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

Round 1

Reviewer 1 Report

Thank you for this contribution. This paper discusses how fuzzy sets can be used to explore the damage state of residential buildings. The conducted analysis is typically standard and falls within the expected work from such a publication and hence the work merits publication. As such, the authors are invited to properly address the following items:

1. The amount of works in AI/ML/fuzzy sets area continues to rapidly rise. The authors are advised to strengthen their literature review section with supplementary material. For example, the following is a result of a quick google scholar search and the authors may option to conduct their won search as well. (Seitllari et al. 2019), (Chung, 2012), (Zen 2010) etc.
2. Table 3 present a large matrix (which is understandable given the analyzed number of parameters). Is there a way to condense this matrix or make a bit aesthetically pleasing?
3. Is there a method to ensure that the procedure outlined in this work can be easily transferable to other projects? This may enable readers from using your approach into their problems.
4. In Table 5, would not "age" of the structure be a key item to consider?

 

Author Response

Wrocław, Poland, 23^rd February 2021

 Dear Reviewer of Applied Sciences,

Thank you for the review of our paper applsci-1125608 entitled “Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses” to be published in the journal Applied Sciences, special issue “Big Data in Construction Engineering and Management”.

We appreciate your thoughtful and  accurate comments as well as appreciation of our research works. We have carefully considered all comments and have now completed the revisions incorporating  your suggestions in the revised uploaded manuscript.

We hope that the revised paper meets your expectations.

Kind regards,

Jarosław Konior and Tomasz Stachoń

Department of Building Engineering, Faculty of Civil Engineering, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

 Here are answers to reviewer’s comments:

REVIEWER 1

General Comment. Thank you for this contribution. This paper discusses how fuzzy sets can be used to explore the damage state of residential buildings. The conducted analysis is typically standard and falls within the expected work from such a publication and hence the work merits publication. As such, the authors are invited to properly address the following items:

Answers to General Comment. We appreciate the reviewer’s valuable view on the presented topic and addressed the presented suggestions the following way:

Some specific suggestions:

Comment 1. The amount of works in AI/ML/fuzzy sets area continues to rapidly rise. The authors are advised to strengthen their literature review section with supplementary material. For example, the following is a result of a quick google scholar search and the authors may option to conduct their won search as well. (Seitllari et al. 2019), (Chung, 2012), (Zen 2010) etc.

Answer 1. We provided a deep search and assessment of biography on fuzziness in the survey presented in the item 1.1 and digest in the table 1. We relied on the source fuzzy literature of Zadeh [8, 9], Yager [10, 11], Sanchez [12], Kaufmann [13] and Kacprzyk [14]. All of them are “Gurus” of fuzzy sets theory and applications. There is quite limited range of accessible literature on fuzziness practically used for engineering and construction, many more refer to computing, automation, programming processing and topology. As suggested, we searched and reviewed the most cited references on the fuzzy algorithms and simulations:

• Seitllari, A. Traffic flow simulation by neuro-fuzzy approach. Proceedings of Second International Conference on Traffic and Transport Engineering (ICTTE), 2014, Belgrade, pp. 97-102.
• Kannana, S. R.; Ramathilagamb, S.; Chung, P. C. Effective fuzzy c-means clustering algorithms for data clustering problems. Expert Systems with Applications. Vol. 39, 7, 2012, pp. 6292-6300.
• Gen, M.; Yu, X. Introduction to evolutionary algorithms. Springer Science & Business Media, 2010, Berlin.

but with neither new value nor practical input to the topic of fuzzy relations. Relevant and up to date references from different parts of the world have also been represented in our survey and analysis for the research [1-2, 16, 35-40, 45-48, 51-54] which constitutes 17 refs out of 55 items (31%) which is in balanced comparison to middle Europe literature: 24 refs out of 55 items (44%). We can keep reviewing further on but with a little value on the research goals already achieved.

Comment 2. Table 3 present a large matrix (which is understandable given the analyzed number of parameters). Is there a way to condense this matrix or make a bit aesthetically pleasing?

Answer 2. Good point. Matrix of fuzzy relation R = Z x U for 10 selected building elements and their 30 characteristic types of damage has been reduced to 300 cells with a clear identification of values which are related to one another (90 fuzzy relations).

