Application of MCDM Model Rough DIBR - Fuzzy LBWA - BONFERRONI and Decision Support System DEXi for the Improvement of Earthquake Risk Level Assessment

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Application of MCDM Model Rough DIBR - Fuzzy LBWA - BONFERRONI and Decision Support System DEXi for the Improvement of Earthquake Risk Level Assessment

https://doi.org/10.21203/rs.3.rs-3248793/v1

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Effective decision-making across various domains of society necessitates the adept use of appropriate methods and software to achieve optimal outcomes. This need becomes especially critical in situations where human lives are in jeopardy, and substantial material damages are at stake. The escalating prevalence of natural disasters worldwide highlights the intrinsic threat they pose to protected values, underscoring the importance of comprehensive risk assessments. The paper explore the implementation of the software DEXi in conjunction with DIBR (Defining Interrelationships Between Ranked criteria) method in a rough environment and Fuzzy LBWA (Level Based Weight Assessment) method. The utilization of the Bonferroni aggregator further enhances the earthquake risk level assessment for protected values in the Republic of Serbia. The Rough DIBR and Fuzzy LBWA methods play a pivotal role in determining the criteria weights, and their values are aggregated with the Bonferroni aggregator. The risk assessment process is conducted using the Decision Support System (DSS) called DEXi. Proposed model undergoes rigorous testing, with authentic data sourced from official Disaster Risk Assessments of three cities and five municipalities in the Republic of Serbia. The validation process firmly establishes the model's credibility, laying a robust foundation for improved earthquake risk assessment practices.

MCDM

DEXi

Fuzzy LBWA

Rough DIBR

Bonfferoni

risk assessment

earthquake

Ensuring the security and stability of a nation is a paramount concern for any independent state. The complex interplay of internal and external factors contributes to the overall security landscape. Among the internal factors, environmental security holds significant importance as it entails threats arising from environmental hazards, whether of natural or human origin. The Republic of Serbia, like many other regions, faces an elevated vulnerability to natural disasters, particularly earthquakes, necessitating a robust identification and risk assessment process for these hazards.

The identification and risk assessment of natural and other disasters play a crucial role in mitigating potential threats. Earthquakes, as a major hazard, bear substantial consequences, posing significant risks to the economy and other vital aspects of the state and society. Thus, effective risk assessment measures become imperative to preclude or minimize the impact of such natural disasters. The main goal when assessing any risk is to ensure comprehensive support to the decision-making process (Rausand and Haugen, 2020).

In daily life, individuals constantly make decisions of varying significance (Bošković et al., 2023). While personal decisions may rely on intuition and affect limited individuals, business decisions demand greater systematicity, often impacting a larger number of employees (Chatterjee and Chakraborty, 2023). Scientific research on risk and organizational behavior has emerged to assist managers in achieving optimal outcomes in their professional endeavors (Sharma et al., 2023; Shekhovtsov et al., 2022). Decision-making processes have gained considerable prominence (Zhou et al., 2022), with numerous scholars affirming its pivotal role in strategic and operational management (Sahoo and Goswami, 2023). Decision-making permeates various levels and disciplines, with an increasing reliance on diverse systems and computer tools for decision support (Planić, 2022). This is particularly significant in the context of risk assessments for various natural and other disasters.

This research contributes to the improvement of the earthquake risk assessment methodology in terms of protected values in the Republic of Serbia, in accordance with current regulations.. The enhancement of this methodology is achieved through the implementation of the DEXi expert system, the application of the Rough DIBR and Fuzzy LBWA methods, along with the Bonferroni aggregator.

The subsequent sections of this paper present a concise elucidation of crucial concepts related to the research, including specific conditions, limitations, and the regulatory framework in the Republic of Serbia governing this domain. Furthermore, the current approach to conducting earthquake risk assessments is detailed, alongside a review of relevant prior research on the subject. Subsequently, a comprehensive description of the proposed decision support model, the employed methods, and software is provided, followed by a literature analysis pertaining to the chosen methodologies. The core of the research entails the application of the DEXi software and MCDM (Multiple Criteria Decision Making) methods, as well as the verification of the proposed model. A summary of the research results and prospective research recommendations is included in the paper's conclusion.

Natural disasters, also referred to as natural calamities or hazards, disrupt the ordinary course of life (Degg, 1992). They result in casualties, extensive property damage, infrastructure disruptions, and substantial environmental threats (Cvetković, 2014). In such scenarios, communities often lack the internal capacity to recover without external assistance (Tobin and Montz, 1997). These disasters arise from natural forces and can manifest as floods, earthquakes, droughts, fires, hurricane winds, snow avalanches, landslides, storms, volcanic eruptions, and more.

