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ScienceDirect Procedia Engineering 137 (2016) 467 – 477

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Urban Rail Transit Risk Evaluation with Incomplete Information Xiaoping Hu, Xiamiao Li, Yin Huang* School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan Province, China

Abstract In recent years, the urban rail transit risk analysis has been obtained great concerns from wide fields in the society. The hazards of urban rail transit evaluation play important role in the urban rail transit risk analysis. However, lacking of guarantee of the source and assurance of the evaluation information, so the characteristics of hazard can hardly be quantized or always be in the context of uncertainty. Under such environment, an improved DS/AHP method is provided in this study for the evaluation of hazard source. Firstly, the identification and evaluation of urban rail transit hazard sources are proposed according to different methods. Secondly, the evaluation system analysis is provided from three aspects--- frequency, extent of damage and uncontrolled. Thirdly, the improved DS/AHP method is employed for risk evaluation to determine the order of different hazard sources. At last, a numerical example is provided for the hazard risk analysis to verify the feasibility of the method. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Department of Transportation Engineering, Beijing Institute of Technology. Peer-review under responsibility of the Department of Transportation Engineering, Beijing Institute of Technology Keywords: hazard evaluation; classification; incomplete information; Dempster–Shafer theory; extension theory; analytic hierarchy process

1. Introduction Urban rail transportation has entered into fast development period and it brings convenience for residents. But urban rail transit operation involves to personnel, facilities, environment, management, more and more hazards need to face. As the foundation for scientific hazard control decision-making, identification and evaluation of the hazards of urban rail traffic can guarantee the safe operations in urban rail transit to some extent. It is not only the basic prevention of all kinds of accidents, but also the premise that the loss falls to the lowest. There are two main purposes of risk evaluation: One is to get a system risk status evaluation, the other is to find the most important various hazards in system. From the current status, quantitative analysis literatures on the

* Corresponding author. Tel.: +1-346-907-1448. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Department of Transportation Engineering, Beijing Institute of Technology

doi:10.1016/j.proeng.2016.01.282

468

Xiaoping Hu et al. / Procedia Engineering 137 (2016) 467 – 477

problem of system risk evaluation have mostly focused on the former. The study literatures about the latter are hardly to be found. The risk degree of hazard varies in different studies. The evaluation for the risk degree of hazard can also be used to system risk analysis because it can get the importance of each hazard which can be used as the criteria in system risk evaluation. Moreover, the evaluation of hazard risk degree is helpful to identify the primary and secondary sequence of risk management. However, in the practical world, complete evaluation information is usually hard to get. The reasons may come from˖1)evaluate in a short time or under the condition of lack of data; 2) Some criteria that reflect the social and environmental impact are difficult to ascertain or quantify;3)The attention and information processing capabilities of evaluation makers are limited, especially the value judgment in complex and uncertain condition. On such basis, the characteristic of the incomplete information in urban rail transit hazard is focused in this study. Firstly, the identification and evaluation of urban rail transit hazard source are proposed according to different method. Secondly, the evaluation system analysis is provided from three aspects--- frequency, extent of damage and uncontrolled. Thirdly, the improved DS/AHP method is employed for risk evaluation to determine the order of different hazard sources. At last, a numerical example is provided for the hazard source risk analysis to verify the feasibility of the method. 2. Literature Review The hazards of urban rail transit are the fundamental reasons or states of the accidents or accidents combination ,which may cause injuries, occupation disease, loss of property and damage to work environment. The hazard identification is to confirm the existence and characteristics of hazards. Xu et al [1] analyzed occurrence rules of accidents and cause mechanization of risk factors through the analyzing of the accidents in China and foreign countries. By the analysis of anthropogenic factor, facility factor, environment factor, and management factor affecting operation safety, they find out the inherent relations among the cause mechanizations. Zhang et al [2] proposed the emphases in hazard identification including operation service activities and the link involved ,conclude intended destroy, passengers and contractors, operation and maintenance of equipment, hazardous materials involved, dangerous operating method , dangerous working environment etc. From the previous literature, the hazard risk degree is often calculated in the form of equation. In hazard evaluation matrix table, the occurrence probability of hazard accident multiply by the consequences of possible accident (severity) is the hazard risk degree, which is used to get the risk rating of each hazard. Liu, Tang and Chen [3] divided the risk value of dangerous hazard into four levels which is determined by the probability and consequences of the accident. “Yes” or “No” judgment method check whether the hazard and the possible consequences of this is consistent with the known condition. If consist, it is regarded as major hazard [4]. The traditional hazard risk degree evaluation criteria appropriate to simple system, and the criteria value span is broad, lacking of subjectivity and focusing on anthropogenic injury. Recently, some methods combining multi-criteria comprehensive evaluation (MCCE) and AI (artificial intelligence) have been explored to develop enhanced methodologies for knowledge based decision support system. By combining MCCE with fuzzy logic theory [5], new methods have been developed such as Fuzzy AHP [6], Fuzzy comprehensive assessment [7, 8]. In addition, some approaches using the framework of evidence theory with MCCE methods have been proposed by Beynon, Curry, and Morgan [9] .They proposed AHP and Dempster Shafer (D–S) Theory [10] for dealing with complex decision problems in the field of management. The DS/AHP method shows potential on dealing with comprehensive evaluation problems with incomplete information [11].The DS/AHP method has been widely used in MCCE with incomplete information. 3. Evaluation approach 3.1. The method of Dempster–Shafer and AHP theory The DS/AHP method was proposed by Beynon, Curry, and Morgan (2000), which incorporates Dempster–Shafer theory with AHP, shows potential on dealing with comprehensive evaluation problems with incomplete information [11]. This frame of discernment contains every possible hypothesis. The elements in ȣ could be enumerated byʹȣ,