Comment 3. Is there a method to ensure that the procedure outlined in this work can be easily transferable to other projects? This may enable readers from using your approach into their problems.

Answer 3. Yes, it is. The fuzzy approach can be for instance adopted in all engineering situations where engineers must act in uncertainty to some extent, e.g. in construction management process. Elaboration of probability of occurrence in a construction project unforeseen building works requires application (in addition to the non-measurable, qualitative criteria) of measurable (quantitative) criteria which still appear during construction project implementation. In reimbursable engineering contracts, a random event described as an extra, supplementary building work has a random character and occurs with a specific likelihood. In lump sum contracts, on the other hand, such a random event has a fuzzy character and its occurrence is defined in a linear manner by the function of affiliation to the set of fuzzy events being identical with unforeseen events. The strive for quantitative presentation of criteria regarded by nature as qualitative and the intention to determine relations between them led to the application of the fuzzy sets theory to this issue. Their properties enable description of the unforeseen works of construction projects in an unambiguous, quantitative way. As to explore the fuzzy vs. probable application for CPM please see: Konior J. “Fuzziness over randomness in unforeseen works of construction projects.” Civil Engineering and Architecture. 2019, vol. 7, nr 2, pp. 42-48, https://doi.org/10.13189/cea.2019.070202 or Konior J. “Random and fuzzy measure of unpredictable construction works.” Archives of Civil Engineering. 2015, vol. 61, nr 3, pp. 75-88, https://doi.org/10.1515/ace.2015-0026

Comment 4. In Table 5, would not "age" of the structure be a key item to consider?

Answer 4. Not exactly. The age of the structure is not a key item to be considered in fuzzy relations. The age of the elements of an old residential building with a traditional construction:

• is of secondary importance in the process of the intensity of the loss of its serviceability value;
• is not a fundamental quantity that determines the course of their technical wear.

The nonlinear regression method indicates that, in some specific building elements and with the proposed mathematical models, at best no more than 30% of the damage of elements is explained by the passage of time. The degree of the technical wear (Z) of the elements of an old residential building is determined by the conditions of its maintenance and use. Therefore, the identified set of defects (U) better than age represents the technical state of the elements and is considered for fuzzy relation R = Z x U. Fore more explanation please look at ref. [27]: Konior, J.; Sawicki, M.; Szóstak, M. “Influence of Age on the Technical Wear of Tenement Houses.” Appl. Sci. 2021, 11, 297. https://doi.org/10.3390/app11010297

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well presented. However, at point 1.2 authost discussed about "folowing groups: I, II, III, IV (Tab. 1)".  But in Table 1 no groups I...IV were presented. The authors must provide information regarding groups I...IV.

Author Response

Wrocław, Poland, 23^rd February 2021

 Dear Reviewer of Applied Sciences,

Thank you for the review of our paper applsci-1125608 entitled “Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses” to be published in the journal Applied Sciences, special issue “Big Data in Construction Engineering and Management”.

We appreciate your thoughtful and  accurate comments as well as appreciation of our research works. We have carefully considered all comments and have now completed the revisions incorporating  your suggestions in the revised uploaded manuscript.

We hope that the revised paper meets your expectations.

Kind regards,

Jarosław Konior and Tomasz Stachoń

Department of Building Engineering, Faculty of Civil Engineering, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

 

 Here are answers to reviewer’s comments:

 REVIEWER 2

Comment 1. The paper is well presented. However, at point 1.2 authors discussed about "following groups: I, II, III, IV (Tab. 1)".  But in Table 1 no groups I...IV were presented. The authors must provide information regarding groups I...IV.

Answer 1. Good point, thank you for spotting the mistake and lack of defects group explanation. The following correction and supplementation were inserted: “The identified defects constitute the following groups of damages:

• I - mechanical defects of the structure and surface of elements
• II - defects of elements caused by water penetration and humidity migration
• III - defects symptomatic of the loss of the original shape of wooden elements
• IV - defects of wooden elements attacked by insects—technical pests of wood”

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is well-written. The authors examined 102 residential buildings provided in a technical report (1984-1996). Why were those buildings selected for this research? Do those buildings represent the general buildings in Poland?

