Trapezoidal Interval Type-2 Fuzzy PIPRECIA-MARCOS Model for Management Efficiency of Traffic Flow on Observed Road Sections
, Marko Subotić 3, Adel F. Alrasheedi 4 and Shiru Sun 5
Round 1
Reviewer 1 Report
This paper has an interesting topic, However, there are some points that should be addressed.
1- The introduction and literature review section should be improved. The table presented in the literature review section is good, but the text of the two mentioned sections should be improved. You can use new references for this. You can use the following references:
https://doi.org/10.3390/app112110392
https://doi.org/10.3390/math10091406
https://doi.org/10.1016/j.epsr.2022.108073
2- The analyzes presented regarding figures 1 and 2 are not enough. Please improve it
3- The conclusion section should be improved
4- There are too many mathematical equations in the text and it is difficult to follow them due to the lack of sufficient explanations. Please add more explanations about the equations to the text
5- You have used type-2 fuzzy and you should provide more explanation about it and its equations.
6- Regarding Table 9, where you have expressed quantitative results, it is necessary to provide more explanations and analysis, and you can use its results in the abstract and conclusion.
Author Response
Reviewer 1:
Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.
This paper has an interesting topic, However, there are some points that should be addressed.
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Comment 1: 1- The introduction and literature review section should be improved. The table presented in the literature review section is good, but the text of the two mentioned sections should be improved. You can use new references for this. You can use the following references:
https://doi.org/10.3390/app112110392
https://doi.org/10.3390/math10091406
https://doi.org/10.1016/j.epsr.2022.108073
Reply: Thank you for your comment, you have right. We have added a paragraph of several sentences. All three literatures are added (After the table 1).
Comment 2: The analyzes presented regarding figures 1 and 2 are not enough. Please improve it.
Reply: Explanations for Figures 1 and 2 are shown as follows.
Figure 1: By analyzing the AADT for the given measuring segments, the AADT values per years are continuously increasing, but not more than 3% annually. A special eccentric value of AADT is on the Rudanka - Doboj section (A6), which is over 10,000 [veh/day]. For alternatives (measuring segments) A2, A5, A11 of the Vrhovi - Šešlije section and A12, A13, A14 of the Obodnik - Klupe section, the value of AADT does not exceed 5000 [veh/day] in the period from 2013 to 2017. These two sections have free traffic flow conditions, which is shown in Figure 1.
The final values of AADT, which is an integral part of the initial decision matrix, were obtained using the Dombi operator:
Figure 2: One of the criteria analyzed in Figure 2 in the period from 2016 to 2019 was the number of traffic accidents (with fatalities, minor and serious physical injuries and material damage). The criterion has been taken from the database on traffic accidents, and it refers to all 14 selected alternatives (measuring road segments). The largest number of accidents occur with material damage, and deviations by years were observed in the number of accidents with material damage in 2017 and the number of accidents with minor injuries in 2019. The highest number of fatalities in traffic accidents for the given alternatives was recorded in 2016 (29 fatalities), and the highest number of accidents with material damage on the given alternatives was recorded in 2017 (615 accidents). Individually, in 2019, the largest number of fatalities (4 fatalities) occurred on the Ivanjska-Šargovac section (A1, A2 and A3).
An example of averaging these values is given below.
Comment 3: The conclusion section should be improved.
Reply: This section has been extended and improved.
Comment 4: There are too many mathematical equations in the text and it is difficult to follow them due to the lack of sufficient explanations. Please add more explanations about the equations to the text.
Reply: We have corrected mistakes in equations and added more explanations. In order to be clearly understanding our new approach we given example of calculation for each step for both methods. Please see 5. Results and analysis.
Comment 5: You have used type-2 fuzzy and you should provide more explanation about it and its equations.
Reply: This is related to the previous comment.
Comment 6: Regarding Table 9, where you have expressed quantitative results, it is necessary to provide more explanations and analysis, and you can use its results in the abstract and conclusion.
Reply: Thank you for observation. We added three senteces (in the paper) after table 9. Also, results have been included in the abstract and conclusion.
Reviewer 2 Report
The present paper extended MCDM methods with Trapezoidal Interval Type-2 Fuzzy numbers. Based on my own reading of the paper, I agree that the topic of the paper is interesting and relevant, but the authors fail to properly motivate their research (what is being studied and why it is important?). In addition, the authors make multiple questionable assumptions without proper justification. The following points should be addressed in the revised version.
1. The abstract should be rewritten clearly, its structure is disorganized, I recommend the authors to reorganize it according to the theme of background, goal, method, result, and conclusions/contributions.