469


which is the power set ofȣ, consisting of all the subsets ofȣ.Let ሺሻ denote the basic probability assignment (BPA) to the subset A, which measures the extent to which the evidence supports A. The BPA is a function:ǣ ʹɅ ՜ ሾͲǡͳሿ, which is called a mass function and satisfies: ߆ ൌ ሼ߆ଵ ǡ ߆ଶ ǡ ‫ ڮ‬ǡ ߆௡ ሽ

(1)

݉ሺ‫׎‬ሻ ൌ Ͳǡ ܽ݊݀ σ஺‫݉ ௵ك‬ሺ‫ܣ‬ሻ ൌ ͳ

(2)

Where ‫׎‬is the null set, A is any subset of ȣ, andʹȣis the power set of ȣ.Given a piece evidence, a belief level between ሾͲǡͳሿ,denoted by ሺήሻ, is assigned to each subset ofȣ. All the BPAs add up to unity. Belief function is an important concept associated with the Dempster–Shafer theory, which is defined as follows: ‫݈݁ܤ‬ሺ‫ܣ‬ሻ ൌ σ஻‫ك‬஺ ݉ሺ‫ܤ‬ሻǡ ݂‫( ߆ ك ܣݕ݊ܽݎ݋‬3) It reflects the exact support to the hypothesis A and is a function Bel:ʹɅ ՜ ሾͲǡͳሿ,Bel(A) is the probability assigned to A considering all the premises of A. Plausibility function is another important concept associated with the Dempster–Shafer theory, which is defined as: ݈ܲሺ‫ܣ‬ሻ ൌ σ஺‫ת‬஻ஷ‫݉ ׎‬ሺ‫ܤ‬ሻǡ ݂‫ ߆ ك ܣݕ݊ܽݎ݋‬

(4)

ሺሻrepresents the possible support to A, and it is the total amount of belief that could be potentially placed in A.ሾሺሻǡ ሺሻሿconstitutes the interval of support to A and can be seen as the lower and upper bounds of the probability to which A is supported. ݉ሺ‫ܣ‬ሻ ൌ

σಳ‫ת‬಴సಲ ௠భ ሺ஻ሻ௠మ ሺ஼ሻ ଵିσಳ‫ת‬಴సಲ ௠భ ሺ஻ሻ௠మ ሺ஼ሻ

ǡ ‫׎ ് ܣ‬ሺͷሻ

3.2. The improvements of DS/AHP 3.2.1. Change the focal elements identification method In the DS/AHP method, the frame of discernment is defined as a collectively exhaustive and mutually exclusive implies set of decision alternatives (DAs) under evaluation: Ʌ ൌ ሼଵ ǡ ଶ ǡ ‫ ڮ‬ǡ ୫ ሽ. The decision ൌ ൣ൫୩ ǡ ୨ ൯൧ ୫ൈ୬ the body of evidence of the hazard evaluation problem. Definition1 [11]: For ‫׊‬୩ଵ ǡ ୩ଶ ‫ א‬ȣand୩ଵ ് ୩ଶ , if ൫୩ଵ ǡ ୨ ൯ ൌ ൫୩ଶ ǡ ୨ ൯,then୩ଵ and ୩ଶ belong to the same focal element for criterion୨ . Definition 2 from improved identification: For ‫׊‬୩୧ ‫ א‬ȣf൫୩ଵ ǡ ୨ ൯ ് Ͳ, then ୩୧ is the focal element of evidence for criterion୨ ሺ ൌ ͳǡʹǡ ǥ ሻሺ ൌ ͳǡʹǡ ǥ ሻ. In previous studies, the focal elements identification put the decision alternatives with same indicator value evidence into a focal element, which is depicted in definition1. But experience shows that when the dimension of knowledge matrix equals the number of alternatives plus one, the validity of evaluation results reach maximum. The focal elements identification for criterion୨ inold and new method is shown in Table1˖ Table 1. The focal elements identification for criterion ୨ in old and new method. Criterion