Author Response

Wrocław, Poland, 23^rd February 2021

 Dear Reviewer of Applied Sciences,

Thank you for the review of our paper applsci-1125608 entitled “Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses” to be published in the journal Applied Sciences, special issue “Big Data in Construction Engineering and Management”.

We appreciate your thoughtful and  accurate comments as well as appreciation of our research works. We have carefully considered all comments and have now completed the revisions incorporating  your suggestions in the revised uploaded manuscript.

We hope that the revised paper meets your expectations.

Kind regards,

Jarosław Konior and Tomasz Stachoń

Department of Building Engineering, Faculty of Civil Engineering, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

 

 Here are answers to reviewer’s comments:

REVIEWER 3

General Comment. The paper is well-written. The authors examined 102 residential buildings provided in a technical report (1984-1996). Why were those buildings selected for this research? Do those buildings represent the general buildings in Poland?

Answers to General Comment. The subject of the research involves tenement houses in a separate part of the downtown district in Wroclaw, Poland. The buildings are situated along downtown streets of secondary importance in an urban layout that has remained unchanged for years. They are front buildings and also outbuildings with a modest architectural design and economical functional standard. The facilities were built of brick in longitudinal, usually three‐bay, structural systems. 102 tenement houses were mainly erected in the second half of the nineteenth century, until the outbreak of World War I. The above-described downtown residential buildings with construction and material solutions typical for the turn of the 19th and 20th centuries, similar functions and standards, and a specific form of ownership (the so-called pre-war "tenement houses") are defined by the term "tenement houses". The research sample, covering 102 technically assessed residential buildings from Wroclaw's Srodmiescie district, was selected from a group of 160 examined buildings. The overriding criterion for the selection of the sample was the obtaining of a comparable group of objects. Mutual comparability of downtown tenement houses meant:

• age coherence, i.e. a similar period of erection, maintenance and exploitation with regards to historical and social aspects;
• compact development in the urban layout that has remained unchanged for years;
• similar location along downtown street routes with an urban, but not representative, character;
• construction and material homogeneity, especially regarding the load-bearing structure of buildings;
• identical functional solutions, which are understood as the standard of apartment amenities and furnishings in force at that time, and also a specific standard of living of residents.   

A method of selecting the research sample at the level of greater detail was based on the mutual similarity of all technical solutions of downtown tenement houses. The selected research sample, according to the criteria presented above, is representative with regards to one of the concepts (specific for the adopted purpose of the study) of representativeness. It contains all the values ​​of the variables, which could be recreated from previous research that had a different objective function than the one adopted in this study. However, these values were compiled and processed in such a way that it is possible to make conclusions about the cause-effect relationships between them in the general population. Thus, the typological representativeness of the sample into which the desired types of homogeneous variables are classified can be assumed. Due to the fact that the structure of the population and its properties were well recognized earlier, such a selection of the research sample can also be considered to be deliberate. It should be noted that the sample may not be representative in terms of the distributions of the examined variables, which may - for the adopted significance level - not correspond to the 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 correspondence between its variables and the identically defined variables in the entire set of downtown residential buildings.

Therefore, the investigated apartment houses do not represent general buildings in Poland but stand for significant part of tenement buildings which in Wroclaw city constitutes like 20% of the overall houses.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Dear Authors,

The paper Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses by Jarosław Konior, Tomasz Stachoń is well suited for journal Applied Sciences The authors of this article analyzed the results of the present studies on the possibility of using fuzzy relations to determine the degree of the technical wear by damages.

The paper is substantially good and maybe scientifically valuable. However, there are several aspects that need to be improved. The reviewer can only recommend for publication if the author satisfactorily address the following comments in the revised version.

- taking into account the authors' use of some of the achievements published in previous articles, it is necessary to indicate in more detail what new achievements present article brings,

- a lot of effort was put into describing the sophisticated mathematical apparatus, but it was not stated at each stage for what purpose (of a given element, in pursuit of the main goal) the particular calculations were used,

- line 232 – the authors should explain the sensitivity of the results, whether the data set can be considered sufficient or whether its variability allows us to believe that the results are "stable",

- line 265 – the range of values seems to be relatively narrow - from 0.44 to 0.68, the authors' commentary could be useful in this regard,

- lines 276-284 - what do mean values close to 0.5 for all relations mean? does this level of fuzzy relations mean not very strong correlation and a significant influence of factors not taken into account here?

