Weights of Road Accident Causes using Analytic Hierarchy Process

More documents

Recommendations

Info

VOL. 2, NO. 2, March 2012 ISSN 2225-7217 ARPN Journal of Science and Technology ©2011-2012. All rights reserved. conditions and other (20.8%), attention in the road (23%) and emergencies such as tyres and brakes failure (1.4%). The tyres and brakes defect usually because of lack of maintenance and services. As mentioned above, drowsiness also leads to road accident with the percentage of 3.9% [2]. Generally the drowsy drivers could contribute themselves to the statistic of the road accident injured and that is why the drowsy can be one of the hazard factors contributing to the road accident. In order to overcome the road accidents problem, there are lots of researches on investigating the causal of road accident, but generally lack of study about the decision on the most important causes contributing to the road accidents. Fuzzy approach can be one of method to recognize the causes associated with road accident since road accident problems are one of the uncertainty cases to happen. Recently, Lazim Abdullah and Nurnadiah Zamri [16] used correlation analysis and Fuzzy TOPSIS to rank the factors of road accidents. Correlation analysis uses statistical data to measures the variables and Fuzzy TOPSIS uses the linguistic data collected from the expert and as part of multi-criteria decision making (MCDM). Hence, the decision making using Fuzzy approach can be use to decide the main factors of the road accidents problem. One of the most well-known methods in determining the weight for priority factors of the problem is Analytic Hierarchy Process (AHP). The AHP is practically used in many fields such as health issues, management and business, banking, sciences and engineering courses. For example, Lazim and Fateen [17] discuss the weight determination of factors related to obesity by using AHP procedures. By AHP procedures, the weight of each the factors associated with obesity is defined by comparison of pair-wise measurement for each of the factors. Recently, Liberatore [18] applied the application of AHP in medical and health care decision making. In business and economics, the AHP method can be used to define the optimum ranking of stocks for the portfolio [19]. Esra et al., [20] has been use AHP procedures to improve employee performance in organization. In addition, Hambali et al., [21] also uses AHP to select the best design concept and emphasizes the importance of making accurate decision in manufacturing and designing industrial. Newly, Sambasivan et al., [22] used the AHP to find the relative weights factors and benefits in the electrical and electronic sectors in Malaysia. Since AHP had been used widely in the many areas, thus the main purposes of this paper is to determine the weight and rank of the factors related to road accident problems. The finding from this research would help the public to understand the causal of the road accident. 2. ANALYTIC HIERARCHY PROCESS The analytic hierarchy process (AHP) is a mathematical device in multi-criteria decision making which designing the decision factors in a hierarchic problem structure [23]. The main target of the AHP is to decide and help decision makers in making resolution for the complex problem by structuring the criterion hierarchy of multi-criteria decision making (MCDM). The AHP is known as the most powerful tools for decision making. As the first part of http://www.ejournalofscience.org AHP procedures, the determination of focus or aim of the problem must identify. It is consider as the first level for the AHP hierarchy, next would be multiple criterion that define alternatives and the last level is the contributing alternatives (causes/factors) for the focus. The standard scale with absolute numbers would use as a measurement in order to manage the weight of each alternatives. The weight can be used as comparing and ranking the alternatives of the problem and lead the decision maker in making choice. The AHP method has the following general steps: a) Construct a hierarchy structure for an MADM problem. Figure-1. Hierarchy of Alternatives Selection. b) Scaling the relative of data and constructing the pairwise comparison matrixes. For this step, construct the comparison matrixes of each attributes (criteria). Thus, the matrixes would be: C 1 C 2 � n C A ij C 1 1 1 / w2 w � w 1 / wn 1 w C 2 w 2 / w1 1 � w 2 / wn 2 w � � � � � = � C n wn / w1 / w2 wn � 1 w n The scale should be measurement from 1 to 9 in a fundamental scale of measurement provided by Saaty (1980). The measurement scale is shown in Table-2.1. Table-2.1. Pair-wise Comparison Scale for AHP Preference. Preference on pair wise Preference comparison number Equally important 1 Moderately more important 3 Strongly more important 5 Very strong more important 7 Extremely more important 9 Intermediate value 2, 4, 6, 8 c) Calculating of matrix eigenvector, Aij and consistency index test (CI) of the criterion. For matrix eigenvector, A multiply the n elements in each row, take the nth ij 40