2. The introduction section sets the relevant context and rationale behind conducting this study. However, many arguments are made without the support of references in this section. Also, the authors failed to clearly and precisely mention what are the research questions, aim and objectives of the study.
3. The authors fail to properly motivate their research. Why did the authors consider Trapezoidal Interval Type-2 Fuzzy numbers(TrIT2F)? and why it is important? How can the data be TrIT2F? What are the advantages?
4. Add a caption to the first Table. It is difficult to figure out the difference between your work and the literature reviews.
5. In my opinion, the paper falls short in terms of discussion and insights into the results. The authors should discuss what the key takeaways here are.
6. Why did the authors apply two different MCDM methods? Is there any advantage over other methods?
7. There is no conceptual comparison with existing approaches and no discussion of the benefits and drawbacks of the new approach. Thus, discussions and comparative analyses should be added, also it is important to compare your method with the literature ones.
8. Conclusions need to highlight the importance and contribution of the study; they also, need to summarize how the objectives proposed were accomplished, the reliability of the method, the capabilities of the study, and list the research's limitations.
9. As the size of the decision matrix has no influence, “…formation of a larger set of road infrastructure segments, and a larger set of evaluation criteria.” could not be a future scope. However, your method could be applied to other extensions of fuzzy sets such as “quasirung orthopair fuzzy sets’. Refer to the articles on quasirung fuzzy sets and include them in the future scope of your paper.
Author Response
Reviewer 2:
Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.
The present paper extended MCDM methods with Trapezoidal Interval Type-2 Fuzzy numbers. Based on my own reading of the paper, I agree that the topic of the paper is interesting and relevant, but the authors fail to properly motivate their research (what is being studied and why it is important?). In addition, the authors make multiple questionable assumptions without proper justification. The following points should be addressed in the revised version.
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Comment 1: The abstract should be rewritten clearly, its structure is disorganized, I recommend the authors to reorganize it according to the theme of background, goal, method, result, and conclusions/contributions.
Reply: The abstract has been extended as per your suggestion.
Comment 2: The introduction section sets the relevant context and rationale behind conducting this study. However, many arguments are made without the support of references in this section. Also, the authors failed to clearly and precisely mention what are the research questions, aim and objectives of the study.
Reply: We have added a few references in the introduction. Also the following has been added.
The aim of the paper is to determine the efficiency of a defined set of 14 segments of road infrastructure based on data collected for light goods vehicles. The evaluation criteria imply a combination of road exploitation parameters and consequent outputs. Based on aims can be set the following research questions: can formed MCDM model offers enough data for sustainable management of road infrastructure, and can obtained results help decision-makers to improve the level of traffic safety?
The application of fuzzy concepts in MCDM models makes it possible to consider complexities and uncertainties in decisions [8], so that is one of the reasons to handle the MCDM model with TrIT2F. The greatest contribution of this paper is the creation of a completely novel model consisting of two MCDM methods extended with Trapezoidal Interval Type-2 Fuzzy numbers. This model offers certain advantages and can be applied in other areas of decision-making. Forming an extension of two MCDM methods (the first for determining criteria values, and the second for ranking potential solutions) with TrIT2F represents an additional contribution because in this way we have offered a completely new model. Some integrated MCDM models applied different theories and it is necessary to make defuzzification to can apply criteria weights in the ranking method, while in our study that isn’t the case that represented advantages. Simply, the obtained criteria weights can be applied in ranking methods without any additional operation.
Comment 3: The authors fail to properly motivate their research. Why did the authors consider Trapezoidal Interval Type-2 Fuzzy numbers(TrIT2F)? and why it is important? How can the data be TrIT2F? What are the advantages?
Reply: The application of fuzzy concepts in MCDM models makes it possible to consider complexities and uncertainties in decisions [8], so that is one of the reasons to handle the MCDM model with TrIT2F. Also, such a model based on an expert’s assessment and quantification of linguistic scale in quantitative data provided more precise decisions.
Comment 4: Add a caption to the first Table. It is difficult to figure out the difference between your work and the literature reviews.
Reply: Thank you for your observation. We have added table caption and it is cited it in the text.
Comment 5: In my opinion, the paper falls short in terms of discussion and insights into the results. The authors should discuss what the key takeaways here are.
Reply: Thank you for your comment, you have right. We have added the text:
The analysis of the impact of the road infrastructure on the efficiency of the traffic flow, in this case, can be compared to the assessment of the vulnerability of the road traffic system. In this research it can be concluded that the vulnerability of a network in different scenar-ios is analyzed from both the structural and functional perspectives, which are also the results of another study [48,49]. The application of a similar methodology is shown in the ranking of qualitative and quantitative criteria of traffic safety and can be accepted as rel-evant in decision-making. [50,51] Also, these studies can assist stakeholders in understanding the current state of transportation networks and planning future sustainability measures through the MCDM approach.
