# Bayes Conditional Probability of Fuzzy Damage and Technical Wear of Residential Buildings
## 2 Research Method
### Problem Identification
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & \\ \cline{3-8}
**No. of** & & & & & & & & & \\
**Damage** & & & & & & & & & \\ \cline{3-8}
**p/o/l & **Name of Damage** & & & & & & & & & \\ \cline{3-8}
**p/o/l & **p/o/l & **p/o/l & **p/o/l** & **p/o/l & **p/o/l** & **p/o/l** & **p/o/l** \\ \hline u1 & Mechanical damage & 0.80 & 0.69 & 0.68 & 0.65 & 0.73 & 0.78 \\ u2 & Leaks & & & & & & & \\ u3 & Brokl losses & & & & & & & \\ u4 & Mortar losses & & & & & & & \\ u5 & Brokl decay & & & & & & & \\ u6 & Mortar decay & & & & & & & \\ u7 & Peeling of plant coatings & 0.90 & 0.76 & 0.86 & 0.59 & 0.91 & 0.96 \\ u8 & Falling of plant coatings & 0.20 & 0.31 & 0.23 & 0.00 & 0.23 & 0.30 \\ u9 & Encls in birds & & & & & & & \\ u10 & Cracks on plastic & 0.50 & 0.78 & 0.91 & 0.41 & 0.86 & 1.00 \\ u11 & Scrubbing on walls & & & & & & & \\ u12 & Scrubbing on plastic & 0.30 & 0.78 & 0.86 & 0.35 & 0.99 & 1.00 \\ u13 & Locongong of plastic & 0.00 & 0.29 & 0.95 & 0.00 & 0.14 & 0.89 \\ u14 & Falling of plastic sheets & 0.00 & 0.00 & 0.36 & 0.00 & 0.20 & 0.22 \\ u15 & Dampensens & 0.00 & 0.00 & 0.23 & 0.00 & 0.00 & 0.53 \\ u16 & Wipping & 0.00 & 0.00 & 0.14 & 0.00 & 0.00 & 0.41 \\ u17 & Biological correlation of birds & & & & & & \\ u18 & Pugus & & & & & & \\ u19 & Modal and rot & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ u20 & Corrosion ratio of soft beams & & & & & & \\ u21 & Surface correction of steel beams & & & & & & \\ u22 & Deep correction of soft beams & & & & & \\ u23 & Flooding with water & & & & & & \\ u24 & Dynamic sensitivity of floor beams & & & & & & \\ u25 & Deformations of wooden beams & & & & & & \\ u26 & Sieving of window jittery & & & & & & \\ u27 & Warping of window jittery & & & & & & \\ u28 & Datamination of wooden elements & & & & & & \\ u29 & Partial insect infestation of wooden elements & & & & & & \\ u30 & Complete insect infestation of wooden elements & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._It should be noted that a slightly simplified approach, in which a fuzzy number is assigned to the probability of fuzzy events, was used here. This is opposed to the _Yager_ approach [5; 6], in which the probabilities are fuzzy events. It is important that the study did not consider the differences between the concepts of fuzziness and randomness. It was only assumed, although these phenomena are different and described differently, that they may nevertheless occur together as two types of uncertainty. Model of Determining the Conditional Probabilities of the Process of Technical Wear in Relation to the Occurrence of Damage  
The preliminary assumption: the process of technical wear of building elements occurs when there is identifiable damage: [ZII, ZIII, ZIV] = Z \(\Leftrightarrow\) U. The technical wear of building elements, determined by a group of experts in the II, III, and IV state of their technical maintenance, takes the following argument values:  
* ZII = {20, 25, 30}% = {z1, z2, z3}, moreover, z4 = 0;
* ZIII = {35, 40, 45, 50}% = {z1, z2, z3, z4};
* ZIV = {55, 60, 65, 70}% = {z1, z2, z3, z4}. Technical inspections of the residential buildings were executed by a team of experts consisted of:  
* 1 architect;
* 1 structural engineer;
* 1 mechanical/sanitary engineer;
* 1 electrical engineer;
* 2 quantity surveyors;
* 1 technician/administrator. In order to simplify the calculations, it was assumed that the domain of sets defined as fuzzy (ZII, ZIII, and ZIV) is interval [0.2, 0.7], and each of the sets contains a sum of N arguments of z1, z2, z3, z4. Each of these arguments occurs n times in the set.