The term "natural disaster" is defined as an event of hydrometeorological, biological, or geological origin, caused by natural forces that can threaten human health or cause extensive damage (Law on Emergency Situations, 2009).

Earthquakes, for example, result from sudden movements of large rock slabs along cracks within the Earth (Bradford and Carmichael, 2007). They are considered short-term disasters that have a long-term impact on people, the economy of the country and infrastructure (Al-Dogom et al., 2021). For instance, the 2010 earthquake with its epicenter 10 km northeast of Kraljevo in the Republic of Serbia caused two deaths, slightly more than 100 injuries, damaged around 6000 buildings (Stojadinović et al., 2021), and incurred substantial material damage.

Given the aforementioned consequences, it becomes essential to assess and evaluate the risks associated with these phenomena in order to mitigate the potential repercussions of their occurrence. Klinke and Renn (2002) describe the risk as "the possibility that human actions or events lead to consequences that harm aspects of things that human beings value." Similarly, Rausand and Haugen (2020) describe risk assessment through "a process in which judgments are made on the tolerability of the risk based on risk analysis and taking into account factors such as socioeconomic and environmental aspects." To identify hazards, consider potential consequences, and determine the need for implementing disaster management measures and activities, the Republic of Serbia has adopted regulations for preparing a disaster risk assessment, specifically the Instruction on the methodology and content of a disaster risk assessment and protection and rescue plan (hereinafter: Instructions 2012; Instructions 2019).

These Instructions create a scenario for identifying the risk of earthquakes, with parameters designed to allow better understanding of the probability of occurrence and its consequences (Instructions 2019). Based on this scenario, the risk level of the hazard is defined, taking into account the consequences and probability of the event (disaster). Consequences refer to the impact of a harmful event on human life, health, economy/ecology, and social stability, and are represented by the magnitude of the loss or damage (Instructions 2012). Probability, on the other hand, relates to the relationship between the frequency of a specific event (and vulnerability) and potential danger. (Instructions 2012), or in the context of this research, the likelihood of an event occurring (Instructions 2019).

Numerous authors have delved into the subject area and implemented MCDM methods to assess earthquake risks and hazards. For instance, Yariyan et al. (2020) conduct an Sanandaj`s (Iran) earthquake risk evaluation, utilizing an Fuzzy AHP (Analytic Hierarchy Process), ANN (Artificial Neural Networks) and GIS. They consider three main groups of criteria, divided into three aspects (demographic, ecological and physical). Similarly, Jena et al. (2020) assess earthquake vulnerability in Northern Sumatra, employing a variety of factors, including buildings, population, and geological and geomorphological traits.

Peng (2015) evaluates earthquake risks in various regions of China, employing MCDM methods such as PROMETHEE II (Preference Ranking Organization METhod for Enrichment Evaluation), VIKOR (VIšekriterijumsko KOmpromisno Rangiranje), ELECTRE III (Elimination Et Choice Transiting Reality),, gray theory, WSM (Weighted Sum Model), and the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method. The criteria they use include all essential segments of this process, demonstrating the feasibility of MCDM methods in this type of assessment.

Yavuz Kumlu and Tüdeş (2019) identify areas in Turkey with an elevated earthquake risk using AHP and TOPSIS methods, with GIS. They use the AHP method to define weight coefficients for geological criteria and superstructure/infrastructure criteria, and TOPSIS to identify the optimal alternative from the set of choices.

Jena and Pradhan (2020) adopt an MCDM model consisting of AHP and TOPSIS method, together with ANN for risk assessment., considering vulnerability and probability criteria, along with several sub-criteria. Tesfamariam et al. (2010) present a decision-making process for defining earthquake risk under conditions of uncertainty, applying economical/social and technical criteria and OWA (Ordered Weighted Averaging) operators, Dempster – Shafer theory, and Fuzzy theory in the heuristic hierarchical structure of the problem. They conclude that the MCDM framework is versatile, enabling decision-making under various conditions of uncertainty.

Alam and Haque (2022) they perform earthquake hazard assessment using GIS-based AHP and VLC (Weighted Linear Combination) methods. Parameters for assessment include systematic earthquake vulnerability, structural earthquake vulnerability, and socio-economic earthquake vulnerability. Shadmaan and Islam (2021) estimate earthquake vulnerability using the AHP method, focusing on social and structural aspects, including several sub-aspects. They also suggest that the results can be beneficial in mitigating earthquake risk and protecting human life and resources.