Old FA identification

New FA Identification

frequency

ሼǡ ሽ,ሼሽ,ሼሽ,Θ

ሼሽ,ሼሽ,ሼሽ,ሼሽ,Θ

severity

ሼሽ,ሼǡ ሽ},ሼሽ,Θ


uncontrollability

ሼǡ ǡ ሽ,ሼሽ,Θ


470


3.2.2. Replace the complementary judgment matrix to reciprocal judgment matrix For scale, the judgment matrix in DS/AHP are always inሾʹǡ͸ሿ.Although which is easy to construct connection between inferring semantic and preference description value. But it is very difficult to accurately segment the relative preference for many schemes from decision makers, especially when the alternatives are numerous. However, the complementary judgment matrix uses the complementary scale to assignment the relative preference of each focal elements. For example, the preference value of focal element X to focal element plus the preference value of focal element Y to focal element X, the sum is 1.And both preference value are between the number ofሾͲǡͳሿ.Replacing the complementary judgment matrix to reciprocal judgment matrix can fully use the tradition method to obtain inferred messages. And it can take an arbitrary number from0.5 to 1 instead of the limitation in the five rating scale. So the complementary judgment matrix can solve the in accuracy inference efficiently because of the problem of scaling distance. The judgment matrix for criterion ୨ in old and new method is shown inTable2. Table 2. The judgment matrix for criterion୨ in old and new method. ୨ ሺଵሻ ୨ ሺଶሻ

୨

ሺଵሻ ୨

ȣ

‫ڮ‬

ሺ୬ሻ

୨

1.00

0.00

‫ڮ‬

0.00

0.00

1.00

‫ڮ‬

0.00

‫ڭ‬ ሺ୬ሻ ୨

ሺଶሻ

୨

‫ڭ‬ 0.00 ሺଵሻ ͳȀ୨

‫ڭ‬ 0.00 ሺଶሻ ͳȀ୨

‫ڭ‬ ‫ڮ‬ ‫ڮ‬

ȣ

୨

ሺଵሻ ୨

ሺଵሻ ୨

ሺଶሻ

୨ ‫ڭ‬

1.00 ሺ୬ሻ ͳȀ୨

ሺଶሻ

୨

‫ڭ‬

‫ڭ‬

ሺ୬ሻ ୨

ሺ୬ሻ ୨

1.00

ȣ

ሺଵሻ

ሺଶሻ

୨

୨

ሺ୬ሻ

୨

‫ڮ‬

ȣ ሺଵሻ

0.50

-

‫ڮ‬

-

୨

-

0.50

‫ڮ‬

-

୨

‫ڭ‬

‫ڭ‬

ͳ െ

‫ڭ‬ ‫ڮ‬

ሺଵሻ ୨

ͳ െ

ሺଶሻ ୨

ሺଶሻ

‫ڮ‬

‫ڭ‬

‫ڭ‬ ሺ୬ሻ ୨

0.50 ሺ୬ሻ

ͳ െ ୨

0.50

3.2.3. New combination rules of BPA A transformation method according to the weight is employed to modify the combination of BPA and combinate independent evidence information from different information sources. It makes decision just like tradition DS/AHP method but reduces calculation. The specific approach is transforming the BPA of each alternative according to the weight. The transformation is the proportion that alternatives amount in focal element (FE) which divide alternatives amount in the frame of discernment. Then it multiplied by the BPA of FE that contains the alternative. The last result is the BPA of the FE. Suppose the frame of discernmentȣ ൌ ሼଵ ǡ ଶ ǡ ‫ ڮ‬୬ ሽ,the BPA in criteria୨ is ଵ ǡ ଶ ǡ ‫ ڮ‬୧ ,the BPA of alternative ୩ ሺͳ ൑ ൑ ሻis˖ ଵ

݉ܲሺሼ‫ܣ‬௞ ሽሻ ൌ ܽଵ ݉ଵ ൅ ܽଶ ݉ଶ ൅ ‫ ڮ‬൅ ܽ௜ ݉௜ ൅ ݉ఏ ௡

(6)

୧ defines the proportion that alternatives amount in focal element divide alternatives amount in the frame of ଵ discernment. When there is no୩ in FE, then ୧ ൌ Ͳ; if the FE contain୩ , then ୧ ൌ (X is the number of alternatives ଡ଼ in FE,N is the number of all alternatives in Θ). The total evaluation value of each alternative can be calculated by the way as follows: suppose there are n criteria and m alternatives. The ൈ matrix of BPAmultiply by the ൈ ͳ matrix of the criterion and get the support from each alternative. For example: when there is 4 criterion and 3 alternatives, the support of the alternative ୩ is as follows: ܲ஺ଵ ߱஺ ݉ଵ ܲሺሼ‫ܣ‬ሽሻ ݉ଶ ܲሺሼ‫ܣ‬ሽሻ ݉ଷ ܲሺሼ‫ܣ‬ሽሻ ݉ସ ܲሺሼ‫ܣ‬ሽሻ ܲ஺ଶ ൦ ൪ ൌ ቎݉ଵ ܲሺሼ‫ܤ‬ሽሻ݉ଶ ܲሺሼ‫ܤ‬ሽሻ݉ଷ ܲሺሼ‫ܤ‬ሽሻ݉ସ ܲሺሼ‫ܤ‬ሽሻ቏ ൈ ൥߱஻ ൩ሺ͹ሻ ܲ஺ଷ ߱஼ ݉ଵ ܲሺሼ‫ܥ‬ሽሻ ݉ଶ ܲሺሼ‫ܥ‬ሽሻ ݉ଷ ܲሺሼ‫ܥ‬ሽሻ ݉ସ ܲሺሼ‫ܥ‬ሽሻ ܲ஺ସ