Comment 6: Why did the authors apply two different MCDM methods? Is there any advantage over other methods?
Reply: The greatest contribution of this paper is the creation of a completely novel model consisting of two MCDM methods extended with Trapezoidal Interval Type-2 Fuzzy numbers. This model offers certain advantages and can be applied in other areas of decision-making. Forming an extension of two MCDM methods (the first for determining criteria values, and the second for ranking potential solutions) with TrIT2F represents an additional contribution because in this way we have offered a completely new model. Some integrated MCDM models applied different theories and it is necessary to make defuzzification to can apply criteria weights in the ranking method, while in our study that isn’t the case that represented advantages. Simply, the obtained criteria weights can be applied in ranking methods without any additional operation.
Comment 7: There is no conceptual comparison with existing approaches and no discussion of the benefits and drawbacks of the new approach. Thus, discussions and comparative analyses should be added, also it is important to compare your method with the literature ones.
Reply: We have added advantages of our model through the whole paper.
Comment 8: Conclusions need to highlight the importance and contribution of the study; they also, need to summarize how the objectives proposed were accomplished, the reliability of the method, the capabilities of the study, and list the research's limitations.
Reply: Conclusion has been extended with suggested elements. Now is:
Constant monitoring of the road infrastructure and assessment of indicators of traffic flow efficiency and road exploitation have become an important parameter of road engineering management. In this paper, a set of 14 road segments was observed based on seven different parameters in order to determine the segments that have sat-isfactory traffic flow efficiency. For these purposes, a novel TrIT2F MCDM model has been developed, and it consists of the TrIT2F PIPRECIA method for determining the weights of criteria and the TrIT2F MARCOS method for evaluating and ranking alter-natives. Forming extensions of two MCDM methods with TrIT2F, the first for deter-mining criteria values and the second for alternative evaluation presents the major contribution of the paper. Also, this model can be applied to any other MCDM prob-lem, so it has a large justification. In such a way, scientific contributions have been en-sured. At the same time, the set aims of assessment of indicators of traffic flow effi-ciency and road exploitation in order to make the mentioned sections of the road sus-tainable have been achieved. The results of the newly developed model, which is the greatest contribution of this research, are: A5 > A8 > A2 > A1 > A4 > A3 > A6 > A12 > A13 = A14 > A11 > A7 > A9 > A10. These results should be base for road management institutions to make necessary changes and bringing new rules for traffic flow on con-sidered road sections, of course taking into account the type of considered vehicle also. After that, the validation of the obtained results has been carried out, which shows a great dependence of the final results on changing the importance of the criteria, while the size of the decision matrix has no influence, i.e. the results remain identical. Besides mentioned advantages of the study can be defined as the following limitations: the small length of road considered in the study through 14 road sections in comparison to the total length of the road, considering data and performing model for only one type of vehicle (light goods vehicles) or a small number of decision-makers.
Future research is related to the formation of a larger set of road infrastructure segments, and a larger set of evaluation criteria. Also, the application of this model is possible in other areas of traffic engineering or in other areas of research. Using other theories such intuitionistic fuzzy sets or quasirung orthopair fuzzy sets can be one of way guidelines for next research.
Comment 9: As the size of the decision matrix has no influence, “…formation of a larger set of road infrastructure segments, and a larger set of evaluation criteria.” could not be a future scope. However, your method could be applied to other extensions of fuzzy sets such as “quasirung orthopair fuzzy sets’. Refer to the articles on quasirung fuzzy sets and include them in the future scope of your paper.
Reply: You are right that the size of the decision matrix has no influence on final results, but we checked it in the MCDM model which consists of 14 alternatives and 7 criteria. We don’t know if the size of the decision matrix will or not have influence in new MCDM model with a larger number of criteria and alternatives.
We have added new way of direction for future research as per your suggestion.
Reviewer 3 Report
The authors have developed a novel TrIT2F (Trapezoidal Interval Type-2 Fuzzy) PIPRECIA (PIvot Pairwise RElative Criteria Importance Assessment) - TrIT2F MARCOS (Measurement of Alternatives and Ranking according to Compromise Solution) was developed in order to, in a defined set of 14 road segments, identify the most efficient one for data related to light goods vehicles.
The abstract is well-written and summarizes the main contributions of the paper.