Vahdat (2015) addresses Seismic Risk Management in his doctoral dissertation, presenting various MCDM methods, systems, and theories for application in this area, such as ANN, ANFIS (Adaptive Neuro Fuzzy Inference System), TOPSIS, MAUT (Multi Attribute Utility Method), AHP, PROMETHEE, ELECTRE, and fuzzy MCDM. He highlights the advantage of applying MCDM methodology in this type of problem, as it efficiently handles both qualitative and quantitative information about risk in conditions of uncertainty.

MCDM methods have also found successful applications in diverse research areas (Bairagi, 2023; Granados et al., 2022; Đukić et al., 2022; Puška et al., 2023; Badi et al., 2023; Narang et al., 2023).

While several procedures have been developed to address this problem, no unique approach has provided a comprehensive assessment thus far. The essence of this research lies in enhancing the aforementioned methodology through the use of the DEXi software and MCDM methods within a fuzzy and rough environment.

For a better understanding of the research problem, the proposed methodology is shown in Fig. 1.

The proposed model consists of four phases: 1) Firstly, the DEXi software presents a model that assesses the level of earthquake risk by formulating logical rules based on valid normative-legal regulations governing this area. The above model was tested on five different fictitious alternatives, and results were obtained regarding the risk level for each of them. 2) Next, input data from official risk assessments of five municipalities and three cities located on Serbia's national territory were entered into the model to verify the proposed model's performance. 3) Subsequently, after verifying the model and analyzing the results, the mentioned model was further improved using the Rough DIBR and Fuzzy LBWA methods. The outcomes of these methods were aggregated using the Bonferroni aggregator, along with expert opinions, to define new criteria weighting coefficients. 4) The model was then verified again, and an analysis of the obtained results was carried out.

3.1 Rough DIBR method

The DIBR method represents a relatively new MCDM method, which is used to define criteria weights using the relationship between criteria that are adjacent (Pamucar et al. 2021). It employs a simple mathematical apparatus which is based on a small number of intercomparisons during application. Since the method was published in 2021, there is a limited number of works in which it has been used (Fig. 2).

The DIBR method is enhanced through the implementation of Rough theory, which effectively addresses uncertainty and imprecision. For more detailed information about this theory, refer to sources such as Zhai et al. (2008).

The steps of application of the Rough DIBR method (Tešić et al. 2022a; Tešić et al. 2022b) are presented in Fig. 3.

It is essential that the values${\gamma _{1n}}$ and $\gamma _{{1,n}}^{\prime }$ are approximately equal (with a permitted deviation of 10%). Otherwise, the relations are not well-defined, and it is necessary to re-formulate the relations (Tešić et al. 2022a; Tešić et al. 2022b).

The crisp value ${\omega _n}^{{crisp}}$ for the rough number$RN({\omega _n})=\left[ {\underline {{Lim}} ({\omega _n}),\overline {{Lim}} ({\omega _n})} \right]$ is obtained by applying expression (11) (Tešić et al. 2022a; Tešić et al. 2022b):

$${\omega _n}^{{crisp}}=\mathop {\hbox{min} }\limits_{i} \left\{ {\underline {{Lim}} ({\omega _n})} \right\}+{\omega _n}^{N} \bullet \,\,\left[ {\mathop {\hbox{max} }\limits_{i} \left\{ {\overline {{Lim}} ({\omega _n})} \right\} - \mathop {\hbox{min} }\limits_{i} \left\{ {\underline {{Lim}} ({\omega _n})} \right\}} \right]$$

where${\omega _n}^{N}$ is the normalized crisp value, obtained using expression (12) (Tešić et al. 2022a; Tešić et al. 2022b):

$${\omega _n}^{N}=\frac{{\underline {{Lim}} ({\omega _n})\,x\,\left\{ {1 - \underline {{Lim}} ({\omega _n})} \right\}+\overline {{Lim}} ({\omega _n})\,x\,\overline {{Lim}} ({\omega _n})}}{{1 - \underline {{Lim}} ({\omega _n})+\overline {{Lim}} ({\omega _n})}}$$

3.2 Fuzzy LBWA method

Similarly to the DIBR method, this approach is relatively new for defining the weights of criteria (Žižović and Pamučar 2019) and has been applied in various areas to date (Table 1).