471


4. Hazard risk degree evaluation 4.1. Decision alternatives(hazards) identification and classification Based on previous urban rail transit operation hazards, we proposes to classify the hazard in different category. (1) Classification according to the accident characteristics: classify into fire, toxic material / gas explosion, water logging), earthquake / wind, structural collapse, enter into limits, unexpected accident, external threats, impact, derail, operation accident, non-operation accident and emergency action. (2) Classification according to the hazard material state: classify into physical hazard, chemical hazard, biological hazard, psychological or physiological hazard, behavioral hazard. (3) Classification according to the hazard principal part: classify into vehicle breakdown, Communication signal breakdown, electricity supply breakdown, electromechanical breakdown, trouble from the passengers, environmental problems, civil engineering facilities breakdown and lines breakdown. 4.2. Weight of criteria The criteria are number of accidents, casualty, direct economic loss , indirect economic loss, and uncontrollability. According to the weight, AHP is required. The pairwise comparison matrix of criteria in six scale is constructed and the latent root is used to get the weight of criteria. Table 3. Pairwise comparison matrix of criteria.

Criterion

ଵ

ଶ

ଷ

ସ

ହ

ଵ ଶ ଷ ସ ହ

1 1/2 1/5 1/2 1/3

2 1 1/2 1/2 1/2

5 2 1 1/4 2

5 2 2 1 2

3 2 1/2 1/2 1

߱௜ ൌ ሺͲǤͶͶ͵ͷǡͲǤʹͳͺ͸ǡͲǤͳͲͷ͸ǡͲǤͲ͹ͻ͸ǡͲǤͳͷʹͺሻ 4.3. Criteria value data collection Using linguistic terms to describe criteria value is hard to quantify. They are expressed in nine particle size evaluation, and the unknown criteria value is expressed in symbol ̶ ‫̶ כ‬Ǥ ‫ ݏ‬ൌ ሼ‫ݏ‬଴ ǡ ‫ݏ‬ଵ ǡ ‫ݏ‬ଶ ǡ ‫ݏ‬ଷ ǡ ‫ݏ‬ସ ǡ ‫ݏ‬ହ ǡ ‫ ଺ݏ‬ǡ ‫ ଻ݏ‬ǡ ‫ ଼ݏ‬ሽ ൌ ሼ݊‫݁݊݋‬ǡ ‫ݎ݋݋݌ݕݎ݁ݒ‬ǡ ‫ݎ݋݋݌‬ǡ ݈݉݅݀݀݁‫ݎ݋݋݌‬ǡ ݂ܽ݅‫ݎ‬ǡ ݈݉݅݀݀݁‫݄ܿ݅ݎ‬ǡ ‫݄ܿ݅ݎ‬ǡ ‫݄ܿ݅ݎݕݎ݁ݒ‬ǡ ݉‫݄ܿ݅ݎݐݏ݋‬ሽ

4.4. Focal element identification and the judgment matrix The hazards are so numerous to analyze in this paper. For convenience, choose one hazard class (trouble from the passengers) as the alternatives in an urban rail system. The criteria value of each hazard list in Table 4. The alternatives are divided into several focal elements in improved FE classification method. The experts give the FE preference inሾͲǤͷǡͳሿscale in Table 5. Get the incomplete complementary judgment matrix in each criterion based on the FE preference. The complementary judgment matrix in criterion ଵ isଵ . Similarly, the complementary judgment matrix in criterionଶ ,ଷ ,ସ ,ହ is obtained.

472


Table 4. The criteria value of each hazard. ଷ

ସ

ହ

Jump off the platform(A)

52

ଵ 1

଺

଼

଼

Passengers crowd(B)

3

4

ହ

ହ

଺

Grill the door(C)

3

*

ଷ

ହ

଻

Passengers fighting(D)

3

1

‫כ‬

ହ

ଶ

Own disease(E)

17

*

ଵ

ଵ

ହ

Excessive drinking(F)

2

*

ସ

ହ

ଶ

Own sake(G)

7

*

ସ

ହ

ହ

Enter the train interval(H)

10

1

଺

*

଼

Hazards

ଶ

Table 5. Focal element classification in each criterion and the FE preference. Criterion

