Fire accident risk assessment of high rise building based on fuzzy bow tie approach

Abstract

Despite the numerous risks that high-rise buildings face, fire accidents happen most frequently. Studying fire accidents in high-rise buildings is crucial because they can result in harm to people’s health, fatalities, property damage, and pollution. The number of accidental fires in buildings is very large since it is difficult to isolate a single cause and all processes and control measures are not appropriately implemented. This paper proposes a fuzzy-bow tie approach to evaluating the risk of fire accidents by taking into account the various fire sources and effects. The fourteen-floor high-rise residential building is used as a case study for the proposed fuzzy bow tie approach. The fuzzy fault tree approach estimates that there is a 0.0968% risk of a fire accident occurring in that high-rise building, with a possibility for 9 out of 100 accidental fires annually. The fuzzy event tree model predicts that loss of life and loss of property are the most likely consequences of an accidental fire. Accordingly, mitigation strategies can be developed by building officials and fire safety practitioners.

Keywords

Risk assessment fire alarm and control system safety fault tree sensitivity analysis

1 Introduction

Due to urban expansion and metropolitan city development, high-rise buildings are in high demand to accommodate a high density of people. The need for high-rise buildings is now inevitable, whether they are used as residential structures or non-residential ones like office buildings, institutions of higher learning, or healthcare facilities. Accidental fires are one of the most dangerous hazards in such structures, requiring immediate action and significant effort to control. The NFPA report [1] states that between 2009 and 2013, U.S. fire departments responded to an estimated average of 14,500 reported structure fires in high-rise structures annually [2, 3]. The report reveals that property losses amount to 154 million dollars, with 40 deaths and 520 injuries every year. In 2017, in Grenfell Tower, North Kensington, West London, which houses a 24-floor high-rise building, 72 people were killed due to a fire started by a faulty refrigerator on the fourth floor [4]. Several people’s lives are already in danger as a result of some of these incidents, which are also causing significant economic losses. Therefore, it is crucial to evaluate the risk of fire in all its facets, including potential accidental, technological, and natural causes.

Building fires that develop accidentally are completely unpredictable and unsafe. Fire risk assessment in buildings is a critical concern for measuring risk issues in residential or industrial activities in such structures. Fuzzy set theory can help to overcome this problem and aid in providing improved understanding of major risks and risk estimates. In order to prevent various risks and economic losses, it is crucial to estimate the fire risk of high-rise buildings. There have been lots of studies carried out so far to develop quantitative and qualitative approaches for identifying and estimating the risk of fire in buildings; however, applying fuzzy logic to risk assessment has significant benefits. Fuzzy algorithms are easy to use and efficient. Fuzzy models are reliable and provide precise results that can be used in future investigations.

The fire risk assessment models employed in high-rise buildings were the focus of a very limited number of studies. Tan and Moinuddin [5] carried out a methodical analysis of high-rise building fire safety modelling. They have examined the human and organizational error-related mistakes that can be used to calculate the risks. They found a lack of theoretical frameworks, empirical quantitative studies, or guidelines describing how human and organizational factors could be reduced to improve the probabilistic risk analysis of fires in high-rise buildings. Using a fire safety assessment, Ming Lo [6] provided a safety evaluation tool and fire risk ranking approaches for existing buildings. The method includes probabilistic or statistical methodologies, event-tree or fault-tree risk studies, stochastic computer simulation models, and fire risk ranking techniques based on multi-criteria evaluation. The aforementioned methods provide a framework for fire risk assessment, but they don’t really put any actual fire risk scenarios into practice. Table 1 outlines the key contributions, limitations, and modelling techniques used in fire risk assessment throughout the literature.

Table 1
Overview of some literature study on fire risk assessment in high rise buildings

Fire Risk Modelling Approach Quantitative method Qualitative method Features Limitations Research by

Statistical and Event tree analysis ✓ – The model included the fire statistics available to measure the frequency of fires and their possibility of developing consequences using an event tree. Rather than conducting a comprehensive examination of the fire’s source, the model concentrated only on statistical information. Xiao-qian SUN and Ming-chun LUO (2014) [7]

Gray risk index and fuzzy Analytic hierarchy process – ✓ Evaluates the degree of risk using a simple fuzzy comprehension evaluation method. Five buildings were rated as having excellent to poor fire protection features, however the consequences of a fire were not considered. Shi-yu Li et al. (2018) [9]

Analytic hierarchy process and fuzzy pattern Recognition model ✓ ✓ Evaluates the degree of risk using a simple fuzzy comprehension evaluation method. The fuzzy pattern recognition model is used by the model to determine relative membership. It also lacks an analysis of the risk’s consequences. YI Guang-wang and QIN Hua-li (2011) [10]

Mathematical fire risk Model ✓ – Uses a simplified risk-based decision support tool to assess the occupants’ risk level. There were several assumptions made. Lacking a study of the causes and effects of the fire’s origin.. N.D. Hansen et al. (2018) [11]

Scoring Method – ✓ The model relies on fire safety scoring systems to assess the level of risk and inherent safety in a building. Possible fire causes and reasons for the fire are not accounted for. Lack of consequence assessment of building fires. Saeed Bakhtiyari et al. (2022) [12]

Statistical Method – ✓ Relies on historical data on fire statistics to determine the factors that influence fire risk. Only a theoretical contribution based on statistical data to estimate the fire risks Jing Xin and Chong Fu Huang (2013) [8]

fuzzy synthetic assessment – ✓ Uses an analytical hierarchy process to assess building fire risk and safety system. The assessment index and its weight are not assessed through continuous practical implementation. YANG Gao-shan and PENG Li-min (2005) [13]

Event tree and Bayesian network – ✓ The model featured many Bayesian network-based parameters for organizational, technical, and human error. The model not relies on actual case study and lack of consequence assessment of fire. Samson Tan et al. (2020) [14]

