the research, it was assumed that a specific research sample occurs in the existing population with the fuzzy phase.  
Tested buildings have been classified into classes, determined by the degree of the technical wear. The technical wear 0-15% has been classified to the class I, 16-30% to the class II, 31-50% to the class III, 51-70% to the class IV, 71-100% to the class V. Owing to the fact that all considering apartment houses belong to the same group of their age it is possible to assume that the class of the technical wear corresponds to the conditions of building maintenance. Therefore, the equivalence has been defined: a poor maintenance--the class IV, V, an average maintenance--the class III, an above than an average maintenance--the class II, a very well cared maintenance--the class I.