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Abstract
The research presented in this article was conducted on a representative and purposefully selected sample of 102 residential buildings that were erected in the second half of the nineteenth and early twentieth centuries in the downtown district of Wroclaw (Poland). The degree of the technical wear of an old residential building is determined by the conditions of its maintenance and operation. The diagnosis of the impact of the maintenance of residential buildings on the degree of their technical wear was carried out using quantitative methods in the categories of fuzzy sets and also by using the authors’ own models created in fuzzy conditions. It was proved that the expression of the operational state of a building, considered as the process that plays the greatest role in its accelerated destruction, is mechanical damage to the internal structure of its elements. This damage is determined in the categories of fuzzy sets and has a high frequency and a cumulative effect of occurrence, which are characteristic for buildings in satisfactory and average maintenance conditions. The use of simple operations in fuzzy set calculus enabled the impact of elementary damage that occurs with a specific frequency, as well as the measure of its correlation on the observed technical wear of building elements to be considered. As a result, it was possible to identify the elementary damage that determines the degree of the technical wear of a building element. For each of the selected building elements, the maximal and minimal fuzzy relational equations (damage and technical wear) were determined. Their solutions were given in the form of clear relational matrixes that constitute big data arrays. They define the domain and range of the maximal and minimal fuzzy relations, the height of the fuzzy relations, their differences, and the place of their occurrence between the maximal and minimal dependencies.
Highlights
Used mathematical methods and broadly understood system analysis deal with real tasks, in which the main goal is the possibility of including all types of indeterminacy among modeled quantities, as well as the relationships between them [1,2,3,4]
The analysis of the results of research concerning the impact of damage to building elements on their technical wear, which was conducted in fuzzy set categories, leads to the following conclusions regarding the cause-effect dependencies of the fuzzy events that are considered as fuzzy relations—R ⊆ Z × U/II, III, IV (Tables 3–5):
The calculations in the fuzzy sets enabled the cause-effect relationships of the fuzzy events, which are defined in the categories of fuzzy relations for the three middle maintenance states of buildings, to be found;
Summary
Used mathematical methods and broadly understood system analysis deal with real tasks, in which the main goal is the possibility of including all types of indeterminacy among modeled quantities, as well as the relationships between them [1,2,3,4]. Every indeterminacy is traditionally identified with an uncertainty of a random type, which enables the use of known probabilistic and statistical tools [5,6,7]. In the technical assessment of building structures, the indeterminacy of the type of inaccuracy, ambiguity, and imprecision of meanings can be found. In the conditions of fuzziness [8,9,10,11,12,13,14], indeterminacy concerns the occurrence of a certain event and its meaning in general, which cannot be captured using probabilistic methods [15,16,17,18]
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