Fire Risk Modelling Approach	Quantitative method	Qualitative method	Features	Limitations	Research by
Statistical and Event tree analysis	✓	–	The model included the fire statistics available to measure the frequency of fires and their possibility of developing consequences using an event tree.	Rather than conducting a comprehensive examination of the fire’s source, the model concentrated only on statistical information.	Xiao-qian SUN and Ming-chun LUO (2014) [7]
Gray risk index and fuzzy Analytic hierarchy process	–	✓	Evaluates the degree of risk using a simple fuzzy comprehension evaluation method.	Five buildings were rated as having excellent to poor fire protection features, however the consequences of a fire were not considered.	Shi-yu Li et al. (2018) [9]
Analytic hierarchy process and fuzzy pattern Recognition model	✓	✓	Evaluates the degree of risk using a simple fuzzy comprehension evaluation method.	The fuzzy pattern recognition model is used by the model to determine relative membership. It also lacks an analysis of the risk’s consequences.	YI Guang-wang and QIN Hua-li (2011) [10]
Mathematical fire risk Model	✓	–	Uses a simplified risk-based decision support tool to assess the occupants’ risk level.	There were several assumptions made. Lacking a study of the causes and effects of the fire’s origin..	N.D. Hansen et al. (2018) [11]
Scoring Method	–	✓	The model relies on fire safety scoring systems to assess the level of risk and inherent safety in a building.	Possible fire causes and reasons for the fire are not accounted for. Lack of consequence assessment of building fires.	Saeed Bakhtiyari et al. (2022) [12]
Statistical Method	–	✓	Relies on historical data on fire statistics to determine the factors that influence fire risk.	Only a theoretical contribution based on statistical data to estimate the fire risks	Jing Xin and Chong Fu Huang (2013) [8]
fuzzy synthetic assessment	–	✓	Uses an analytical hierarchy process to assess building fire risk and safety system.	The assessment index and its weight are not assessed through continuous practical implementation.	YANG Gao-shan and PENG Li-min (2005) [13]
Event tree and Bayesian network	–	✓	The model featured many Bayesian network-based parameters for organizational, technical, and human error.	The model not relies on actual case study and lack of consequence assessment of fire.	Samson Tan et al. (2020) [14]

From Table 1, it is clear that the studies on the methodology for assessing fire risks in high-rise buildings are very few and only focus on a few standard methods for a certain situation; they do not offer adequate safety precautions to lessen the accident. In many developing countries, there is no active fire protection department to record accurate fire statistics for research as in [7] and [8]. In the case of a lack of data availability, FBTA acts as a quantitative risk assessment (QRA) approach that employs expert data and estimates the risk probability values. Therefore, a proper investigation of the fire risk assessment in high-rise buildings that identifies the potential root cause is highly needed. The empirical study and description of operational, technical, and human errors are made possible by the use of a robust probabilistic solution that combines fault tree analysis (FTA) and event tree analysis (ETA) in a fuzzy sets environment.

The goal of this study is to identify the risks and potential severity of fire, property damage, loss of life, and environmental pollution risks and offer mitigation measures. So, the following objectives will be pursued:

Identification of all organizational, technical, natural, and human error-related factors that contributed to the top event

The proposed fuzzy bow tie approach makes use of expert judgments and data from the US National Fire Protection Association to obtain the probability of the accidental fire.

Factors that contribute to the top event were grouped into intermediate and basic events and employed in the fault tree.

Obtain the risk probability values of all the basic events and the probability of fire occurrence (the top event).

The risk probability of the initiating event is assigned to the event tree analysis as input, and the consequence assessment of that top event is evaluated.

Finally, the method is implemented in a case study of a fourteen-floor building, followed by a discussion of its sensitivity analysis results.

The structure of the paper is as follows: The background of the research and related papers are presented in this section. The concepts and methodology are explained in further detail in Section 2. A comprehensive risk assessment technique for an accidental fire and its application in a fourteen-story building are described in Section 3. The findings of the proposed approach to risk assessment are analyzed in Section 4. The final section concludes with suggestions, limitations on the research problem, and guidance for future work.

2 Methodology

The fuzzy bow tie approach [15 –18] is a comprehensive approach that combines the processes of the fuzzy fault tree approach and the fuzzy event tree approach. Numerous application-oriented studies on fire risk assessment using the fuzzy bow tie approach are available. Chemical industries [19], oil and natural gas pipelines [20], processing power plants [21], nuclear power plants [22], and underground tunnels [23] are examples from the literature.

2.1 Fuzzy bow tie approach

FBTA is extensively used in analyzing a risk problem or hazard from its origin of occurrence to its series of consecutive events. The typical fuzzy-bow tie approach (see Fig. 1) provides the potential causes of the risk and its consequences. The failure and risk probabilities of the basic events are provided by preventive measures along the path of identifying the causes of risk. The mitigation measures are deployed, and they estimate the severity of the consequences of the risk problem. This knowledge of the causes and effects of a risk helps formulate the controlling and corrective techniques needed to alleviate the accident or hazard. In the case of a lack of data availability, FBTA acts as a quantitative risk assessment (QRA) approach that employs expert data and estimates the risk probability values. The fuzzy set theory [24] is implemented in the traditional bow tie method to estimate crisp and precise risk values and to avoid vagueness and knowledge-based uncertainties. In this study, fuzzy bow tie analysis (FBTA) is applied to the analysis of accidental fire risk in high-rise buildings, which estimates the probability of a fire accident occurrence by applying the method of the trapezoidal fuzzy membership function. The detailed step-by-step flowchart of the fuzzy bow tie approach is shown in Fig. 2.

Fig. 1

Typical bow tie diagram.

Fig. 2

Flowchart of the fuzzy bow tie approach.

2.2 Identification of the risk problem

The first step in applying the FBTA approach is to define the risk issue and any relevant risk variables that could be harmful. The identification of risks is an important part of the analysis that addresses society’s unsolved problems. Once the hazard or undesirable event is selected, all the causes and effects of the hazard are studied and analyzed. Obtaining accurate probabilities for all the causes and effects is usually costly and time-consuming. It is very important to study about that event or hazard in order to obtain an expert’s knowledge or real-time data on that particular event or hazard, and the consequences of the event are listed out in the order of their occurrence. This can be used for the next step that involves creating or constructing the fault/event tree diagram such that none of the causes affecting the event or hazard are missed out. The causes, aftermath effects, and consequences of the event are listed out in the order of occurrence.

2.3 Creating a fault tree and event tree diagram

The fault tree diagram is constructed after selecting a risk or undesirable event in the system that needs to be addressed. A fault tree analysis [25 –27] is a logic block diagram consisting of “AND” and “OR” gates that define the major characteristics of the system. The gates connect the middle and bottom events, which can be undesirable or hazardous to a system. It is widely used for obtaining the probabilities of risk factors or undesirable events in complex systems. The top event in the fault tree diagram is the system’s undesirable event or hazard. The intermediate events are the average range of events that cause effects. The final causes are the basic events that are represented by a circle. It is the bottom event that does not need further analysis or improvement.

