Introduction
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11.3 B€ in mortality;
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23.1 B€ for hospitalizations;
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4.0 B€ n for light victims;
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1.2 B€ for the material damage of these bodily injuries.
Related work
Case description
Motivation
Analysis bulletin of corporal accident
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The general characteristics of the accident (date, hour, place, atmospheric conditions, type of collision);
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Places (type of track, profile, condition, amenities, signage, environment);
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The vehicles (category, loading, condition, point of impact, obstacle struck, maneuvers before the accident);
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Users (place, gender, age, socio-professional category, injuries, possible alcohol, driving license characteristics, nature of the path, use of security systems).
Configuration of the BAAC
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The characteristics of the accident;
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The place where the accident occurred;
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The vehicles involved in the accident;
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The users involved in this accident.
Knowledge discovery in database process
Steps of the knowledge extraction process
Data mining programs
Definition of an association rule
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Let I = {i1, i2, …, im} a set of items and T = {t1, t2, …, tn} a set of transaction, called data base of transactions, such as ti a subset of I (ti ⊂ I).
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m is the total number of elements and n is the considered number of transactions.For the above supermarket example, each transaction ti of the database T represents the market basket relating to a single customer where we find all the products purchased. All the products offered for sale, such as the “Onions”, “Potatoes” and “Meat” values, represent the set I of the items.
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An association rule is defined as an implication of the form given by the formula (1).$$X \to Y,\quad where \, X \subseteq I, \, Y \subseteq T \, and \, X \cap Y = \emptyset$$(1)
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The itemset X is called “premise” or Left-Hand-Side “LHS”
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The second Y is called “conclusion” or Right-Hand-Side “RHS”
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Extraction of the most relevant association rules
The measure of support
The measure of confidence
The measure of lift
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A lift greater than 1 reflects a positive correlation between the premise X and the conclusion Y.
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A lift equal to 1 indicates a zero correlation.
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A lower lift of 1 indicates a negative correlation, also called anti-correlation.
Apriori algorithm for extract the association rules
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Step 1: Extraction of frequent itemset based on the anti-monotonicity property: «All subsets of a frequent itemset are frequent». In order to find the itemset (pattern) with support greater than or equal to the minimum support threshold “minsup” (support ≥ minsup). At this step we use the Algorithm 1.
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Step 2: Apriori exploit the frequent itemset found in the previous step 1 to generate association rules. At this step we use the Algorithm 3.×××
Overview of the ELECTRE II method
Motivation of the ELECTRE II method
Basic principle the ELECTRE II method
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a is at least as good as b for the majority of criteria,
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Without being too much worse for the other criteria.
Building outranking relations
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i ∈ {1,2}
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F is the family of criteria to be considered for ranking problem
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a and b are two alternatives of the set A of the all alternatives considered
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wj represents the weight of importance relative to criterion gj. In case of an equal weighting, we take wj = 1
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m is the number of criteria considered (m ≥ 2)
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gj(a) and gj(b) are the respective performances of the alternative a and b on criterion gj.
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In the formula (6), we assume the case of the maximization of all criteria gj. However, for the case of the minimization of a criterion gj, it just to replace all the evaluations gj(a) by the opposite evaluations: − gj(a), then we apply the same calculations of the case the maximization.
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The first relation S1 is called the strong outranking relation and the second S2 is called the weak outranking relation. We prove that: S1 ⊂ S2. Indeed, the thresholds of requirement of S1 are tighter than those of S2, and one has: for every pair of alternatives a and b: if aS1b then aS2b. Indeed:
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We suppose that: aS1b, for any two alternatives a and b, then that’s mean by formulas (6): C(a,b) ≥ c1 and \(\forall gj \in F/gj(b) > gj(a) : gj(b) - gj(a) \le dj1\)
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Moreover, we know by hypothesis that: c1 > c2 and d1 < d2
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That implies: C(a,b) ≥ c2 and \(\forall gj \in F/gj(b) > gj(a) : gj(b) - gj(a) \le dj2\)
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That finally justifies: S1 ⊂ S2
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Exploitation of outranking relations
The proposed approach
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Step 1: Collection of data
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Step 2: Transformation of the data for construction the set of transactions: T