Focal element

FE preference

ሼሽ,ሼሽǡ ሼሽǡ ሼሽǡ ሼሽǡ ሼ ሽǡ ሼ ሽǡ ሼሽǡ ሼȣሽ

Accidents number

ሼሽ,ሼሽǡ ሼሽǡ ሼሽǡ ሼȣሽ

Casualty

ሼሽǡ ሼሽǡ ሼሽǡ ሼሽǡ ሼ ሽǡ ሼ ሽǡ ሼȣሽǡ

Indirect economic loss

ሼሽ,ሼሽǡ ሼሽǡ ሼሽǡ ሼሽǡ ሼ ሽǡ ሼ ሽǡ ሼሽǡ ሼȣሽ

Uncontrollability 0.5

‫ ۍ‬0 ‫ ێ‬0 ‫ ێ‬0 ‫ ێ‬0 ‫ێ‬ 0 ‫ێ‬ 0 ‫ێ‬ ‫ ێ‬0 ‫ܭ‬ଵ ൌ ‫ ۏ‬0.15

0.55;0.80;0.60;0.55;0.60;0.50

ሼሽǡ ሼሽǡ ሼሽǡ ሼሽǡ ሼ ሽǡ ሼ ሽǡ ሼሽǡ ሼȣሽ

Direct economic loss

0.85;0.75;0.65;0.7;0.55;0.70;0.65;0.95;0.50

0

0

0

0

0

0

0

0.5 0

0 0.5

0 0

0 0

0 0

0 0

0 0

0

0

0.5

0

0

0

0

0

0

0

0.5

0

0

0

0.55

0

0

0

0

0.5

0

0

0.70

0

0

0

0

0

0.5

0

0

0

0

0

0

0

0.5

0.25 0.35 0.30 0.45 0.330 0.35 0.05

0.65 ;0.55;0.60;0.55;0.65;0.60;0.75;0.50 0.80;0.70;0.70; 0.55;0.70;0.65;0.50 0.8;0.70;0.65;0.70;0.60;0.60;0.75;0.90;0.50

0.85

0.75 ‫ې‬ 0.65 ‫ۑ‬

0.70 ‫ۑ‬

‫ۑ‬ ‫ۑ‬ ‫ۑ‬ 0.65 ‫ۑ‬ 0.95 ‫ۑ‬ 0.5 ‫( ے‬8)

4.5. Basic probability assignment (BPA) of focal element According to the construction of improved complementary judgment matrix, the Basic probability assignment (BPA) of focal element is defined as the standard normalized preference. When the focal elements under ሺଵሻ ሺଶሻ ሺ୬ሻ criterion୨ is˖൫୨ ǡ ୨ ǡ ‫ ڮ‬ǡ ୨ ǡ ȣ൯, the function from the complementary judgment matrix୨ to BPA is˖

ሺ௡ሻ ݉௝

‫ۓ‬ ۖ ۖ ۖ ൌ

‫۔‬ ۖ ۖ ۖ ‫ە‬

ఏೕ೙

n j 1

¦ >T

n j

/(1 T jn )

@

ǡ ݊ ൌ ͳǡʹǡ ‫݊ ڮ‬௝

ቀଵିఏೕ೙ ቁ n 1

ሺͻሻ

ଵ n j 1

¦ >T

n j

/(1 T jn )

@

ǡ݊ ൌ ݊௝ାଵ

n 1

Transform the preference judgment matrix into BPA (Please see Table 6):

473


Table 6. BPA of each focal element. ଵ

ଵ

ଶ

ଶ

ଷ

ଷ

ସ

ସ

ହ

ହ

ሼሽ

0.1483

ሼሽ

0.1171

ሼሽ

0.1411

ሼሽ

0.2653

ሼሽ

0.1508

ሼሽ

0.0785

ሼሽ

0.3831

ሼሽ

0.0929

ሼሽ

0.1547

ሼሽ

0.0880

ሼሽ

0.0486

ሼሽ

0.1437

ሼሽ

0.1140

ሼሽ

0.1547

ሼሽ

0.070

ሼሽ

0.0611

ሼሽ

0.3831

ሼሽ

0.0929

ሼሽ

0.0810

ሼሽ

0.0880

ሼሽ

0.0320

ሼȣሽ

0.0958

ሼ ሽ

0.1411

ሼ ሽ

0.1547

ሼሽ

0.0566

{G}

ሼ ሽ

0.0611

ˉ

ˉ

ሼ ሽ

0.1140

0.1232

ሼ ሽ

0.0566

ሼ ሽ

0.0486

ˉ

ˉ

ሼሽ

0.2280

ሼȣሽ

0.0663

ሼ ሽ

0.1131

ሼሽ

0.4974

ˉ

ˉ

ሼȣሽ

0.0760

ˉ

ˉ

ሼሽ

0.3394

ሼȣሽ

0.0261

ˉ

ˉ

ˉ

ˉ

ˉ

ˉ

ሼȣሽ

0.0377

4.6. BPA combination According to the equation (6), the BPA of each alternative indifferent criterion is transformed. The BPA by combination is as follows: 0.1512

‫ ۍ‬0.0814 ‫ ێ‬0.0515 ‫ێ‬ ‫ ێ‬0.0640 ‫ ێ‬0.0349 ‫ ێ‬0.0640 ‫ێ‬ ‫ ێ‬0.0515 ݉ܲሺሼ‫ܣ‬௞ ሽሻ ൌ ‫ ۏ‬0.5003

0.1363 0.4023 0.0192 0.1629 0.0192 0.0192 0.0192 0.4023

0.1506 0.1024 0.1235 0.0095 0.1024 0.1506 0.1235 0.2375

0.2748 0.1642 0.1642 0.0095 0.0905 0.1642 0.1327 0.0095

0.1550 0.0922 ‫ې‬ ‫ۑ‬ 0.0704 ‫ۑ‬ 0.0922 ‫ۑ‬ 0.0608 ‫ۑ‬ 0.0608 ‫ۑ‬ ‫ۑ‬ 0.1173 ‫ۑ‬ 0.3436 ‫ے‬ሺͳͲሻ