The probability of the undesirable or top event is the outcome of the fault tree diagram, and it is the input to the fuzzy event tree process. Failure of the mitigating measures leads to the rise of unwanted consequences, which can be dealt with by solving the branches of the event tree. The branch of an event tree splits into “yes” (success) or “no” (failure) by satisfying the operating conditions or whether the consequence occurs or not. The branches of the event tree keep splitting till all the consequences or conditions in the event tree are evaluated.

2.4 Expert evaluation

Experts are the skilled persons who have adequate knowledge of the root causes and experience with a particularly complex system or hazard. They provide information and resources about the occurrence and nature of the complex system or hazard. The risk probability of the hazard, top event, and basic events can be determined from the expert’s information about the hazard. The experts’ opinions may differ from each other as everyone treats the hazard from their own view of risk perception and experience. In the evaluation of reliable resources, experts are asked to deliver their knowledge about each basic event, and these data are aggregated to evaluate the risk probabilities of the hazard. Their opinions or data that are obtained in the form of linguistic terms are then converted into fuzzy values. The fuzzy values denote uncertainty and vagueness. There are various types of membership functions to represent the fuzzy numbers. The triangular and trapezoidal membership functions are commonly used in risk analysis and safety issues. These membership functions interpret the fuzzy number, which lies in the range [0, 1], that can be assigned as a risk probability value or the probability of an undesirable event.

2.5 Fuzzy fault tree process

The linguistic terms obtained from the experts are processed and aggregated to convert them into the risk probability of the hazard. The equations (1)–(9) explain the fuzzy fault tree approach.

2.5.1 Fuzzification

This process makes use of the trapezoidal member function, which has a range of [0, 1]. It is essential to convert the expert’s data from linguistic expressions into numerical values. The probability of the risk, which denotes the probability that an undesirable occurrence will occur, increases the closer it gets to the value “1”. The risk is lower and an undesirable event is less likely to occur the closer it gets to “0.” The experts may have various industrial and academic backgrounds and have varying knowledge and work experience in the field. As a result, their perceptions of risk may differ. So it is important to determine the aggregate value of the expert opinions with the help of a weighting factor.

Assessing the Degree of Similarity or Agreement

The aim of this step is to aggregate all the experts’ opinions and determine a consensus. Consider that there are n expert opinions in linguistic terms from n experts. Assume ‘S’ is the agreement degree of a pair of experts and ‘B’ is the similarity index symbol. The degree of agreement between the pair of experts’ (Ep, p = 1 to N) opinions Bi and Bj are represented by Sij (Bi, Bj). In this fuzzy fault tree approach, Bi = (bi1, bi2, bi3, bi4) and Bj = (bj1, bj2, bj3, bj4) are the two standard fuzzy numbers.

The degree of agreement [28] is calculated as,

${S (B}_{i} {, B}_{j}) = 1 - \frac{1}{4} \sum_{k = 1}^{4} | b_{ik} {- b}_{jk} |$ (1)

Where S (Bi, B_j) is in the range (0, 1). If the obtained degree of similarity is closer to 1, it indicates more similarity between the opinions of the experts. If the value of the degree of similarity is 1, it indicates that the experts’ opinions are identical.

Assessing the average degree of agreement

The average agreement of the experts [28] is calculated as

$AvgA (Ep) = \frac{1}{AA (E_{p})}$ (2) where $A A (E_{p}) = N - 1 (\sum \underset{j = 1}{_{i}^{N} \neq j} S (B_{i}, B_{j}))$ and N denotes the number of experts.

Assessing the Degree of the relative agreement of every pair

The relative agreement degree [28] of N experts is determined as,

${RA (E}_{p}) = \frac{AvgA (E_{p})}{\sum_{p = 1}^{N} AvgA (E_{p})}$ (3)

Assessing the consensus coefficient CoC [28] of an expert is as follows,

${CoC (E}_{p}) = α . W (E_{p}) + (1 - α) . RA (E_{p})$ (4)

Where the relaxation factor falls within the range implies a significance of less than.0, indicating that no significance has been assigned to the expert’s data indicates that the weighting factor and consensus degree of the expert data are similar.

Finally, the aggregated result [29] of the expert data is determined as

$RAG = \sum_{i = 1}^{N} CoC (E_{p}) . R_{p}$ (5)

2.5.2 Defuzzification

The fuzzy risk probabilities of the top or undesirable event need to be treated through defuzzification to get more reliable results. The aggregated trapezoidal fuzzy values are transformed into crisp values called “fuzzy risk probability.” The defuzzification step can be carried out by the centroid formula to defuzzify the trapezoidal fuzzy values [30].

$Y * = \frac{\int p_{k} (y) y . dy}{\int p_{k} (y)}$ (6) where Y* is the defuzzified value and is the membership function. Y is the output variable. The modified centroid [30] formula for the trapezoidal number B_i is (b_i1, b_i2, b_i3, b_i4). The risk probability value is given by

$\begin{matrix} RPV = \frac{1}{3} \cdot \\ \frac{(b_{i 4} + b_{i 3})^{2} - b_{4 i} b_{3 i} - (b_{i 1} + b_{i 2})^{2} + b_{i 1} b_{i 2}}{(b_{i 4} + b_{i 3} - b_{i 2} - b_{i 1})} \end{matrix}$ (7)

2.5.3 Generation of basic event risk probability values

The fuzzy risk probability is given in [31] and [32]

$\begin{matrix} FRP = {\begin{matrix} \frac{1}{10^{k}}, RPV \neq 0 \\ 0, RPV = 0 \end{matrix}}, \\ K = [(\frac{1 - RPV}{RPV})] * 2.301 \end{matrix}$ (8)

2.5.4 Generation of the top event risk probability

The top event risk probability is obtained by determining the probabilities of the intermediate events. The basic events and the intermediate events together are represented by the minimal cut sets (MinCS). The probability of an undesirable or top event [20] is given by

$\begin{matrix} P (Top Event) = & P {(MinSC}_{1} {U MinSC}_{2} {U MinSC}_{3} \\ \dots \dots \dots {MinSC}_{N}) \end{matrix}$ (9)

2.6 Minimal cut set ranking

The risk level generated by each individual intermediate event is examined using the ranking of the intermediate events. It is also possible to calculate the risk that that intermediate event will cause the top event hazard to occur. A Fussell-Vesely Importance Measure is used to analyze the ranking of each intermediate event in the fault tree process [29]. By presenting the numerical relevance of each event in the fault tree, this strategy aids in risk-related decision-making and prioritizes the fundamental and intermediate events. FV-I is denoted in (10) as,

${FV - I}_{measure} = \frac{R_{I} (i)}{R_{T} (i)}$ (10)

R_I(t) represents the risk probability of the intermediate event I.