Table 1

Different areas in which the LBWA method was applied (Scopus 2023)
Subject area	Number of documents
Computer Science	14
Decision Sciences	10
Environmental Science	7
Energy	6
Business, Management and Accounting	5
Mathematics	5
Social Sciences	4
Materials Science	2
Agricultural and Biological Sciences	1

In Fig. 4, a brief summary of the literature on the use of the LBWA method is presented.

Like the DIBR method, the Fuzzy LBWA method employs a simple mathematical apparatus, comprising six steps (Pamucar and Görçün, 2022; Pamučar et al., 2020), as demonstrated in Fig. 5.

3.3 Bonferroni aggregator

To determine the most valid values of the criteria weights, a comparison of the criteria in the Rough DIBR and Fuzzy LBWA methods was performed by seven experts. To aggregate the experts' opinions and the values of the weight coefficients obtained from the mentioned methods, the Bonferroni aggregator (Bonferroni, 1950) was used in this study, employing the expression (17):

$$B{M^{r,s}}({\omega _1},{\omega _2},...,{\omega _n})={\left( {\frac{1}{{n(n - 1)}}\sum\limits_{\begin{subarray}{l} i,j=1 \\ i \ne j \end{subarray} }^{n} {\omega _{i}^{r}\omega _{j}^{s}} } \right)^{\frac{1}{{r+s}}}}$$

where r,s ≥ 0 (stabilization parameters), and ${\omega _{ij}}$ represent the values of the criteria weights for each of the experts.

3.4 DEXi Decision Support System

Decision support systems (DSS) essentially represent a combination of management and informatics. There is no universal definition of the term "decision support system." In (Čupić et al., 1992), this term is defined as "information systems that are similar and complementary to standard information systems and aim to support, mainly, business decision-making processes. They represent a symbiosis of information systems, the application of a number of functional knowledge, and the ongoing decision-making process." On the other hand, in (Mišković, 2013), a decision support system is understood as an "interactive computer system or subsystem that helps in decision-making." Decision support systems enable simpler decision-making in all stages of the decision-making process, from problem formulation through design, selection, implementation, and control. However, they are intended to support, not replace, the decision maker.

As part of the project entitled "Expert Systems in Education," involving teachers from the Jožef Stefan Institute in Ljubljana and the University of Maribor, Faculty of Organizational Sciences in Kranj, Slovenia, the DEXi expert system was created. This computer software serves as an aid to decision makers in multi-attribute decision-making, using only qualitative attributes. It employs an approach that decomposes the decision-making problem into less complex sub-problems, based on the DEX method (Bohanec et al., 2013). The chronological development of the DEXi software is presented in Fig. 6.

The DEX method requires the decision maker to form a qualitative hierarchical model with multiple attributes. This model consists of (Bohanec et al., 2013):

Attributes: Representing the basic characteristics and values of attribute characteristics;
Scales of attributes: Used to evaluate/assess attributes;
Hierarchy of attributes;
Decision rules.

The modeling of the hierarchical DEXi model involves the following phases:

Phase 1. Structuring the model: Realized through the formation of attributes and sub-attributes.

Phase 2. Defining attribute value scales: These are qualitative scales.

Phase 3. Creation of decision rules: Rules that define the aggregation of attributes from the bottom to the top of the attribute hierarchy.

Phase 4. Definition of alternatives: Definition of all attribute values of all alternatives that are evaluated.

Phase 5. Evaluation and analysis of alternatives: The software evaluates the defined alternatives according to the defined attribute values and provides the possibility of analyzing the obtained results through "plus/minus-1" analysis, Selective Explanation, and comparison of alternatives.

By analyzing the regulations that govern this area (Instructions 2019), the attributes for assessing the level of earthquake risk in the Republic of Serbia, from the aspect of protected values, are derrived (Table 2):

Table 2

Attributes (criteria) that determine the risk level assessment
Criterion	Criterion Description
Criterion 1 (C₁)	Risk to human life and health (HL)
Criterion 11 (C₁₁)	Consequences for human life and health (HL)
Criterion 12 (C₁₂)	Event Probability (HL)
Criterion 2 (C₂)	Risk to economy/ecology (EE)
Criterion 21 (C₂₁)	Consequences for economy/ecology (EE)
Criterion 22 (C₂₂)	Event Probability (EE)
Criterion 3 (C₃)	Risk to social stability (SS)
Criterion 31 (C₃₁)	Consequences for social stability (SS)
Criterion 32 (C₃₂)	Event Probability (SS)

For each of the attributes, based on the valid normative-legal regulation (Instructions 2019), evaluation scales are defined (Fig. 7).