VOL. 2, NO. 2, March 2012 ISSN 2225-7217 ARPN Journal of Science and Technology ©2011-2012. All rights reserved. root, and prepare a new column for the resulting values. Then divide each number by the sum of resulting values of the new column [21]. ij Eigenvector, A = ⎡ n ⎢ ⎢⎣ i= ⎡ ∑ 1 ∑ ⎢∑ ⎢⎣ ( w / w × w / w × ... × w / w ) n i= 1 1 1/ n n ( w / w × w / w × ... × w / w ) 1 1 1 1 1 2 2 1 1 1 n http://www.ejournalofscience.org ⎤ ⎥ ⎥⎦ ⎤ / n ⎥ ⎥⎦ (1) Eigenvalue, λ i = Consistency test, CI = ⎛ n n ⎜ A ⎟ ∑⎜∑ ij ⎟ j i=1 ⎝ A ij ⎞ w ⎠ λmax − n n −1 Table-2.2. Random indices of sizes of matrices (Saaty, 1980). n 1-2 3 4 5 6 7 8 9 RI 0.0 .58 .90 1.12 1.24 1.32 1.41 1.45 Consistency ratio (CR) is acceptable if it is does not exceed 0.10 [21]. If the CR of CI is greater than 0.10, the judgment matrix should be considered as inconsistent. Thus, the comparison should be repeated. d) Constructing the pair-wise comparisons of alternatives with respect to factors (criteria) in a matrix. Find the eigenvector, A ij and CR. e) Computing the relative weight and ranking the alternatives. w ∑ i = Ai K ij Where: w i = Overall relative rating for factors i A i = Average normalized weight for factors i K ij = Average normalized rating for alternatives j with respect to factors i. f) Ranks the alternatives These six general steps are practically used to decide the most preferred factors contributing to road accidents. 3. CASE STUDY The AHP questionnaire was designed to compare the causes associated with road accidents. The questionnaire was used as a guideline in personal interview with the road accidents experts. Three road accident experts were sought to provide linguistic judgement data based on the AHP questionnaire. Three of the experts were traffic police inspector, road transport department officer and fire brigade department officer. The experts need to judge the relative measurement between the criterion and the alternatives using pair-wise comparison proposed by Saaty [24]. The scale and the relative importance are presented in Table-2.1. To find the contributing causes related to road accident, the criteria and alternatives are defined. The alternatives of road accident are ‘driving faster than limited speed’ (A1), ‘driving carelessly (i.e., failed to look, misjudged distance and decision)’ (A2), ‘adverse road and traffic conditions’ (A3), ‘tyre and brake defects’ (A4), and ‘obstructions’ (i.e., CI Consistency Ratio, CR = (4) RI animals or weather) (A5). The selected criteria are Cars (C1), Motorcycles (C2), Buses (C3) and Lorries (C4). The hierarchical structure of focus, criteria and alternatives are shown in Figure-2. Figure-2. Hierarchical Structures of Road Accident Factors. The experts were asked to specify rating the alternatives with the linguistic expression (for example driving faster than limited speed vs. driving carelessly) and to indicate whether they felt that one factor was ‘strongly more important’ or ‘extremely more important’ to another factor on a nine-point degree of association scale. The judgement must strongly aim to all of the focus; criterion and alternatives for getting consistently result. 4. COMPUTATIONAL PROCEDURES AND RESULTS The relationships among the alternatives and criteria related to road accident are computed using AHP procedures. The computations are executed using the proposed six steps of AHP. Step 1 : Construct hierarchy structure for the problems. The hierarchical structure of road accidents problem is given in Figure-2.1 Step 2 : Construct the matrix of criteria and scale the matrix based on relative scale measurement. The scale of relative measurement of the criteria in pairwise comparison is presented in Table-4.1 j 41 (2) (3)
Page 1: VOL. 2, NO. 2, March 2012 ISSN 2225
Page 5 and 6: VOL. 2, NO. 2, March 2012 ISSN 2225

Weights of Road Accident Causes using Analytic Hierarchy Process

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?