R_T(t) represents the risk probability of the top event T.

2.7 Sensitivity analysis

In sensitivity analysis, each intermediate event and its contribution to the top event or hazard occurrence are studied. It analyses the limit at which changes in intermediate events lead to the top event occurring. The risk reduction worth method [20] (given in eqn. 11) is utilized to obtain the sensitivity analysis. It is used to analyze the probability of the top event’s occurrence in the absence of the given intermediate or basic events. The particular intermediate or basic event is assumed not to have occurred, and hence the improvement in the probability of the top event’s occurrence is studied. It is given by

$\begin{matrix} RRW = [Probability of the undesirable event / \\ top event)] \\ - [Top {event}^{'} s probability with \\ intermediate event probability set to zero] \end{matrix}$ (11)

The intermediate events can be ranked depending on the RRW values. This ranking can be used to plan an effective risk management procedure. It also specifies the maximum number of contributing intermediate or basic events required for the undesirable event to occur. Several potential causes of the top event can be identified, and safety measures can be taken a priori.

2.8 Calculation of consequence probability

The traditional event tree equation is employed to analyze the possibilities of every consequence occurring. According to the linguistic terms of the expert data, the severity of every consequence and the intermediate events are evaluated. The impact and outcomes of the top events were calculated using the probabilities of the intermediate events.

3 Application

3.1 Case analyses

In this work, the above discussed methodology is applied to a case study of a fourteen floor high rise building in Chennai, as shown in Fig. 3. The high rise building is surrounded by numerous industries, educational institutions, hospitals, and many more amenities. The high rise residential is a gated community that consists of 949 individual apartments that are divided into three blocks and cover almost 7.6 acres of land. This building site is equipped with fire safety measures such as a fire sprinkler system, a fire indication smoke alarm, and fire extinguishers at every floor. With almost exclusively luxurious facilities and a highly populated area, it is a vulnerable place to face a fire accident. Based on the annual accident report summaries released by the National Fire Protection Association [1, 3], the causes and consequences of fire accidents were identified in the first stage of the study.

Fig. 3

Layout of the high rise building.

The fuzzy bow tie methodology developed for risk analysis in the case study is discussed here. Structured fuzzy fault trees are employed to indicate the various causes that induce fire ignition, fire control, and rescue operations, as shown in Fig. 4. A fire accident happens with the combination of a fire ignition source and a failure of fire monitoring and control. Without fire control and monitoring failures, fire ignition can be a mere accident without any loss or damage. If the entire fire control and evacuation system fails, the damage and risks are likely to increase. Figure 4 also shows that fire ignition causes can be due to electrical malfunctions, cooking equipment malfunctions, intentional causes, and unintentional causes such as careless fires and natural fires.

Fig. 4

Structural fault tree diagram for cause of fire occurrence and fire control in the high rise buildings.

High-rise structures are significantly at risk due to a variety of factors. The significant ones are shown in Fig. 5, such as loose connections, mechanical damage, short circuits, etc. Similarly, the significant risk factors for equipment malfunction and technical failure are shown in Figs. 6 and 7, respectively. There are various risk perceptions associated with equipment and electrical failure. The cooking gas spills have been identified as being highly vulnerable, which leads to fire outbreaks and other severe, unpredicted scenarios.

Fig. 5

Fault tree diagram –Electrical Malfunction.

Fig. 6

Fault tree diagram –Equipment Malfunction.

Fig. 7

Fault tree diagram –Technical failure.

3.2 Rating stage

Insufficient data is the main drawback for the risk assessment of high rise buildings. Six experts were asked to suggest every possibility of a fire’s occurrence and the basic events of a fire in the high rise building. The experts are from both the building and fire rescue departments. Based on the expert’s recommendations and fire data, the weighting factors are generated. Tables 2 and 3, which demonstrate the weighing points and weightage calculation, respectively, Table 5 explains the symbolism and significance of the basic and intermediate events. Table 6 shows their response. As previously said, linguistic expressions will be converted into fuzzy numbers by applying the suitable numerical approximation technique created by Chen and Hwang [33]. Language expressions are converted to fuzzy numbers using the linguistic scales Extremely Low, Low, Mild, High, and Extremely High that are provided in Table 4. All fuzzy numbers must be transformed into trapezoidal fuzzy numbers in order to apply the method displayed in Fig. 8.

Table 2
Weighting points for the expert group

Category Points

Designation Director,Scientist,CEO,GM,General Secretary. 5

Chief Engineer,Officers, Manager 4

Site Engineer, Interior Designer 3

Supervisor,Driver,Operators 2

Working Experience Workers,Firemen 1

Greater than 25 5

15 –25 4

7 –15 3

3 –7 2

Less than 7 1

Educational Level PhD, MBA 5

ME, MTECH, MPhil 4

BE, MSC 3

Diploma,B.sc 2

ITI, 1

	Category	Points
Designation	Director,Scientist,CEO,GM,General Secretary.	5
	Chief Engineer,Officers, Manager	4
	Site Engineer, Interior Designer	3
	Supervisor,Driver,Operators	2
Working Experience	Workers,Firemen	1
	Greater than 25	5
	15 –25	4
	7 –15	3
	3 –7	2
	Less than 7	1
Educational Level	PhD, MBA	5
	ME, MTECH, MPhil	4
	BE, MSC	3
	Diploma,B.sc	2
	ITI,	1

Table 3

Weightage calculation of the expert group

Experts	Designation	Educational level	Work experience	Weighing points	Weight factor
EP1	Station Officer	ME,PhD	26	14	0.22
EP2	Manager	MBA	22	15	0.25
EP3	Civil Engineer	MTech	15	10	0.16
EP4	Operator	ME	10	9	0.15
EP5	Firemen	Diploma	15	6	0.09
EP6	Senior Consultant	BSc	2	7	0.11

Table 4

Fuzzy values of the linguistic terms

Linguistic terms	Probability set
Extremely Low (EL)	(0 0 0.1 0.2)
Low(L)	(0.1 0.2 0.3 0.4)
Mild(M)	(0.3 0.4 0.5 0.6)
High(H)	(0.5 0.6 0.7 0.8)
Extremely High(EH)	(0.7 0.8 0.9 1.0)