In the Introduction, the most important notions used in the paper such as traffic flow, flow rate, access point, TrIT2F PIPRECIA-TrIT2F MARCOS model, Trapezoidal Interval Type-2 Fuzzy numbers, etc. are mentioned briefly. Overall, the introduction is sufficiently detailed but some sentences are not clear. For example, the sentence between lines 42 and 45 mentions the notion of ‘geometric conditions of road’ which is unclear and needs further explanation. Further, some notions such as “traffic flow” have well-established definitions which should be included either in the Introduction or in a separate section “Preliminaries”.
The literature review is presented in section 2. Most of the references are up-to-date and related to the problem but there are some papers that must be included. For example, in the paper:
Atanassov, K. et. al., (2018). Generalized Net Model of Multicriteria Decision Making Procedure Using Intercriteria Analysis. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_10
describes an intuitionistic fuzzy approach to mulitcriteria decision making procedure based on intercriteria analysis. The method proposed in the paper is extremely similar to the one applied by the authors of the present paper and that is why it must be included in the literature review. Namely, an index matrix the elements of which are intuitionistic fuzzy evaluations of dependencies between the criteria is employed to find out the positive or negative consonance between pairs of criteria.
In the paper
Amiri, M. et al., A Fuzzy Extension of Simplified Best-Worst Method (F-SBWM) and Its Applications to Decision-Making Problems. Symmetry 2023, 15, 81. https://doi.org/10.3390/sym15010081
a simplified best-worst method (SBWM), which is one of the methods based on pairwise comparisons, has been developed using triangular fuzzy numbers (TFNs) to propose a fuzzy extension of SBWM (F-SBWM). Triangular fuzzy numbers in different symmetric and asymmetric forms have widely been used in MCDM approaches and pairwise comparisons. It is noteworthy that symmetric numbers are used when we are using equal division of the domain due to an increased ambiguity and lack of information.
The table on page 3 is very helpful for the readers to compare the various approaches to the problem in the literature. It should be labeled and a title should be added.
The authors should include more references in this section and explain the advantages of their approach presented in the paper.
Section 3 gives the preliminaries and presents the methods used by the authors of the present paper. The definitions which are taken from other sources should follow the template: ‘Definition 1 ([‘source’]).’ When an equation appears at the end of a sentence it must end with ‘.’ (see equations 1,2,3,4,5, etc. ).
The Trapezoidal Interval Type-2 fuzzy PIPRECIA is correctly described.
The results are clearly presented in section 5 and they seem to be correctly obtained – I have not found any problem with them.
The section Conclusion is way too short. I recommend to the authors to consider the possibility of using intuitionistic fuzzy sets as an alternative to the type-2 fuzzy sets in the evaluation of the criteria.
Overall, the paper presents some significant contributions. I recommend that the paper be published once the authors address adequately my remarks above.
There are some grammar errors and some sentences are unclear.
Author Response
Reviewer 3:
Thank you very much for the useful suggestions. We accepted all of the suggestions and we are sure that this will improve the quality and contribute to a better understanding of the paper.
The authors have developed a novel TrIT2F (Trapezoidal Interval Type-2 Fuzzy) PIPRECIA (PIvot Pairwise RElative Criteria Importance Assessment) - TrIT2F MARCOS (Measurement of Alternatives and Ranking according to Compromise Solution) was developed in order to, in a defined set of 14 road segments, identify the most efficient one for data related to light goods vehicles.
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Comment 1: The abstract is well-written and summarizes the main contributions of the paper.
Reply: Thank you for your positive comment. We slightly improved it according to the suggestion of another reviewer.
Comment 2: In the Introduction, the most important notions used in the paper such as traffic flow, flow rate, access point, TrIT2F PIPRECIA-TrIT2F MARCOS model, Trapezoidal Interval Type-2 Fuzzy numbers, etc. are mentioned briefly. Overall, the introduction is sufficiently detailed but some sentences are not clear. For example, the sentence between lines 42 and 45 mentions the notion of ‘geometric conditions of road’ which is unclear and needs further explanation. Further, some notions such as “traffic flow” have well-established definitions which should be included either in the Introduction or in a separate section “Preliminaries”
Reply: We have added relevant sources in which these elemets properly defined and explained.
Comment 3: The literature review is presented in section 2. Most of the references are up-to-date and related to the problem but there are some papers that must be included. For example, in the paper:
Atanassov, K. et. al., (2018). Generalized Net Model of Multicriteria Decision Making Procedure Using Intercriteria Analysis. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_10
describes an intuitionistic fuzzy approach to mulitcriteria decision making procedure based on intercriteria analysis. The method proposed in the paper is extremely similar to the one applied by the authors of the present paper and that is why it must be included in the literature review. Namely, an index matrix the elements of which are intuitionistic fuzzy evaluations of dependencies between the criteria is employed to find out the positive or negative consonance between pairs of criteria.