- line 289 – this chapter needs more elaboration; the whole chapter is very "general", at this point it is necessary to indicate the achievements specifically, explain how to use them,

- line 290 – in reviewer opinion instead of “The size of the technical wear”  will be better “The degree of the technical wear”,

- line 300 - “it was possible to identify the elementary damage that determines the degree of destruction” - the authors are asked for a detailed explanation - since "elementary damage" has been identified, please indicate in the summary where the result is in the article; there is a lack of clarity for the reviewer,

- lines 312-316 - „The use of simple operations in fuzzy set …. building element.” - almost the same piece of text is in the lines 297-301,

The article was written enough well in English, is understandable for a reviewer, a person who does not speak English as a mother tongue.

Author Response

Wrocław, Poland, 2^nd February 2021

 Dear Reviewer of Applied Sciences,

Thank you for the review of our paper applsci-1125608 entitled “Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses” to be published in the journal Applied Sciences, special issue “Big Data in Construction Engineering and Management”.

We appreciate your thoughtful and  accurate comments as well as appreciation of our research works. We have carefully considered all comments and have now completed the revisions incorporating  your suggestions in the revised uploaded manuscript.

We hope that the revised paper meets your expectations.

Kind regards,

Jarosław Konior and Tomasz Stachoń

Department of Building Engineering, Faculty of Civil Engineering, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

 Here are answers to reviewer’s comments:

REVIEWER 4

General Comments. The paper Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses by Jarosław Konior, Tomasz Stachoń is well suited for journal Applied Sciences The authors of this article analyzed the results of the present studies on the possibility of using fuzzy relations to determine the degree of the technical wear by damages. The paper is substantially good and maybe scientifically valuable. However, there are several aspects that need to be improved. The reviewer can only recommend for publication if the author satisfactorily address the following comments in the revised version. The article was written enough well in English, is understandable for a reviewer, a person who does not speak English as a mother tongue.

 Answers to General Comments. Thank you for appreciation of value of or research works. Please note that the presented topic of fuzzy relations between damages and technical wear is a continuation of the set of publications on the subject both by probabilistic and fuzzy approaches [4, 17-18, 24-29]. All accurate reviewer’s comments were addressed in the revised paper, in particular:

Comment 1. Taking into account the authors' use of some of the achievements published in previous articles, it is necessary to indicate in more detail what new achievements present article brings.

Answer 1. There are several new achievements presented in the article clearly laid out in lines 233 – 288 focused on reliance measurable technical wear on fuzzy defects. All fuzzy relations RÍZ×U corresponding to 30 mostly appeared pinpointed defects U_ij in 4 groups of 10 selected for research technical wear degrees Z_j have been determined in fuzzy relation matrix R=Z×U. It was possible to calculate the range, the domain and the height of the fuzzy relations RÍZ×U as quantitative values. There are two main novelties from elaborating the relations RÍZ×U in fuzzy sets categories:

• exactly 30% out of 300 Uij and Zj relations pair are linked with each other in “i” columns, 1/3 of them with R over 0.5 which indicates significant alliances
• the height h(R) of the tested fuzzy relations RÍZ×U is getting to normal h(R)=1 not only as one maximum in the relation matrix but appears in 9 cases (3% of U_ij and Z_j relations)

This enabled to determine the most significant alliances between the damages and technical wear of examined buildings elements.

Comment 2. A lot of effort was put into describing the sophisticated mathematical apparatus, but it was not stated at each stage for what purpose (of a given element, in pursuit of the main goal) the particular calculations were used.