Table 5

Significance of the basic events

SYMBOL	Meaning	SYMBOL	Meaning
T	Fire Accident in the High rise building	B17	Careless smoking
X	Fire occurrence due to electrical malfunction	B18	Children playing with fire
Y	Fire occurrence due to an equipment malfunction	B19	Spark caused by lightning entered the building
Z	Fire occurrence due to a technical failure	B20	Sensor indication failure
B1	Bulb/lamp malfunction (Bulb/Lamp)	B21	Battery expired in the fire alarm system
B2	Cord/plug malfunction	B22	Physically damaged fire alarm system
B3	Electrical distribution malfunction in power supplies/transformers	B23	Improper positioning of the fire alarm in the ceiling
B4	Faulty insulation due to loose connections	B24	Poor fire alarm maintenance
B5	Faulty insulation due to mechanical damage	B25	Lack of fire extinguishers handling knowledge
B6	Short circuit arc from operating equipment	B26	Poor maintenance of fire extinguishers
B7	Short circuit arc from faulty contact	B27	Physically damaged fire extinguishers
B8	Cooking material/equipment malfunction	B28	Material leaked from extinguishers
B9	Gas spill/leakage	B29	Automatic sprinkler system shut off
B10	Grill cooking equipment malfunction	B30	System shut off manually
B11	Spark from welding and cutting equipment	B31	Physically damaged components
B12	Spark from soldering equipment	B32	Damaged firefighting equipment
B13	Water heater malfunction	B33	Insufficient amount of firefighters
B14	Space heater malfunction	B34	Lack of firefighting training
B15	Malfunction of other home appliances	B35	Lack of firefighting experience and equipment handling experience
B16	Setting fire intentionally	B36	Improper evacuation strategy/occupants unaware of the evacuation route

Table 6

Expert’s data on the basic events for fuzzy fault tree

Basic Events	E1	E2	E3	E4	E5	E6
B1	M	VL		L	M	L
B2	L	M	EL	L	L	EL
B3	L	EL	M	L	L	M
B4	EL	L	L	L	EL	EL
B5	L	L	EL	M	EL	L
B6	M	H	EL	L	L	EL
B7	EL	L	M	L	L	L
B8	H	EH	EH	M	H	M
B9	EH	H	H	EH	H	H
B10	M	L	EL	L	L	H
B11	L	L	L	EL	L	M
B12	EL	EL	L	M	L	M
B13	M	L	L	M	L	EL
B14	L	L	M	M	L	EL
B15	L	M	M	M	EL	M
B16	L	EL	M	L	L	EL
B17	EL	L	L	L	L	M
B18	L	M	H	L	M	EL
B19	H	L	M	M	EL	L
B20	EL	M	M	H	H	L
B21	L	M	H	L	H	H
B22	EH	L	L	M	L	EL
B23	L	M	EH	L	L	EL
B24	EL	M	M	H	EL	EL
B25	L	M	H	H	EL	L
B26	EH	L	L	L	H	EL
B27	L	M	M	EL	H	EL
B28	L	L	H	H	EL	EL
B29	M	EL	L	L	M	M
B30	M	H	EH	H	L	L
B31	H	M	M	L	L	EL
B32	H	M	EH	L	H	H
B33	H	M	M	H	L	EH
B34	M	M	M	H	H	EH
B35	H	M	M	H	EH	M
B36	EH	H	M	M	M	H

Fig. 8

Linguistic terms of the trapezoidal member function.

3.3 Aggregation stage

For the purpose of this study, the risk of a structure fire was assessed using the trapezoidal fuzzy membership function. 36 quantifiable data points collected from the experts were used in the aggregate procedure. When deciding how much weight to give the risk problem, experts from the construction industry and the fire rescue agency were consulted. To come to an agreement on each fundamental occurrence, the final quantitative data is produced. All basic event aggregate calculations were performed with a relaxation factor of 0.5 [27]. The fuzzy values and aggregate calculations for B32 are shown in Tables 7 and 8 as illustrations. In Table 9, the degree of similarity, average degree of agreement (AA), relative degree of agreement (RA), consensus coefficient (CC), and degree of similarity were calculated and displayed. In Table 10, the combined result of expert opinions for B32 is shown as fuzzy values.

Table 7
Fuzzy values of the experts opinion for the basic event B32

Experts Opinion

EP1 0.5 0.6 0.7 0.8

EP2 0.3 0.4 0.5 0.6

EP3 0.7 0.8 0.9 1.0

EP4 0.1 0.2 0.3 0.4

EP5 0.5 0.6 0.7 0.8

EP6 0.5 0.6 0.7 0.8

	Experts Opinion
EP1	0.5	0.6	0.7	0.8
EP2	0.3	0.4	0.5	0.6
EP3	0.7	0.8	0.9	1.0
EP4	0.1	0.2	0.3	0.4
EP5	0.5	0.6	0.7	0.8
EP6	0.5	0.6	0.7	0.8

Table 8

Degree of similarity calculation for the basic event B32

D (1,2)	D(1,3)	D(1,4)	D(1,5)	D(1,6)	D(2,3)	D(2,4)	D(2,5)	D(2,6)	D(3,4)	D(3,5)	D(3,6)	D(4,5)	D(4,6)	D(5,6)
1	1	0.825	1	0.825	0.8	0.425	0.8	0.425	0.625	1	0.625	1	1	0.625

Table 9

Average Agreement, Relative Agreement and consensus coefficient calculation for B32

Average agreement		Relative agreement		Consensus
of experts		of experts		coefficient
EP1	0.8182	EP1	0.3767	EP1	0.2984
EP2	0.4651	EP2	0.0964	EP2	0.1732
EP3	0.5714	EP3	0.1184	EP3	0.1392
EP4	0.5714	EP4	0.1184	EP4	0;1392
EP5	1	EP5	0.2072	EP5	0.1486
EP6	0.4	EP6	0.0829	EP6	0.0964

Table 10

Average Aggregated fuzzy values for B32

Aggregated result for basic event B32
0.2028	0.2787	0.3777	0.4767

3.4 Defuzzification and generation of a basic event probability value from expert opinion

These fuzzy values must be transformed into a crisp value, or risk probability, in order to assess the likelihood that the basic events will fail to occur. For this, Sugeno’s [30] centroid defuzzification algorithm was applied. The risk probability of the basic event occurrences was then converted into a fuzzy risk probability using the formula developed by Onisawa [34]. All basic events’ risk probability values and fuzzy risk probabilities were calculated, and the results are shown in Tables 11 and 12, respectively. Figure 9 displays the range of risks for the basic events. Figure 10 displays the various fuzzy risk probabilities.