After defining the assessment scales, decision rules were formed for each level of the hierarchy, and in Fig. 8, an example of logical rules for assessing the final level of earthquake risk is presented.

For the purposes of testing the model, seven fictitious cities (alternatives) were defined, and the qualitative values of the attributes based on which the assessment is made were defined as well (Fig. 9).

Applying the DEXi software to the evaluation of alternatives, in accordance with the defined attributes, leads to the following results presented in Fig. 10:

The preceding figure (Fig. 10) demonsrated that the proposed model works well, and the logical rules are well defined. Additionally, the highest level of risk is with the alternative City 4, and the lowest with the alternative City 6.

In order to validate the proposed model, data from official disaster risk assessments (hereinafter: Risk assessment) of five municipalities (Risk assessment Mali Zvornik 2020; Risk assessment Knić 2021; Risk assessment Mionica 2019; Risk assessment Sremski Karlovci 2019) and three cities (Risk assessment Leskovac 2021; Risk assessment Kragujevac 2018; Risk assessment Valjevo 2022) from Serbia's national territory are used as input data, as shown in Fig. 11.

After processing the results using the DEXi software, the following risk levels are obtained (Fig. 12).

The results obtained using the DEXi software are identical to the results from the official risk assessments for the mentioned cities and municipalities, which confirms the validity of the proposed model. The positive verification of the model speaks in favor of the improvement of the prescribed methodology using the DEXi software.

Further analysis of the obtained results, based on the legislation governing this area in the Republic of Serbia, revealed that the sub-criteria in all criteria have a ratio of Consequences:Probability = 70:30. In other words, the local value of the weighting coefficients for sub-criteria C₁₁, C₂₁, and C₃₁ is 0.7, while for criteria C₁₂, C₂₂, and C₃₂ it is 0.3. Moreover, it can be inferred from the software that the weighting coefficients of all criteria are equal, indicating that they have the same influence on making the final decision.

Given the fact that in previous research in this area, as well as those listed in this paper, the weight coefficients of the criteria are not identical, and the criterion related to the risk to human life is generally considered the most important, it is important to consider that human life is inviolable according to the Constitution of the RS 2006. Therefore, it can be concluded that the mentioned methodology lacks the evaluation of defined criteria, specifically the definition of weight coefficients for each of the criteria, where the primacy in making a decision would be the risk to human life. It should be noted that the values of the weight coefficients of the sub-criteria have not been modified, due to their systematic relationship to risk.

By applying the steps of the Rough DIBR method and applying expressions (1–12), with the help of seven experts, and applying the Bonferroni aggregator (17), the following values of the weight coefficients of the criteria are obtained (Table 3).

Table 3

The weights of the criteria obtained using the Rough DIBR method
	Weight
C1	0.4284
C2	0.3062
C3	0.2654

After applying the Rough DIBR method, the same seven experts compared the criteria using Fuzzy LBWA, and following all the steps of this method (expressions 14–16), and aggregating their opinions using the Bonferroni aggregator (expression 17), the following weightcoefficients of the criteria were defined (Table 4).

Table 4

The weights of the criteria obtained using the Fuzzy LBWA method
	Weight
C1	0.4232
C2	0.3049
C3	0.2721

By using the Rough DIBR and Fuzzy LBWA methods, and aggregating the results using the Bonferroni aggregator, along with incorporating expert opinions, new criteria weighting coefficients were defined, further improving the aforementioned methodology. The values of the weight coefficients of the criteria obtained by aggregation are presented in Table 5.

Table 5

Final values of criteria weights (attributes)
Criterion	Value of the weighting coefficient of criteria/sub-criteria
Criterion 1 (C₁)	0,4258
Criterion 11 (C₁₁)	0,2981
Criterion 12 (C₁₂)	0,1277
Criterion 2 (C₂)	0,3056
Criterion 21 (C₂₁)	0,2139
Criterion 22 (C₂₂)	0,0915
Criterion 3 (C₃)	0,2687
Criterion 31 (C₃₁)	0,1881
Criterion 32 (C₃₂)	0,0806

By implementing the values from Table 5 in the DEXi model, with the input data of real alternatives, the following results are obtained (Fig. 13).