Answer 2. We cannot agree with the comment to a full extent. After setting the problem and inducting fuzzy relations idea in item 2.1 the domain, scope and height of the maximal and minimal fuzzy relations RÍZ×U for 10 selected elements in the II, III and IV maintenance class of a residential building were given in the table 4. The purpose of that stage was to present quantitative and measurable values of the damages and technical wear that can be easily quantified, not only described. The fuzzy relational equations (maximal and minimal) transformed in items 2.2.1 and 2.2.2 for the purpose of the following examination: the middle compositions (ZIII-UIII) are identical and that they unambiguously define the value of fuzzy relation ("technical wear - damage") RÍZ×U in interval [0; 1], which is equal to:

• for foundations: 0.50
• for basement walls: 0.48
• for solid floors above basements: 0.46
• for structural walls: 0.48
• for internal stairs: 0.45
• for roof constructions: 0.41
• for window joinery: 0.50
• for inner plasters: 0.44
• for facades: 0.44

This is why the particular calculations (though still selected) were used.

Comment 3. Line 232 – the authors should explain the sensitivity of the results, whether the data set can be considered sufficient or whether its variability allows us to believe that the results are "stable".

Answer 3. Good point. We propose to include the following allowance but in item 4 (Discussion), rather than in item 3 (Results): “Attention should be paid to the individual character of the research results, which were based on the analysis of a homogeneous, coherent group of downtown tenement houses. The transfer of the results of the technical assessment to a different population of residential buildings with a traditional construction should be subjected to great caution and the necessity to conduct surveys. Undoubtedly, such studies should be preceded by the careful and purposeful selection of a typological sample that is representative for the general population.”

Comment 4. Line 265 – the range of values seems to be relatively narrow - from 0.44 to 0.68, the authors' commentary could be useful in this regard.

Answer 4. Useful remark. The supplementary explanation was inserted after the line 265: “the span of values is relatively narrow which indicates the minimal heights of fuzzy relations may be expected above 0.5 (average 0.56) in the interval [0; 1]”

Comment 5. Lines 276-284 - what do mean values close to 0.5 for all relations mean? does this level of fuzzy relations mean not very strong correlation and a significant influence of factors not taken into account here?

Answer 5. Not exactly. Fuzzy relations are not correlation coefficients “r”. Usually when r(Z) are close to 1 (strong correlations) then fuzzy relations RÍZ×U are in the middle of membership function which means close to 0.5 (strong relations). But both associations are not mathematically linked to each other, it is only my observations as a result of research presented in [4, 17-18, 24-29]. We enclosed this supplementary information in the revised paper.

Comment 6. Line 289 – this chapter needs more elaboration; the whole chapter is very "general", at this point it is necessary to indicate the achievements specifically, explain how to use them.

Answer 6. We cannot agree at all, sorry. Section 4 stands for Discussion of Results presented in item 3 and should not repeat conclusions of the research. Usefulness and achievements have been clearly laid out in Discussion, e.g.:

• as a result of simple operations in fuzzy sets it was possible to identify the elementary damage that determines the degree of destruction of a building element;
• the research procedure in the paper was prepared in a way that allows the previously prepared qualitative model to be transformed into a quantitative model;
• it was established 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;
• for each of the selected building elements, the maximal and minimal fuzzy relational equations - "damage - technical wear" - were determined;
• it was proved that the sought relationship has a significant strength: its minimum height and value in average compositions exceeds 0.50 within the range [0; 1] which indicates strong fuzzy relations "damage - technical wear".

Comment 7. Line 290 – in reviewer opinion instead of “The size of the technical wear”  will be better “The degree of the technical wear”.

Answer 7. Good point. Corrected as suggested.

Comment 8. Line 300 - “it was possible to identify the elementary damage that determines the degree of destruction” - the authors are asked for a detailed explanation - since "elementary damage" has been identified, please indicate in the summary where the result is in the article; there is a lack of clarity for the reviewer.

Answer 8. This is initial information presented in item 1.2 prior to the core research model described in entire section 2: “The result of an in-depth analysis of technical reports of the examined group of 102 downtown tenement houses was the identification (at the elementary level) of all the damage to building elements. The identified defects constitute the following groups of damages:

• I - mechanical defects of the structure and surface of elements
• II - defects of elements caused by water penetration and humidity migration
• III - defects symptomatic of the loss of the original shape of wooden elements
• IV - defects of wooden elements attacked by insects—technical pests of wood

The synthesis of the type of elementary failures with regards to their common cause of occurrence (II, IV), as well as the similarity of the consequences that are caused by them (I, II, III) enabled the damage to be semantically and generically ordered into the following groups: I, II, III, IV. The scope of research, which concerned 102 residential buildings, allowed the frequency of the occurrence of 30 elemental examples of damage to be determined (Tab. 2). The presentation of the type and probability of the occurrence of damage was limited to the 10 elements that had the highest share in the tested tenement houses.”