Finally we compute the BPA matrix and criteria weight matrix according to the equation: ‫ ܯ‬ൌ ݉ܲሺሼ‫ܣ‬௞ ሽሻ ൈ ߱ሺͳͳሻ BPA and the order of each alternatives in all criteria is shown in Table 7: Table 7. The BPA and order of each alternatives in all criteria. ሼሽ

ሼሽ

ሼሽ

ሼሽ

ሼሽ

ሼ ሽ

ሼ ሽ

ሼሽ

M

0.1583

0.1620

0.0639

0.0798

0.0470

0.0708

0.0686

0.3882

Order

3

2

7

4

8

5

6

1

Hazards

From table.8, the risk degree of hazards are obtained˖entering the train interval˚Passengers crowd˚Jump off the platform˚Passengers fighting˚excessive drinking˚own sake˚own disease. From the equation (1),we know the sum of all alternatives BPA is 1,and the BPA reflects the importance of each hazard .So we can use the BPA of each alternative as the criteria weight in system risk evaluation in next section. 5. System risk evaluation 5.1. Evaluation criteria Potential risk, existing frequency and triggering probability are used as risk evaluation criteria. The specific meaning of the criteria is given as follows:

474


L–The possibility of accident or hazards events(potential risk); E–Frequency of exposure to hazards environments(existing frequency); C–The possible outcomes of accident or hazardous events (triggering probability) 5.2. Evaluation steps The basic extension theory idea is: combining the matter element theory and extension theory. Use the formal tools to solve the complex problem from the perspective of qualitative and quantitative. Specific steps are as follows: (1) System risk status rating collection According to the railways hazard management rules in China and the experience of experts, rate the system risk status into four levels from risk to safe. (2) Definition of evaluation matter element Matter-element, an essential concept of the extension theory, joins a matter’s quantity with its quality reasonably. Defining the name of a matter by N, one of the characteristics of the matter by C, and the value of c of N by V, a matter-element in extension theory can be described as follows:

ൌሺǡǡሻሺͳʹሻ Where N is defined as the urban rail transit risk evaluation object, C is defined as the criteria of hazard risk status grade, V is defined as the criteria value of hazard ୧ in criterion୩ . (3) Find the submitter matter elements ୭୨ and extensional matter element ୮ a. Get the submitter matter elements ୭୨ ൌ ൫୭୨ ǡ ǡ ୭୨ ൯ based on evaluation rating୭୨ .

ܴ௢௝

ܰ ǡ ‫ܥ‬ଵ ǡ ‫ܽۃ‬௢௝ଵ ǡ ܾ௢௝ଵ ‫ۄ‬ ܰ௢௝ ǡ ‫ܥ‬ଵ ǡ ܸ௢௝ଵ ‫ ۍ‬௢௝ ‫ې‬ െ ‫ܥ‬ଶ ǡ ܸ௢௝ଶ െ ‫ܥ‬ଶ ǡ ‫ܽۃ‬௢௝ଶ ǡ ܾ௢௝ଶ ‫ۑۄ‬ ൌ൦ ൪ൌ‫ێ‬ ሺͳ͵ሻ െ ‫ڭ‬ ‫ڭ‬ ‫ڭ‬ ‫ڭ‬ ‫ ێ‬െ ‫ۑ‬ െ ‫ܥ‬௡ ǡ ܸ௢௝௡ ‫ ۏ‬െ ‫ܥ‬௡ ǡ ‫ܽۃ‬௢௝௡ ǡ ܾ௢௝௡ ‫ے ۄ‬

Where ୭୨ is defined as the jሺሺ ൌ ͳǡʹǡ ‫ ڮ‬ǡͷሻrate urban rail transit risk status evaluation;୭୨ defined as the criteria in j grade; ୭୨ is the criteria value span in criterion k when the risk grade is j. Based on suggestion of the experts, the matter element in each grade is shown in following: ܰ௢ଵ ܴ௢ଵ ൌ ቎ െ െ