In the paper
Amiri, M. et al., A Fuzzy Extension of Simplified Best-Worst Method (F-SBWM) and Its Applications to Decision-Making Problems. Symmetry 2023, 15, 81. https://doi.org/10.3390/sym15010081
a simplified best-worst method (SBWM), which is one of the methods based on pairwise comparisons, has been developed using triangular fuzzy numbers (TFNs) to propose a fuzzy extension of SBWM (F-SBWM). Triangular fuzzy numbers in different symmetric and asymmetric forms have widely been used in MCDM approaches and pairwise comparisons. It is noteworthy that symmetric numbers are used when we are using equal division of the domain due to an increased ambiguity and lack of information.
Reply: Thank you for your suggestion. We have added both studies.The first in introduction, and the second in conclusion.
Comment 4: The table on page 3 is very helpful for the readers to compare the various approaches to the problem in the literature. It should be labeled and a title should be added.
Reply: Thank you for your observation. We have added table caption and it is cited it in the text.
Comment 5: The authors should include more references in this section and explain the advantages of their approach presented in the paper.
Reply: A few new references have been added in the introduction and literature review sections.
Comment 6: Section 3 gives the preliminaries and presents the methods used by the authors of the present paper. The definitions which are taken from other sources should follow the template: ‘Definition 1 ([‘source’]).’ When an equation appears at the end of a sentence it must end with ‘.’ (see equations 1,2,3,4,5, etc.)
Reply: Thank you for your suggestion. Corrected.
Comment 7: The Trapezoidal Interval Type-2 fuzzy PIPRECIA is correctly described.
Reply: Thank you for your positive comment.
Comment 8: The results are clearly presented in section 5 and they seem to be correctly obtained – I have not found any problem with them.
Reply: Thank you for your positive comment.
Comment 9: The section Conclusion is way too short. I recommend to the authors to consider the possibility of using intuitionistic fuzzy sets as an alternative to the type-2 fuzzy sets in the evaluation of the criteria.
Reply: Conclusion has been extended with suggested elements. Now is:
Constant monitoring of the road infrastructure and assessment of indicators of traffic flow efficiency and road exploitation have become an important parameter of road engineering management. In this paper, a set of 14 road segments was observed based on seven different parameters in order to determine the segments that have sat-isfactory traffic flow efficiency. For these purposes, a novel TrIT2F MCDM model has been developed, and it consists of the TrIT2F PIPRECIA method for determining the weights of criteria and the TrIT2F MARCOS method for evaluating and ranking alter-natives. Forming extensions of two MCDM methods with TrIT2F, the first for deter-mining criteria values and the second for alternative evaluation presents the major contribution of the paper. Also, this model can be applied to any other MCDM prob-lem, so it has a large justification. In such a way, scientific contributions have been en-sured. At the same time, the set aims of assessment of indicators of traffic flow effi-ciency and road exploitation in order to make the mentioned sections of the road sus-tainable have been achieved. The results of the newly developed model, which is the greatest contribution of this research, are: A5 > A8 > A2 > A1 > A4 > A3 > A6 > A12 > A13 = A14 > A11 > A7 > A9 > A10. These results should be base for road management institutions to make necessary changes and bringing new rules for traffic flow on con-sidered road sections, of course taking into account the type of considered vehicle also. After that, the validation of the obtained results has been carried out, which shows a great dependence of the final results on changing the importance of the criteria, while the size of the decision matrix has no influence, i.e. the results remain identical. Besides mentioned advantages of the study can be defined as the following limitations: the small length of road considered in the study through 14 road sections in comparison to the total length of the road, considering data and performing model for only one type of vehicle (light goods vehicles) or a small number of decision-makers.
Future research is related to the formation of a larger set of road infrastructure segments, and a larger set of evaluation criteria. Also, the application of this model is possible in other areas of traffic engineering or in other areas of research. Using other theories such intuitionistic fuzzy sets or quasirung orthopair fuzzy sets can be one of way guidelines for next research.
Comment 10: Overall, the paper presents some significant contributions. I recommend that the paper be published once the authors address adequately my remarks above.
Reply: Thank you for your valuable opinion and very constructive suggestions. We have adopted all your comments and revise the paper.
Round 2
Reviewer 1 Report
Dear Authors
Thanks for addressing my previous comments
Best wishes
Reviewer 2 Report
The paper can be accepted in its present form.
