For safety priority analysis of selected roads, Absolute ratings are taken with help of field experts on the scale of 1 to 5 based on contribution of indicator in road safety as shown in Table 4.
Table 3
Severity score of roads selected for study
Indicator
|
Alternatives
|
G.D. Goenka Public School – Kurnaghat crossing
|
Kurnaghat crossing - University crossing
|
Paidleganj crossing - Transport Nagar
|
Charphatak road
|
Stopping sight distance
|
3.68
|
4.80
|
2.80
|
3.50
|
Sharp curves
|
2.94
|
4.40
|
3.90
|
4.40
|
Super elevation
|
4.87
|
5.00
|
3.59
|
4.34
|
Severity of road side environment
|
3.12
|
3.44
|
3.38
|
3.90
|
Drainage
|
5.00
|
1.00
|
3.00
|
1.00
|
Potholes
|
4.30
|
4.65
|
2.58
|
1.30
|
Width of shoulder
|
1.30
|
3.00
|
3.11
|
3.00
|
Shoulder quality
|
1.00
|
3.00
|
3.00
|
1.00
|
Edge failure of pavement
|
2.00
|
2.00
|
1.00
|
1.00
|
Delineation
|
2.00
|
4.00
|
5.00
|
3.00
|
Table 4
Average absolute ratings for indicators
Indicator
|
Average of absolute ratings
|
Normalized values
|
Stopping sight distance
|
3.98
|
0.76
|
Sharp curves
|
3.69
|
0.69
|
Super elevation
|
3.00
|
0.43
|
Severity of road side environment
|
2.13
|
0.21
|
Drainage
|
3.00
|
0.49
|
Potholes
|
3.98
|
1.00
|
Shoulder quality
|
2.76
|
0.13
|
Width of shoulder
|
2.11
|
0.34
|
Edge failure of pavement
|
3.44
|
0.76
|
Delineation
|
2.62
|
1.00
|
5.1 Simple additive weighting method (SAW): Simple Additive Weighting (SAW) method is used to solve problem related to multi-attribute decision making. The fundamental concept of this method is to find the sum of the weighted performance rating for each alternative on all attributes. Average criteria weights (From Table no. 4) and individual scores of each alternative (From Table no. 3) is taken for calculations as per below equation no. 1 to find score corresponding to particular indicator.
Ai = Wi * Xi (1)
The final weighted score of specific alternatives is then calculated by using equation no. 2. The results opted from this method is presented in table no. 5.
SLi = \(\frac{{\sum }_{i=1}^{n}{A}_{i}}{{\sum }_{i=1}^{n}{W}_{i}}\) (2)
Where,
Ai = Self score of specific alternatives
Wi = Weight involved with ith service attribute
XI = Value scores for ith service attribute
S.L. = Safety level of each selected alternative
n = No. of attribute defining the overall safety
Table 5
Ranking of alternatives by SAW method
Alternative
|
Final Score
|
Rank
|
G.D. Goenka Public School – Kurnaghat crossing
|
3.43
|
2
|
Kurnaghat crossing - University crossing
|
3.96
|
1
|
Paidleganj crossing - Transport Nagar
|
2.94
|
3
|
Charphatak road
|
2.31
|
4
|
5.2 Analytical hierarchy process (AHP): The Analytical Hierarchy Process (AHP) is well known techniques for multi criteria decision making (popularly known as MCDM) developed by researcher Saaty [9] in year 1980. AHP is an organized procedure for getting sorted out and dissecting complex choices or issues which includes abstract decisions. As such, an AHP is a conventional amazing dynamic method to deciding needs among various rules, contrasting the choice options for every standard and deciding a general positioning of the choice other options. The primary points of interest of AHP are taking care of different measures, straightforward and viably managing both subjective and quantitative information
In present study, goal is to achieve safety using normalized values shown in table no. 4. Now, priorities are extrapolated for performance of each alternatives on every criterion and they are based on a pair-wise assessment. Satty’s rating scale (Table 6) is used for pairwise comparison rating of various criteria and alternatives. After above approaches, weighting and adding processes are done to get overall priorities for each alternative to see how they are contributing to the desired aim.
With the help of Expert choice software, steps involved in AHP got simplified because it automates many computational steps itself. Input required for above software are alternative scores and criteria weights and results obtained are presented in table no. 7. For matrices which involve human decision and also incoherent to a higher and lower degree, Researcher Saaty suggested a value of 0.1 for that ratio. If that ratio is greater than limiting value of 0.1, then the number of judgements might be too incoherent to be sound. In present study, the gross inconsistency found was 0.04 which is lesser than limiting value of 0.1.
From above study, Charphatak road was emerged as critical in terms of safety. Critical parameters of Charphatak road are also listed rank wise and shown in Table 8. From Table 8, it is clearly visible that potholes are most influencing parameter and road side environment is least.