‫݇ݏ݅ݎ݈ܽ݅ݐ݊݁ݐ݋݌‬ ݁‫ݕܿ݊݁ݑݍ݁ݎ݂݃݊݅ݐݏ݅ݔ‬ ‫ݕݐ݈ܾܾ݅݅ܽ݋ݎ݌݃݊݅ݎ݁݃݃݅ݎݐ‬

‫ۃ‬Ͷǡͷ‫ۄ‬ ܰ௢ଶ ‫ۃ‬Ͷǡͷ‫ۄ‬቏ሺͳͶሻܴைଶ ൌ ቎ െ ‫ۃ‬Ͷǡͷ‫ۄ‬ െ


‫͵ۃ‬ǡͶ‫ۄ‬ ‫͵ۃ‬ǡͶ‫ۄ‬቏ሺ15) ‫͵ۃ‬ǡͶ‫ۄ‬

ܰ௢ଷ ܴைଷ ൌ ቎ െ െ


‫ʹۃ‬ǡ͵‫ۄ‬ ܰ௢ସ ‫ʹۃ‬ǡ͵‫ۄ‬቏ሺͳ͸ሻܴைସ ൌ ቎ െ ‫ʹۃ‬ǡ͵‫ۄ‬ െ


‫ͳۃ‬ǡʹ‫ۄ‬ ‫ͳۃ‬ǡʹ‫ۄ‬቏ሺͳ͹ሻ ‫ͳۃ‬ǡʹ‫ۄ‬

b. Extensional matter element (the criteria value span) The criteria value span in each grade of each criterion is a range from lowest to highest value. ܰ ǡ ‫ܥ‬ଵ ǡ ‫ܽۃ‬௣ଵ ǡ ܾ௣ଵ ‫ۄ‬ ܰ௣ ǡ ‫ܥ‬ଵ ǡ ܸ௣ଵ ‫ ۍ‬௣ ‫ې‬ െ ‫ܥ‬ଶ ǡ ܸ௣ଶ െ ‫ܥ‬ଶ ǡ ‫ܽۃ‬௣ଶ ǡ ܾ௣ଶ ‫ۑۄ‬ ܴ௣ ൌ ൦ ൪ൌ‫ێ‬ ሺͳͺሻ െ ‫ڭ‬ ‫ڭ‬ ‫ڭ‬ ‫ڭ‬ ‫ێ‬െ ‫ۑ‬ െ ‫ܥ‬௡ ǡ ܸ௣௡ ‫ ۏ‬െ ‫ܥ‬௡ ǡ ‫ܽۃ‬௣௡ ǡ ܾ௣௡ ‫ے ۄ‬

475


Where ୮ is all risk grades in evaluation,୮୩ is span of୩ . ܰ௣ ܴ௣ ൌ ቎ െ െ


‫ͳۃ‬ǡʹ‫ۄ‬ ‫ͳۃ‬ǡʹ‫ۄ‬቏ሺͳͻሻ ‫ͳۃ‬ǡʹ‫ۄ‬

(4) Object evaluation information matter element For the object of evaluation, the evaluation information of object (hazard) m such as measured data or analysis result is expressed by matter element: ܰ௠ ǡ ‫ܥ‬ଵ ǡ ܸ௠ଵ െ ‫ܥ‬ଶ ǡ ܸ௠ଶ ൪ሺʹͲሻ ܴ௠ ൌ ൦ െ ‫ڭ‬ ‫ڭ‬ െ ‫ܥ‬௡ ǡ ܸ௠௡ The criteria value of each hazard given by experts in the form of scoring is shown in Table 8: Table 8.The criteria value of each hazard Hazard

Potential risk

Existing frequency

Triggering probability

Jump off the platform(A)

3

2

2

Passengers crowd(B)

1

3

3

Grill the door(C)

1

2

1

Passengers fighting(D)

3

1

1

Own disease(E)

2

1

2

Excessive drinking(F)

3

2

3

Own sake(G)

2

1

1

Enter the train interval(H)

3

1

3

ܰ ܴ஺ ൌ ൥െ െ


͵ ܰ ʹ൩ ܴ஻ ൌ ൥െ ʹ െ


ͳ ͵൩ ͵

ܰ ܴ஼ ൌ ൥െ െ


ͳ ܰ ʹ൩ ܴ஽ ൌ ൥െ ͳ െ


͵ ͳ൩ ͳ

ܰ ܴா ൌ ൥െ െ


ʹ ܰ ͳ൩ ܴி ൌ ൥െ ʹ െ


͵ ʹ൩ ͵

ܰ ܴீ ൌ ൥െ െ


ʹ ܰ ͳ൩ ܴு ൌ ൥െ ͳ െ


͵ ͳ൩ ͵

(5) The correlation between evaluation and each grade

476


The correlation function in extension theory is employed to calculate the nearness between the evaluation matter element and submitter matter element. The function that the correlation between the evaluation object i in criterion k and grade j is ˖ ିఘ൫௏೔ೖ ǡ௏೚ೕೖ ൯ ห௏೚ೕೖ ห

‫ܭ‬௜௝ ൌ ൞

ǡ ܸ௜௞ ‫ܸ א‬௢௝௞

ఘ൫௏೔ೖ ǡ௏೚ೕೖ ൯ ఘ൫௏೔ೖ ǡ௏೛ೖ ൯ିఘ൫௏೔ೖ ǡ௏೚ೕೖ ൯

ǡ ܸ௜௞ ‫ܸ ב‬௢௝௞

ሺʹͳሻ

ଵ

ଵ

ଶ

ଶ

ߩ൫ܸ௜௞ ǡ ܸ௢௝௞ ൯ ൌ ቚܸ௜௞ െ ൫ܽ௢௝௞ ൅ ܾ௢௝௞ ൯ െ ൫ܾ௢௝௞ െ ܽ௢௝௞ ൯ቚሺʹʹሻ ଵ

ଵ

ଶ

ଶ

ߩ൫ܸ௜௞ ǡ ܸ௣௞ ൯ ൌ ቚܸ௜௞ െ ൫ܽ௣௞ ൅ ܾ௣௞ ൯ െ ൫ܾ௣௞ െ ܽ௣௞ ൯ቚሺʹ͵ሻ Calculate the correlation between evaluation and each grade in the above function. (6) The correlation degree between matter element and each risk grade The correlation degree of evaluation object (hazard) of urban rail transit operation system risk degree in grade t is: ‫ܭ‬௜௧ ൌ σ ߱௝ ‫ܭ‬௜௝ ൫ܸ௜௝ ൯ሺʹͶሻ ‫ܭ‬௜௧଴ ൌ σ ߱௞ ‫ܭ‬௜௧ ሺʹͷሻ For convenience, the criteria weight is given directly. ɘ ൌ ሺͲǤ͵͵ǡͲǤ͵͵ǡͲǤ͵͵ሻ 5

