Damage and Technical Wear of Tenement Houses in Fuzzy Set Categories

Abstract

The results and conclusions of the research presented in the article concern the topic of the technical maintenance and wear of traditionally erected residential buildings. The cause and effect relations between the occurrence of damage to the elements of tenement houses, which are treated as an expression of their maintenance conditions, and the size of the technical wear of these elements were determined in a representative and purposefully selected sample of 102 apartment houses built in the second half of the 19th and early 20th centuries in the Wroclaw, Poland downtown district “Srodmiescie”. Recognition of the impact of the maintenance of residential buildings on the level of their technical wear was carried out using quantitative methods from fuzzy set categories, and also with the use of the authors’ own model. The created model, based on the Zadeh function, was created in fuzzy conditions for the purpose of assessing the degree of damage to selected building elements. The treatment of the problem with regard to fuzzy criteria allowed for the synthesis of elementary criteria, which give the greatest approximations at the technical research stage of a residential building, into a global assessment of the degree of the wear of its elements. Moreover, it also significantly reduced the subjective factor of this assessment, which had a significant impact on the results of the research obtained in the case of good, medium and poor conditions of tenement houses. It was proven that the conditions of maintenance and use of buildings determine the amount of technical wear of their elements. The state of exploitation of the examined tenement houses is reflected in the mechanical damage to the internal structure of the elements (determined in fuzzy categories). This damage has a significant frequency and cumulative effects, and is characteristic for buildings with satisfactory and average maintenance.

Bayes Conditional Probability of Fuzzy Damage and Technical Wear of Residential Buildings

“…In the last stage of the developed model, the Bayes formula [37][38][39] for a posteriori probabilities was used. It determines the conditional probabilities of fuzzy events (i.e., the processes of the technical wear of building elements) in relation to another fuzzy event, i.e., the occurrence of their damage.…”

“…The above calculations of the conditional and partial probabilities (33)(34)(35)(36)(37)(38)(39) enabled the probability of the occurrence of technical wear processes to be determined in the middle, non-acute technical maintenance states of the analyzed residential buildings:…”

“…Methods, models, and methodological tools for the assessment of the technical condition of buildings, which are considered in the article with regards to the research sample, were described and summarized by Konior in papers [30][31][32][33][34] with co-authors [35][36][37] and in a collective study under the supervision of Kapliński, which is entitled "Methods and Models in the Engineering of Building Processes" [38].…”

Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses

“…Authors Year Topic of Study Type of Approach [1][2][3][4] Zavadskas, Antuchevičienė, Kapliński, Konior 2007Konior -2015 Decision making Models and methods [5][6][7] Hellwig, Morrison, Jackson 2001 Randomness Statistics [8][9][10][11][12][13][14] Zadeh, Yager, Kaufmann, Sanchez, Kacprzyk 1965Kacprzyk -2007 Uncertainness Fuzzy sets [15][16][17][18] Knight, Menassa, Konior 2011-2020 Uncertainty Appraisal of buildings [19][20][21][22][23][24][25][26][27][28][29] Nowogońska, Konior…”

“…The problem of the damage and destruction of residential buildings is widely described in the literature [19][20][21][22][23][24][25][26][27][28][29]. There is even a classification of damage that is characteristic for different types of buildings [30][31][32][33][34][35][36][37][38], e.g., those erected using industrialized methods or those with traditional construction.…”