Analyzing the obtained results (Fig. 13) and comparing them with the results obtained with identical criteria weights (Fig. 12), it can be clearly concluded that changes occurred in the alternatives Knic, Sremski Karlovci, Kragujevac, and Leskovac, where the key influence on the decision was the risk to human lives. Among the alternatives Knic, Sremski Karlovci, and Kragujevac, there was a decrease in the level of risk, while with the alternative Leskovac, there was an increase in the level of risk.

In Fig. 14, the graph shows the dependence of the final decision in relation to the risk to life and health of people, which is the attribute with the highest value of the weight coefficient, i.e., the greatest influence on decision-making. Based on the results obtained and the analysis performed, it is concluded that in the case of the Mali Zvornik and Valjevo alternatives, this attribute directly affects the highest risk value.

Figure 15 presents the results of the analysis of the Mali Zvornik and Valjevo alternatives. It can be observed that the values of the criteria of the alternatives Mali Zvornik and Valjevo directly influenced the decision, as these criteria have the highest values.

In Fig. 16, a summary analysis of all alternatives is provided.

The repercussions of natural disasters are often quantified in terms of millions of euros, accompanied tragically by human casualties. The cost of mitigating these consequences often exceeds the scale of the damage itself. Such natural disasters pose direct negative impacts on a nation's economy and the security of its inhabitants, potentially leading to catastrophic implications for the country's protected values and overall national security. Hence, it becomes imperative to develop a distinctive approach for hazard and risk assessment to avert undesired outcomes.

The process of decision-making is a daily activity, evident in both private life, where decisions are often intuition-driven, and in business processes, where a systematic, rational, and interdisciplinary approach is employed to avoid known decision-making pitfalls, thus yielding effective and efficient business outcomes. The progressive evolution of risk management, nuanced understanding of human behavior, and technological advancements that support and emulate cognitive processes have revolutionized decision-making across all facets of life, especially in contexts where human lives and material assets are at stake, such as natural disasters.

This research aims to enhance the decision-making process in earthquake risk assessment within the Republic of Serbia, utilizing the DEXi software and MCDM methods to define the weighting coefficients for the criteria. Following normative-legal regulations and scientific insights pertinent to this domain, the study employs the DEXi software to model the assessment. The methodology involves an initial analysis of relevant literature to determine the attributes/criteria and their respective significance. Subsequently, decision rules and alternatives are formulated, based on which the software evaluates the alternatives using the predefined attribute parameters. The efficacy of the model is validated through real data obtained from hazard assessments of cities and municipalities within the Republic of Serbia, demonstrating its robust functionality. Acknowledging that current regulations equalize the influence of each criterion on the final decision, whereas various research studies suggest differing influences of criteria, and recognizing human life as the utmost value for a state/society, an expert survey was conducted to ascertain the interrelationships between criteria. By applying the Rough DIBR and Fuzzy LBWA methods, adept at handling uncertainties and inaccuracies, and aggregating the outcomes using the Bonferroni aggregator, the final weighting coefficients for the criteria were determined, and subsequently integrated into the DEXi software. This process greatly improves the accuracy of earthquake risk assessment.

It shouldbe noted that this research is tailored exclusively to the Serbia's national territory, adhering to the pertinent normative-legal regulations governing this field within the country. However, the proposed model's potential applicability in other countries, adopting similar methodologies for risk level assessments, cannot be disregarded.

Moreover, further enhancements to the model could involve detailed elaboration of attributes/criteria, adopting intricate hierarchies, and reducing the number of decision rules required within the DEXi software. Additionally, exploring alternative methods to define weighting coefficients, involving a larger cohort of domain experts, could augment the model's efficacy.

Decision support systems exhibit immense potential across diverse domains to enhance efficient decision-making, particularly in intricate contexts where extensive alternatives necessitate evaluation against multifaceted attributes/criteria. However, it is crucial to underscore that while decision support systems offer substantial assistance, they cannot wholly supplant human judgment, given that the ultimate responsibility for decision-making lies with the human decision-maker.

Funding: The authors have not disclosed any funding.

Data availability: Enquiries about data availability should be directed to the authors.

Declarations

Conflict of interest: The authors have not disclosed any competing interests.

Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

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Application of MCDM Model Rough DIBR - Fuzzy LBWA - BONFERRONI and Decision Support System DEXi for the Improvement of Earthquake Risk Level Assessment

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Abstract

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Introduction

Background of the study

Methodology

3.1 Rough DIBR method

3.2 Fuzzy LBWA method

3.3 Bonferroni aggregator

3.4 DEXi Decision Support System

Application of the proposed methodology

Discussion and Conclusions

Declarations

References

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