‫ۍ‬3 ‫ێ‬2 ‫ێ‬3 ‫ێ‬0 ‫ێ‬ ‫ێ‬1 ୧୲ ൌ ‫ ۏ‬3

1 2 3 1 3 1 3

5 3 5 3 2 3 0

7 3 4 3 2 3 1 3

5 3 4 3 1 3 0

4 3 1 3 0 2 3

2 5 3 2 3 0

5 3‫ې‬ 2‫ۑ‬ 3‫ۑ‬ 1‫ۑ‬ 3‫ۑ‬ 2‫ۑ‬ 3 ‫ے‬ሺʹ͸ሻ

5

୧୲଴

‫ۍ‬3 ‫ێ‬2 ‫ێ‬3 ‫ێ‬0 ‫ێ‬ ‫ێ‬1 ൌ ሺ 0.1523,0.149,0.0525,0.08,0.0421,0.0653,0.061,0.4273 ሻ ‫ ۏ‬3

1 2 3 1 3 1 3

5 3 5 3 2 3 0

7 3 4 3 2 3 1 3

ൌ ሺͳǤ͸͹ͷǡͲǤͺͺ͸ǡͲǤ͵ͶͳǡͲǤͶ͵ͻሻ

5 3 4 3 1 3 0

4 3 1 3 0 2 3

2 5 3 2 3 0

5 3‫ې‬ 2‫ۑ‬ 3‫ۑ‬ 1‫ۑ‬ 3‫ۑ‬ 2‫ۑ‬ 3 ‫ے‬

(27)

According to ୧୲଴ , we can know that the risk degree grade of given system is divided into three level. The given system is nearly safe. 6. Conclusion The paper proposed a study on identifying and classifying the hazard into different group according to different objectives on the basis of characteristics of hazards. Five criteria are chosen to evaluate the hazard risk degree. The DS/AHP is used to solve the incomplete and uncertainty information evaluation. Then we improve the DS/AHP


477

from three aspects to increase the accuracy and reduce the calculation. The risk degree and importance order of hazards are obtained. At last, a numerical example is provided to support the method. The extension theory is used for evaluating the system risk status. This method for hazard risk rate and system risk evaluation can not only be applied in solving the urban rail transit risk evaluation problem, but also be utilized in other areas with incomplete information. The hazards selected in this paper are based on the previous accident data in China. Other some unknown hazards in other countries still need to be considered, such as terrorist attacks. Therefore, the hazards selection can be more comprehensive. References [1] Xu, T.K., 2012. Study on risk assessment theory and methods on urban rail transit network operation. Beijing. Ph.D. thesis, Beijing Jiaotong University. [2] Zhang, Z.G., Yuan, C.Q., Xu S.L., 2011.Nanjing Subway Operation Hazard Identification and evaluation. Urban Rail Transportation,24(5):34-37. [3] Liu, H., Tang,Y.X., Chen,Y.H., 2007. Study on Hazard evaluation based on Hazard Management. Chinese Safety Science Journal, 17(6):145150. [4] Du, J., 2014. Rail Hazard Identification and Control. Network security technology and Application. [5] Zadeh ,L.A. , 1965. Fuzzy sets. Information and Control, 8(3):338-353. [6] Simos. 1990. Evaluer I’impac sur I’environnement, une approche originale par I’analyse multicritère et la négociation, PPUR. Suisse, Lausanne . [7] Lu, R.S., Lo, S.L., Hu, J.Y. 1999. Analysis of reservoir water quality using fuzzy synthetic evaluation’Stochastic. Environmental Research and Risk Assessment, 13, 327–336. [8] Yang, T., Yang, X., 1998.Fuzzy comprehensive assessment, fuzzy clustering analysis and its application for urban traffic environment quality evaluation. Transportation Research D, 3 (1), 51–57. [9] Beynon, M., 2002. An investigation of the role of scale values in the DS/AHP method of multi-criteria decision making. Journal of MultiCriteria Decision Analysis, 11, 327–343. [10] Dempster, A.P., 1968. A generalisation of Bayesian inference. Journal of the Royal Statistical Society,205–247. [11] Hua, Z., Gong, B., Xu X. ,2008. A DS–AHP approach for multi-attribute decision-making problem with incomplete information.Expert Systems with Applications, 34(3), 2221–2227. [12] Liu, Z.G., Tan, F.X., 2010.Urban Rail Transportation Safety Engineering Introductory. Chinese Railway Press. [13] Xu, D.L., Yang, J.B., Wang, Y.M., 2005. The ER approach for multi attribute decision analysis under interval uncertainties. European Journal of Operational Research. [14] Peter, Wigger, 2012. MODSafe-Modular Urban Transport Safety and Security Analysis. Procedia - Social and Behavioral Sciences, 26162625.