A reference to this information was added in the summary for the better clarity but it has still not been thoroughly discussed as the fuzzy relations are the topic of the paper, not the degree of damages. These were presented in the papers [26, 28].

Comment 9. Lines 312-316 - „The use of simple operations in fuzzy set …. building element.” - almost the same piece of text is in the lines 297-301.

Answer 9. Thank you for spotting the repetition. The text in the lines 297-301 was re-written and simplified.

Author Response File: Author Response.pdf

Reviewer 5 Report

Dear authors, judging by the materials presented, your article is undoubtedly relevant and reflects the modern understanding of the formation and course of wear and tear in apartment buildings. The modern stage of development is associated with technologies associated with the development and implementation of intelligent systems and technologies that provide for the formation of clear decisions based on fuzzy rules, fuzzy inference, fuzzy control. Therefore, the use of the mathematical apparatus of the theory of fuzzy logic determines in solving the problems indicated in the article is justified. Dear author, a question is raised by the fact that your article is overloaded with theoretical dependencies and this makes it difficult to perceive and analyze your contribution.
I think that there is a need to provide an assessment of literary sources on this issue in different parts of the world. I think that there are many more researchers who are interested in this issue, so my strong recommendation is to pay attention to the list of references. Regarding the sampling of experimental data, it is necessary to process all the information using modern statistical software tools, and show for the reader of your article that your research is sufficiently reliable.

Author Response

Wrocław, Poland, 23^rd February 2021

 Dear Reviewer of Applied Sciences,

Thank you for the review of our paper applsci-1125608 entitled “Fuzzy Relations Matrixes of Damages and Technical Wear Related to Apartment Houses” to be published in the journal Applied Sciences, special issue “Big Data in Construction Engineering and Management”.

We appreciate your thoughtful and  accurate comments as well as appreciation of our research works. We have carefully considered all comments and have now completed the revisions incorporating  your suggestions in the revised uploaded manuscript.

We hope that the revised paper meets your expectations.

Kind regards,

Jarosław Konior and Tomasz Stachoń

Department of Building Engineering, Faculty of Civil Engineering, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

  Here are answers to reviewer’s comments:

REVIEWER 5

General Comments. Dear authors, judging by the materials presented, your article is undoubtedly relevant and reflects the modern understanding of the formation and course of wear and tear in apartment buildings. The modern stage of development is associated with technologies associated with the development and implementation of intelligent systems and technologies that provide for the formation of clear decisions based on fuzzy rules, fuzzy inference, fuzzy control. Therefore, the use of the mathematical apparatus of the theory of fuzzy logic determines in solving the problems indicated in the article is justified.

Answers to General Comments. Thank you for appreciation of value of or research works. Please note that the presented topic of fuzzy relations between damages and technical wear is a continuation of the set of publications on the subject both by probabilistic and fuzzy approaches [4, 17-18, 24-29].

• Konior, J. Decision assumptions on building maintenance management. Probabilistic methods, Arch. Civ. Eng., 2007, 53, pp. 403–423.
• Konior, J. Technical assessment of old buildings by fuzzy approach, Archives of Civil Engineering, 2019, 65(1), pp.129–142, https://doi.org/10.2478/ace-2019-0009.
• Konior, J. Technical Assessment of old buildings by probabilistic approach., Archives of Civil Engineering, 2020, 66(3), pp. 443–466, https://doi.org/10.24425/ace.2020.134407.
• Konior, J. Maintenance of apartment buildings and their measurable deterioration, Tech. Trans. Czas. Tech. 2017, 6, pp. 101–107, https://doi.org/10.4467/2353737xct.17.090.6566.
• Konior, J. Bi-serial correlation of civil engineering building elements under constant technical deterioration, J. Sci. Gen. Tadeusz Kosciuszko Mil. Acad. L. Forces. 2016, 179, pp. 142–150.
• Konior, J. Intensity of defects in residential buildings and their technical wear, Tech. Trans. Civ. Eng. 2014, 111(2-B), pp. 137–146.
• Konior, J.; Sawicki, M.; Szóstak, M. Influence of Age on the Technical Wear of Tenement Houses. Appl. Sci. 2021, 11, 297. https://doi.org/10.3390/app11010297
• Konior, J.; Sawicki, M.; Szóstak, M. Intensity of the Formation of Defects in Residential Buildings with Regards to Changes in Their Reliability. Appl. Sci. 2020, 10, 6651. https://doi.org/10.3390/app10196651
• Konior, J.; Sawicki, M.; Szóstak, M. Damage and Technical Wear of Tenement Houses in Fuzzy Set Categories. Appl. Sci. 2021, 11, 1484. https://doi.org/10.3390/app11041484