Table 11
Risk probability values of the basic events

Basic events Risk probability Basic events Risk probability Basic events Risk probability Basic events Risk probability

B1 0.0770 B11 0.3941 B21 0.1082 B31 0.2714

B2 0.1883 B12 0.1816 B22 0.2611 B32 0.3349

B3 0.1058 B13 0.1804 B23 0.3731 B33 0.5587

B4 0.067 B14 0.1491 B24 0.1949 B34 0.0770

B5 0.1626 B15 0.1984 B25 0.3942 B35 0.2475

B6 0.5493 B16 0.2377 B26 0.1026 B36 0.5945

B7 0.1339 B17 0.1735 B27 0.2786

B8 0.5718 B18 0.1358 B28 0.3081

B9 0.6561 B19 0.1026 B29 0.4178

B10 0.2290 B20 0.1506 B30 0.2436

Basic events	Risk probability	Basic events	Risk probability	Basic events	Risk probability	Basic events	Risk probability
B1	0.0770	B11	0.3941	B21	0.1082	B31	0.2714
B2	0.1883	B12	0.1816	B22	0.2611	B32	0.3349
B3	0.1058	B13	0.1804	B23	0.3731	B33	0.5587
B4	0.067	B14	0.1491	B24	0.1949	B34	0.0770
B5	0.1626	B15	0.1984	B25	0.3942	B35	0.2475
B6	0.5493	B16	0.2377	B26	0.1026	B36	0.5945
B7	0.1339	B17	0.1735	B27	0.2786
B8	0.5718	B18	0.1358	B28	0.3081
B9	0.6561	B19	0.1026	B29	0.4178
B10	0.2290	B20	0.1506	B30	0.2436

Table 12

Fuzzy risk probability values of the basic events

Basic events	Fuzzy risk probability	Basic events	Fuzzy risk probability	Basic events	Fuzzy risk probability	Basic events	Fuzzy risk probability
B1	5.491E-05	B11	0.0022	B21	2.252E-05	B31	0.340E-04
B2	1.798E-04	B12	1.587E-04	B22	5.563E-04	B32	0.0013
B3	2.053E-05	B13	1.544E-04	B23	0.0018	B33	0.0075
B4	5.291E-05	B14	7.732E-05	B24	2.031E-04	B34	5.491E-05
B5	1.063E-04	B15	2.164E-04	B25	0.0022	B35	4.6404E-04
B6	0.0070	B16	4.041E-04	B26	1.815E-05	B36	0.0094
B7	5.167E-05	B17	1.342E-04	B27	7.056E-04
B8	0.0083	B18	5.450E-05	B28	9.697E-04
B9	0.0140	B19	1.817E-05	B29	0.0027
B10	3.559E-04	B20	8.016E-05	B30	3.807E-04

Fig. 9

Risk probabilities of the basic events.

Fig. 10

Fuzzy risk probabilities of the basic events.

3.5 Calculation of top event risk probability

36 basic events were linked together in the fault tree by AND and OR gates. They combined to produce 11 minimal cut sets. The basic events in the fault tree were grouped to obtain the probabilities of all the smallest cut sets (Intermediate events fuzzy occurrence probability) (see Table 13). The probability of the top event, a fire occurring in a high-rise building, was then calculated to be 9.684 E-04.

Table 13
Importance and sensitivity ranking of intermediate events

Intermediate events Sensitivity analysis

FVI-M FVIM- RANK RRW RRW RANK

Electrical distribution & Lighting Equipment Malfunction 0.2632 10 6.6707E-05 8

Wiring & related Equipment Malfunction/failure 9.1735 3 9.179E-05 7

Cooking Equipment Malfunction 26.1466 1 4.6124E-03 2

Heating Equipment Malfunction 2.324 7 2.439E-05 10

Fire Alarm equipment Failure 2.654 6 2.9725E-05 9

Lack of fire alarm indication 2.736 5 2.4127E-05 11

Human Error in handling Equipment 3.099 4 1.0467E-04 6

Unintentional fire occurrence 0.2134 11 1.2250E-04 5

Intentional fire occurrence 0.4174 9 1.48567E-04 4

Fire Fighting Failure 0.9699 8 6.4414E-04 3

Evacuation & Rescue Operation Failure 10.330 2 9.8765E-03 1

Intermediate events	Sensitivity analysis
Electrical distribution & Lighting Equipment Malfunction	0.2632	10	6.6707E-05	8
Wiring & related Equipment Malfunction/failure	9.1735	3	9.179E-05	7
Cooking Equipment Malfunction	26.1466	1	4.6124E-03	2
Heating Equipment Malfunction	2.324	7	2.439E-05	10
Fire Alarm equipment Failure	2.654	6	2.9725E-05	9
Lack of fire alarm indication	2.736	5	2.4127E-05	11
Human Error in handling Equipment	3.099	4	1.0467E-04	6
Unintentional fire occurrence	0.2134	11	1.2250E-04	5
Intentional fire occurrence	0.4174	9	1.48567E-04	4
Fire Fighting Failure	0.9699	8	6.4414E-04	3
Evacuation & Rescue Operation Failure	10.330	2	9.8765E-03	1

3.6 Calculation of the probabilities for event tree consequences

According to the data provided by the expert in Table 14, the probability of each accidental fire immediate consequence was calculated. The event tree risk assessment uses the probability of an accidental fire occurrence as determined by the fuzzy fault tree. Figure 11 depicts the fuzzy bow tie diagram and the probability of each intermediate event.

Table 14
Expert’s data on the intermediate events for event tree

Intermediate Event E1 E2 E3 E4 E5 E6

IE1: Monitoring and Alarm Device H L M H EH M

IE2: Human Evacuation M M EH L M EL

IE3: Fire Fighting L H H EL L M

IE4: Environmental Impact EH H M M H EH

IE5: Damage to the building H H EH M M EH

Intermediate Event	E1	E2	E3	E4	E5	E6
IE1: Monitoring and Alarm Device	H	L	M	H	EH	M
IE2: Human Evacuation	M	M	EH	L	M	EL
IE3: Fire Fighting	L	H	H	EL	L	M
IE4: Environmental Impact	EH	H	M	M	H	EH
IE5: Damage to the building	H	H	EH	M	M	EH

Fig. 11

Fuzzy bow tie diagram-accidental fire occurrence in the high rise building.