Table 6
Saaty scale used in AHP [9]
Intensity of significance
|
Definitions
|
Explanations
|
1
|
Equal significance
|
Two tasks contribute equally to objective
|
3
|
Moderate significance of one over other
|
Experience and judgment strongly favor one task over other
|
5
|
Essential of strong significance
|
Experience and judgment strongly favor one task over other
|
7
|
Very strong significance
|
A task is favored very strongly over other; its dominance illustrated in practice
|
9
|
Extreme significance
|
The evidence favoring one task over other is of the highest possible order of assertion
|
2,4,6,8
|
Intermediate values between the two adjacent judgement
|
When compromise is needed
|
Table 7
Alternative
|
G.D. Goenka Public School – Kurnaghat crossing
|
Kurnaghat crossing - University crossing
|
Paidleganj crossing - Transport Nagar
|
Charphatak road
|
Final Scores
|
0.237
|
0.398
|
0.243
|
0.115
|
Rank
|
3
|
1
|
2
|
4
|
Table 8
Critical parameters found in Charphatak road
Indicators
|
Ranking
|
Potholes
|
1
|
Drainage
|
2
|
Delineation
|
3
|
Super elevation
|
4
|
Edge failure of pavement
|
5
|
Stopping sight distance
|
6
|
Width of shoulder
|
7
|
Sharp curves
|
8
|
Shoulder quality
|
9
|
Severity of road side environment
|
10
|
5.3 Fuzzy AHP method: “AHP combined with fuzzy logic commonly known as Fuzzy AHP is practically popular method to deal with uncertainty and fuzziness and aid decision maker in complex problems with multiple conflicting criteria’s [3]”. Fuzzy AHP is widely popular in multi-criteria decision-making methodology which have vast range of applications [5, 12]. Fuzzy AHP methodology is helpful for making decisions with multiple preferences having fuzziness and uncertainty [14]. As of now there are no much supportive surveys on FAHP application in multi criteria decisions problems. In this research paper, The Fuzzy AHP calculations are done by steps described by researchers Srdjevic and Yvonide [11]
5.3.1 Fuzzifying judgment scale: For making of pair-wise comparisons in the fuzzy AHP method, Saaty’s 9-point scale should be fuzzified. Now, it is assumed that “membership functions for 1 ≤ 𝑥𝑥 ≤9 should be symmetrically triangular, different for internal pair and odd integers and adjusted for edge values along the scale”, [15]. The previously described crisp values of saaty’s scale are now fuzzified and presented in Table no. 9. In present study, analysis of Fuzzy AHP approach was performed by triangular fuzzification of values taking a fuzzy distance (∂) of 1.
Table 9
Original and fuzzified Saaty’s scale for pairwise comparison
Saaty’s 9-point scale
|
Definitions
|
Fuzzified Saaty’s scale
|
1
|
Equal significance
|
(1, 1, 1 + δ*)
|
3
|
Infirm dominance
|
(3- δ, 3, 3 + δ)
|
5
|
Strong dominance
|
(5- δ, 5, 5 + δ)
|
7
|
Illustrated dominance
|
(7- δ, 7, 7 + δ)
|
9
|
Universal dominance
|
(9- δ, 9, 9)
|
2,4,6,8
|
Intermediate values
|
(x-1, x, x + 1) where x = 2, 4, 6, 8
|
5.3.2 Evaluating Criteria: A fuzzy reciprocal judgement matrix is determined by using above fuzzified scale.
B =\(\left[ \begin{array}{ccc}{b}_{11}& \dots & {b}_{1M}\\ :& {b}_{22}& :\\ {b}_{M1}& \dots & {b}_{MM}\end{array}\right]\)
Where, bij = 1 for all I = j = 1, 2, …, M, and aij = 1/aji
Respective weights of indicator can be calculated by below equation no. 3 by using fuzzy synthetic extent.
Wi = \({\sum }_{j=1}^{M}{b}_{ij}\) x [ \(\sum _{k=1}^{M}\sum _{l=1}^{M}{b}_{kl}\) ]-1, i= 1, …., M (3)
Each Wi, where i = 1, ..., M, is normalized fuzzy number having medium value equal to 1. x represents here “fuzzy multiplication operation”. This is clearly understood that fuzzy extent could be expressed as either outcome of “fuzzy arithmetic” or by using “extension principle”. The last one is somehow more onerous, but this will diminish uncertainty.
For Calculation of alternatives, after finding K fuzzy judgments, the fuzzy extent then produces a decision matrix.
Wk = \(\left[ \begin{array}{ccc}{b}_{11}& \dots & {b}_{1M}\\ :& {b}_{22}& :\\ {b}_{M1}& \dots & {b}_{MM}\end{array}\right]\), k = 1…., k
Xij = \({\sum }_{k=1}^{k}{b}_{ik}\) x [ \(\sum _{l=1}^{N}\sum _{m=1}^{k}{b}_{lm}\) ]-1, i= 1, …., N; j= 1, …, K (4)
X =\(\left[ \begin{array}{ccc}{x}_{11}& \dots & {x}_{1k}\\ :& {x}_{22}& :\\ {x}_{N1}& \dots & {x}_{nk}\end{array}\right]\)
In this decision matrix X, xij is symbolizing resultant fuzzy performance assessment of alternatives Bi (i = 1, 2..., N) with respect to jth sub criterion (j = 1, 2..., K).
After this, for gross performance of every alternative for all indicators are now shown by performance matrix. The procedure followed to obtain this is by multiplying the “weighting vector” by corresponding “column values” of above decision matrix and by pertaining fuzzy interval arithmetic. After performing last evaluations and synthetics, defuzzification was done. Since, for fuzzy AHP, defuzzification is a very important step in end to attain crisp weights and to provide ranking to alternatives. Hence in present study, an easy and efficient method of defuzzification is adopted named as “total integral value method”. For a given triangular fuzzy number B = (b1, b2, b3), total integral value is then defined as in Eq. 6.
\({I}_{T}^{ƛ}\) (B) = (1/2) [\(ƛb\)3 +b2 + (1-\(ƛ\) )b1], \(ƛ\)Ɛ[0,1] (5)
Where, \(ƛ=\)optimism index (express the decision makers’ attitude towards a risk). Higher values of \(ƛ\) shows a higher degree of optimism. Three values of \(ƛ (\)0, 0.5 and 1) are generally used in practical applications. These three values respectively show “pessimistic, moderate and optimistic” view of a decision maker. Final defuzzified values obtained using above Eq. 5 are given in table no. 10.