All accurate reviewer’s comments were addressed in the revised paper, in particular:

Comment 1. Dear author, a question is raised by the fact that your article is overloaded with theoretical dependencies and this makes it difficult to perceive and analyze your contribution.

Answer 1. We are sorry but cannot agree to full extent. Operations based on fuzzy sets are not extremally complicated in comparison to stochastic, systematic or random analysis but maybe not commonly met therefore we had to introduce at least fundamental transformations leading to fuzzy relation equations. All achievements (results and conclusions) and contributions (discussion and summary) have been clearly laid out in sections 3 and 4 of the paper, in a nutshell: There are several new achievements presented in the article clearly laid out in lines 233 – 288 focused on reliance measurable technical wear on fuzzy defects. All fuzzy relations RÍZ×U corresponding to 30 mostly appeared pinpointed defects U_ij in 4 groups of 10 selected for research technical wear degrees Z_j have been determined in fuzzy relation matrix R=Z×U. It was possible to calculate the range, the domain and the height of the fuzzy relations RÍZ×U as quantitative values. There are two main novelties from elaborating the relations RÍZ×U in fuzzy sets categories:

• exactly 30% out of 300 Uij and Zj relations pair are linked with each other in “i” columns, 1/3 of them with R over 0.5 which indicates significant alliances
• the height h(R) of the tested fuzzy relations RÍZ×U is getting to normal h(R)=1 not only as one maximum in the relation matrix but appears in 9 cases (3% of U_ij and Z_j relations)

This enabled to determine the most significant alliances between the damages and technical wear of examined buildings elements.

Comment 2. I think that there is a need to provide an assessment of literary sources on this issue in different parts of the world. I think that there are many more researchers who are interested in this issue, so my strong recommendation is to pay attention to the list of references.

Answer 2. We provided a deep search and assessment of biography on fuzziness in the survey presented in the item 1.1 and digest in the table 1. We relied on the source fuzzy literature of Zadeh [8, 9], Yager [10, 11], Sanchez [12], Kaufmann [13] and Kacprzyk [14]. All of them are “Gurus” of fuzzy sets theory and applications. There is quite limited range of accessible literature on fuzziness practically used for engineering and construction, many more refer to computing, automation, programming processing and topology. As suggested we searched and reviewed the most cited references on the fuzzy algorithms and simulations:

• Seitllari, A. Traffic flow simulation by neuro-fuzzy approach. Proceedings of Second International Conference on Traffic and Transport Engineering (ICTTE), 2014, Belgrade, pp. 97-102.
• Kannana, S. R.; Ramathilagamb, S.; Chung, P. C. Effective fuzzy c-means clustering algorithms for data clustering problems. Expert Systems with Applications. Vol. 39, 7, 2012, pp. 6292-6300.
• Gen, M.; Yu, X. Introduction to evolutionary algorithms. Springer Science & Business Media, 2010, Berlin.

but with neither new value nor practical input to the topic of fuzzy relations. Relevant and up to date references from different parts of the world have also been represented in our survey and analysis for the research [1-2, 16, 35-40, 45-48, 51-54] which constitutes 17 refs out of 55 items (31%).

Comment 3. Regarding the sampling of experimental data, it is necessary to process all the information using modern statistical software tools, and show for the reader of your article that your research is sufficiently reliable.