4 Findings and discussion

A key goal of any risk assessment is to identify the basic or intermediate event that poses the most risk so that additional attention may be paid to mitigating it. Through FV importance (FV-I) measurements, it can be demonstrated that the significant intermediate event in the fire accident that led to the fire occurrence in the high rise structure was reasonable. The FV-I measures of the intermediate events in the fire accident fault tree are computed using Eq. (8), and their rankings are displayed in Table 13. The risk reduction worth performance metric is also computed in order to increase the analysis’s dependability. These metrics support the analysis of those events that will contribute most to the top event. Cooking equipment malfunction, evacuation and rescue operation failure, electrical distribution and lighting equipment malfunction, fire extinguisher failure, sprinkler system failure, fire alarm and indication system failure, heating equipment failure, intentional fire risk, other home appliance malfunction, and unintentional fire risk are the top ten critical events that increase risk (see Table 13 for more information). According to the RRW ranking (see Table 13), the failure of the evacuation and rescue operation is the most crucial event that requires immediate care, followed by the failure of the cooking equipment. The difference between the RRW ranking and the FVI-M ranking is quite small.

According to the fuzzy fault tree approach, the chance of a fire accident in that high-rise building, which we have chosen as a case study, is estimated to be 0.0968%, with a potential for 9 out of 100 fire accidents annually. Table 13 makes it abundantly evident that the main causes of fire accidents in tall buildings are faulty cooking equipment, fire ignition, and poor fire management. Cooking equipment failure is frequently caused by a gas leak or a grill fire. [35]. According to the NFPA high rise building report [1], cooking equipment causes 75% of fires in apartments or multi-family dwellings, 45% in hotels, 73% in dormitories for students, 36% in office buildings, and 51% in hospital buildings. As a result of equipment failure in the cooking area, the gas spill poses a serious risk and ends up being a very high-risk factor for fire occurrence [36]. Human evacuation and rescue operation failure [37] have also been observed to play a significant role in fire disasters. If the evacuation is improper and the fire fighters are ineffective, the risk is very high. Physical disability, crowding, panic, and failure to follow evacuation routes are examples of human incompetence that significantly contribute to fire accidents [38]. Due to faulty evacuation procedures and a lack of human coordination, firefighting and rescue operations face increasingly difficult problems. Lack of firefighters [39], Firefighting failure is caused by inadequate training, equipment, and experience. This could have negative effects on how residents are evacuated once a fire occurs. It is observed that the intermediate event of electrical equipment failure in electrical malfunction is the next maximum contributor, represented by the basic events of faulty insulation, short circuits, and mechanical damage.

Human error is caused by incorrect sensor positioning [40] and poor maintenance. Because the risk probability is extremely low, these factors are insignificant. It is clear that the least common contributors to fire incidents in high-rise buildings are natural causes of fire, such as lightning, kids playing with fire, and intentional setting of fire [41].

Finally, the fuzzy bow tie diagram shown in Fig. 11 shows that consequence (Cons6) (9.6088E-03) resulted in a substantial loss of life when the fire alarm control systems and fire rescue operations failed. Considerable property destruction (1.6584 E-04) and significant environmental pollution (2.1056 E-06) resulting from the fire smoke are the next two major impacts. Table 15 compares a number of developed risk assessment strategies in high-rise buildings and explains how the proposed strategy and those already described in the literature complement each other.

Table 15
Comparison of the proposed method with the previous Fire risk assessment methods in High rise buildings

Approaches Techniques used Probability of fire accident per year Consequence analysis Inference

Xiao Li et al., (2013) [42] CUrisk software 6.0E-06 ✓ The CURISK computer model was used to assess the risk of loss of life and economic loss.A six-story residential building is presented as a case study

Shi-yu li et al., (2018) [9] Gray risk and Fuzzy AHP – – The fire safety levels of five buildings were categorized as excellent, good, medium, and poor using the fuzzy matrix evaluation method.

Xiao-Qian Sun and Ming-Chun Luo (2014) [7] Event tree Analysis 0.024 ✓ A case study is used to evaluate the probability and consequences of building fires.

Yi Guang Wang and Qin Hua Li (2011) [10] AHP &Fuzzy Pattern Recognition Model – – A case study of a hotel building is analyzed as safe, below safe, normal, risky, and dangerous as risk levels.

Jin Xin and Chong Fu Huang (2014) [8] Statistical Model 3.57E-03 ✓ Analyses the fire situation in China from 1991 to 2010. To understand fire features and the factors impacting fire risks, the temporal, geographical, and causal fire event data over the past six years have been investigated.

Yang Gao Shang and Peng Li Min (2005) [13] Analytic Hierarchy Process – – Uses a fuzzy synthetic assessment to assess a building’s fire safety level.

Saeed Bakhtiyari et al., (2022) [12] Scoring Method – – Uses a safety scoring method and identifies six parameters as the highest factors according to their relative weights.

Samson Tan et al., (2020) [14] Event tree Analysis and Bayesian Network 5.51 E-03 to 4.25 E-01 ✓ Three case studies have been conducted to demonstrate the application of a comprehensive technical-human organizational risk using Bayesian networks and statistical data.

Proposed Fuzzy Bow Tie Approach Fuzzy Fault tree and Fuzzy Event Tree 9.684 E-04 ✓ Studies the contributions of technical, accidental, and natural sources of fire and does not require additional statistical data over time. The bow tie’s use of fuzzy set theory makes it able to deliver accurate and clear results.

Approaches	Techniques used	Probability of fire accident per year	Consequence analysis	Inference
Xiao Li et al., (2013) [42]	CUrisk software	6.0E-06	✓	The CURISK computer model was used to assess the risk of loss of life and economic loss.A six-story residential building is presented as a case study
Shi-yu li et al., (2018) [9]	Gray risk and Fuzzy AHP	–	–	The fire safety levels of five buildings were categorized as excellent, good, medium, and poor using the fuzzy matrix evaluation method.
Xiao-Qian Sun and Ming-Chun Luo (2014) [7]	Event tree Analysis	0.024	✓	A case study is used to evaluate the probability and consequences of building fires.
Yi Guang Wang and Qin Hua Li (2011) [10]	AHP &Fuzzy Pattern Recognition Model	–	–	A case study of a hotel building is analyzed as safe, below safe, normal, risky, and dangerous as risk levels.
Jin Xin and Chong Fu Huang (2014) [8]	Statistical Model	3.57E-03	✓	Analyses the fire situation in China from 1991 to 2010. To understand fire features and the factors impacting fire risks, the temporal, geographical, and causal fire event data over the past six years have been investigated.
Yang Gao Shang and Peng Li Min (2005) [13]	Analytic Hierarchy Process	–	–	Uses a fuzzy synthetic assessment to assess a building’s fire safety level.
Saeed Bakhtiyari et al., (2022) [12]	Scoring Method	–	–	Uses a safety scoring method and identifies six parameters as the highest factors according to their relative weights.
Samson Tan et al., (2020) [14]	Event tree Analysis and Bayesian Network	5.51 E-03 to 4.25 E-01	✓	Three case studies have been conducted to demonstrate the application of a comprehensive technical-human organizational risk using Bayesian networks and statistical data.
Proposed Fuzzy Bow Tie Approach	Fuzzy Fault tree and Fuzzy Event Tree	9.684 E-04	✓	Studies the contributions of technical, accidental, and natural sources of fire and does not require additional statistical data over time. The bow tie’s use of fuzzy set theory makes it able to deliver accurate and clear results.