Answer 3. Reliability of our research has been already proved by means of modern statistical software tools and was published in the papers applying probabilistic and correlation methodology [4, 18, 24-28]. The fuzzy contributions are only supplementing probabilistic analysis and are bearing out the basic findings concluded in random approach. The correctness of the test results for a representative group of old downtown apartment houses with traditional structure, erected in Wrocław (Poland) at the turn of the 19th and 20th centuries, can be therefore summed up by the following conclusions:

1. Age of elements of old apartment houses with a traditional structure:

• is of secondary importance in the process of the intensity of loss of its useful values;
• is not the essential size determining the course of their technical wear and tear;

1. The technical extent of wear and tear of the components of an old residential building is determined by the conditions for its maintenance and use;
2. The previous theoretical methods for measuring the technical wear and tear of the building and its components do not sufficiently describe the actual states, which is called into question:

• how these methods are assigned to the maintenance conditions of the building;
• not precise selection of too general forms of mathematical functions;

1. Quantitative damage analysis carried out by experiential methods of assessing the technical condition of the building shall indicate the nature and magnitude of the damage to its components which are characteristic of the relevant maintenance conditions;
2. A study analysis of the processes of operation of residential objects and the basic dependencies of reliability theory made in it indicates that for the useful life of an object in which the working time to damage has an exponential distribution (this is in principle the life expectancy corresponding to the length of service of the dwellings concerned), the average remaining time of unsafe operation is constant at all times. Theoretically, therefore, residential objects, after some time of trouble-free operation, perform their functions as new. The age of the elements of an old residential building is then of secondary importance in the process of the intensity of loss of its useful value;
3. If assumed that the measure of matching the nonlinear mathematical models tested in the nonlinear regression method, as a function of the technical consumption of building elements over time, is the determination factor, then no more than 30% of the destruction of the elements is explained by the passage of time. Age is therefore not a determinant of the technological consumption of the elements of the buildings analysed;
4. Previous theoretical methods for measuring the technical wear and tear of the building and its components do not reflect the actual course of the deterioration process over time. Two facts pay attention:

• an assessment of the significance of the differences between the theoretical and observed technical consumption distribution values of building elements by WILCOXON test and the Sign Test in most cases confirmed the conclusions of their comparative analysis and showed the significance of the differences between the distributions of theoretical and observed wear, although the Sign Test indicated their identity in the case of foundation distributions, underground walls and structural walls in the all five conditions of maintenance, while both WILCOXON test and the Sign Test confirmed the identity of the distributions only in individual maintenance groups of the building;
• adopting too general and not always appropriate forms of parabolic and linear functions to describe the theoretical side of the progress of the technical consumption of the building's elements with age; of the four nonlinear regression separable tested, new mathematical models, none of the power (parabolic) models represent the nature of the designated trend of the time-consuming process (very low determination factor and unnatural size of parameterized durability); analysis of variance in the nonlinear regression method also indicates a much better representation of the modelled trend by exposive and hyperbolic dependencies and slightly worse by linear functions;

1. The quantitative analysis of damage, carried out by empirical (visual) methods of assessing the technical condition of the buildings, indicates the type and determines the magnitude of these damage to its components which are characteristic of the appropriate conditions of maintenance. Studies of cause - effect "damage - technical wear" in observed states allow a numerical recognition of the impact of the building's maintenance conditions on the degree of technical wear of its components:

• the direction of the relationship is right-hand (positive) for all test elements of the building, but the correlation force between the defect occurring and their technical wear shows a significant span (from 0.00 to 0.84) depending on the conditions of the buildings maintenance;
• the rule is that correlations of at least moderate strength always show damage caused by water penetration and moisture penetration (on average 0,54); only in the case of internal plasters and façade, individual mechanical damage to their structure and texture can also be considered moderate and quite strong;
• for the accepted confidence level of 95%, the dependence of moderate force can be applied to 34-48% of the general population size, and the correlations quite strong - to 49-71%.

Therefore, we reckon that our research works – presented both in random and fuzzy approaches – are coherent, consistent, comprehensive, solid and reliable.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thanks for your et

Reviewer 4 Report

The authors took into account my comments and added new elements to increase the value of the article. I recommend this article to print.