The probability of a fire occurring in the Xiao Li et al. study [42], which used CUrisk software to determine the risk of high rise structures, was 6E-06. The study by Sun and Chung Lo [7] revealed that the probability of a fire occurring was 0.024. This study’s objective was to quantitatively quantify the risk of high rise buildings using event tree analysis. The probability of a fire accident was estimated to be 0.024 by the fire statistical model in the study, which used historical data from China. According to the study [8], the risk of fire due to various technical, organizational, and human-related factors ranged from 5.1E-03 to 4.25E-01. The results of the previous research and those of the proposed method were essentially equivalent and consistent. The results of the proposed work have been obtained by applying fuzzy logic to the bow tie risk assessment in order to calculate the probability of a fire in a fourteen-story building. The use of fuzzy bow tie assessment to calculate the risk of identified hazards leads to increased study accuracy and decreased uncertainty in risk calculation because of the lack of historical information in the investigated building and the existing uncertainty in estimating and calculating the risk probabilities using existing risk assessment methods such as event trees, AHP, or Bayesian networks.

5 Conclusion

The fuzzy logic-based bow-tie method was used to determine the risk of an accidental fire catastrophe in high rise buildings. This work validates the use of fuzzy logic in addressing fire situations as quantitative data to assess the basic events in a fault tree with the aid of linguistic terms supplied by experts in a fourteen floor building as a case study. This is important because there is no fire data for the basic event occurrences in the investigated building. The quantitative data in this work has been described using risk probabilities, which are represented as fuzzy integers. Fuzzy numbers offer the advantage of making it easy to characterize fire data, something that is hard with merely quantitative data. The probability of an accidental fire was assessed using the proposed FBTA framework, and intermediate event failures were ranked using F-VIM and RRW. The most contributing factor that leads to a fire accident was found to be BE9BE36, which is the combination of “cooking gas spill and improper evacuation strategy” and “lack of awareness of the evacuation route to the occupants.” In event tree analysis, potential event series were defined and evaluated. It was found that the most probable consequence is the loss of human lives and property damage, which may be prevented at a minimum level by planning proper evacuation strategies and fire-fighting techniques. As a result, the following preventive and mitigation steps are suggested in order to enhance the safety status of the building investigated:

Standard building safety code to avoid design deficiencies.

Proper maintenance and operational training of technical systems are required for security officials.

Installing a gas and fire monitoring system exclusively in the cooking area.

Conduct regular fire drills to become familiar with handling accidental fires.

Prepare an emergency evacuation plan and protocol.

Educate the community about the emergency evacuation route.

In comparison to previous risk assessment techniques, fuzzy bow tie risk assessment gives building engineers and fire safety officials more data about the risks and their ranks, enabling them to suggest more effective safety management measures apart from those mentioned above to reduce the number of significant hazards. It is important to note that uncertainty handling is still a concern, even though this methodology decreases uncertainties while evaluating the risk of a fire accident. By implementing hybrid type-2 approaches that combine fuzzy bow-tie and deep learning approaches, this work could be further enhanced.

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Intermediate events	Sensitivity analysis
	FVI-M	FVIM- RANK	RRW	RRW RANK
Electrical distribution & Lighting Equipment Malfunction	0.2632	10	6.6707E-05	8
Wiring & related Equipment Malfunction/failure	9.1735	3	9.179E-05	7
Cooking Equipment Malfunction	26.1466	1	4.6124E-03	2
Heating Equipment Malfunction	2.324	7	2.439E-05	10
Fire Alarm equipment Failure	2.654	6	2.9725E-05	9
Lack of fire alarm indication	2.736	5	2.4127E-05	11
Human Error in handling Equipment	3.099	4	1.0467E-04	6
Unintentional fire occurrence	0.2134	11	1.2250E-04	5
Intentional fire occurrence	0.4174	9	1.48567E-04	4
Fire Fighting Failure	0.9699	8	6.4414E-04	3
Evacuation & Rescue Operation Failure	10.330	2	9.8765E-03	1

Fire accident risk assessment of high rise building based on fuzzy bow tie approach

Abstract

Keywords

1 Introduction

2.1 Fuzzy bow tie approach

2.3 Creating a fault tree and event tree diagram

2.4 Expert evaluation

2.5 Fuzzy fault tree process

2.5.1 Fuzzification

3 Application

3.1 Case analyses

Table 7 Fuzzy values of the experts opinion for the basic event B32 Experts Opinion EP1 0.5 0.6 0.7 0.8 EP2 0.3 0.4 0.5 0.6 EP3 0.7 0.8 0.9 1.0 EP4 0.1 0.2 0.3 0.4 EP5 0.5 0.6 0.7 0.8 EP6 0.5 0.6 0.7 0.8

Table 14 Expert’s data on the intermediate events for event tree Intermediate Event E1 E2 E3 E4 E5 E6 IE1: Monitoring and Alarm Device H L M H EH M IE2: Human Evacuation M M EH L M EL IE3: Fire Fighting L H H EL L M IE4: Environmental Impact EH H M M H EH IE5: Damage to the building H H EH M M EH

References

Table 7
Fuzzy values of the experts opinion for the basic event B32

Experts Opinion

EP1 0.5 0.6 0.7 0.8

EP2 0.3 0.4 0.5 0.6

EP3 0.7 0.8 0.9 1.0

EP4 0.1 0.2 0.3 0.4

EP5 0.5 0.6 0.7 0.8

EP6 0.5 0.6 0.7 0.8