Attribute name | Possible values: items | Description |
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Attributes retained from the table characteristics
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num_Acc | Alphanumeric code | Accident identification number |
Month | January, February, …, December | Month of the accident |
hour_of_the_accident | Morning, night | Day part of the accident |
Light | Full day, dawn, night with public lighting lights, night without public lighting, Night with public lighting not lit | lighting conditions in which the accident occurred |
Urbain | In-urban, Extra-urban | Location |
Intersection | Out of intersection, gyratory, intersection in T, intersection in X, intersection in Y, intersection with more than 4 branches, place, level crossing | Intersection |
atmospheric_condition | Normal, light rain, heavy rain, snow–hail, fog–smoke, strong wind–storm, dazzling time, overcast | Atmospheric conditions |
Type_of_collision | Two vehicles—frontal, two vehicles—from the rear, two vehicles—by the side, three vehicles and more—in chain, three or more vehicles—multiple collisions, other collision, without collision | The type of collision |
indicator_of_source | Metropole, antilles, guyane, reunion, mayotte | Indicator of source |
Attributes retained from the table places
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num_Acc | Alphanumeric code | Accident identification number |
category_of_the_road | Highway, national road, departmental road, communal road, off public network, parking lot open to public traffic or other road | Category of the road |
traffic_regime | One-way, bidirectional, separate pavements, with tracks assignment variable | Traffic regime |
reserved_lane | Bike path, cycle bank, reserved lan, reserved_lane | Indicates the existence of a reserved lane |
declivity_of_the_road | Dish, slope, peak of coast, down of coast | declivity of the road at the place of the accident |
drawing_in_plan | Straight part, curved on the left, curved right, in S | Drawing in plan of the road |
state_of_surface | Normal surface, wet, puddles, flooded, snow, mud, icy, oily material, other surface state | State of surface |
equipment | Underground, bridge, exchanger, railway, carrefour amenaged, pedestrian area, toll area | Equipment and infrastructure |
Accident_Situation | On the pavement, on emergency stop band, on the verge, on the sidewalk, On bike path | Accident situation |
Attributes retained from the table vehicles
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num_Acc | Alphanumeric code | Identifier of the accident |
num_veh | Alphanumeric code | Identification of the vehicle |
category_of_vehicle | Bicycle, Moped < 50 cm3, VL only, VL + caravan, VL + trailer, VU only 1.5 T, PL only ≤ 7.5 T, PL only > 7.5 T, PL > 3.5 T + trailer, Tractoronly, Tractor + semi-trailer, Specialmachinery, FarmTractor, Scooter < 50 cm3, Motorcycle ≤ 125 cm3, Scooter > 50 cm3, Motorcycle > 125 cm3, Scooter > 125 cm3, LightweightQuad ≤ 50 cm3, HeavyQuad > 50 cm3, Bus, Coach, Train, Tramway, Othervehicle | Category of vehicle |
fixed_Obstacl_struck | Vehicle parked, tree, metal crash barrier, concrete crash barrier, other crash barrier, building, vertical sign, pole, urban equipment, parapet, ilot, sidewalk border, ditch, another obstacle on the road, another obstacle on sidewalk, unobstructed causeway exit | Fixed obstacle eventually hit by vehicle |
mobile_obstacle_struck | Pedestrian, vehicle, rail vehicle, domestic animal, wild animal, other mobile | Mobile obstacle eventually hit by vehicle |
initial_shock_point | Before, front right, left front, rear, right back, left rear, right side, left side, multiple shocks | Initial shock point |
manoeuvre | No change of direction, same direction and same file, between 2 files, In reverse, reverse direction, crossing the median, in the bus corridor in the same direction, in the bus lane in the opposite direction, by inserting, turning back on the roadway, changing lane left, changing lane right, deported left, deported right, turning left, turning right, exceeding left, exceeding right, crossing the roadway Parking maneuver, avoidance maneuver, opening of door, stopped off parking | Principal maneuver before the accident |
nb_occupants_pub_trans | Integer | Number of occupants of the vehicle |
Attributes retained from the table users
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num_Acc | Alphanumeric code | Identifier of the accident |
num_veh | Alphanumeric code | Identification of the vehicle |
place_of_user | An Integer between 1 and 9 | Allows to locate the place occupied in the vehicle by the user at the time of the accident |
category_of_user | Driver, passenger, pedestrian, pedestrian in rollerblade or scooter | Category of user |
Severity_accident_user | Unharmed, Killed, Hospitalized wounded, Wounded light | Severity of the accident for each user |
user_gender | M, F | Gender of user |
age_of_user | < 20, [20, 30], [31, 45], [46, 60], > 60 | Age of user |
reason_displacement | Home-work, home-school, shopping, professional use, promenade, other reason for displacement | Reason for displacement the user at the time of the accident |
security_equipment | Belt, helmet, child device, belt used, belt unused, belt indefinite use, helmet used, helmet unused, helmet indefinite use, child device used, child device unused, child device indefinite use, reflective equipment used, reflective equipment unused, reflective equipment indefinite use, other security equipment used, other security equipment unused, other security equipment indefinite use | the existence and use of security equipment |
location_pedestrian | On pavement A + 50 m from the pedestrian crossing, on pavement A − 50 m from the pedestrian crossing, on pedestrian crossing without light signalling, on pedestrian crossing with light signalling, on the sidewalk, on the accoutrement, on refuge or BAU, on against aisle | Location of the pedestrian at time the accident |
pedestrian_action | Moving unspecified, moving in the direction striking vehicle, moving opposite direction of the striking vehicle, crossing, hidden, playing-current, with animal, other pedestrian action, on against aisle | Pedestrian action at time the accident |
accompanying_pedestrian | Alone, accompanied, in a group | This variable indicates if the injured pedestrian was alone or not |
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Characteristics: This table describes the general circumstances of the accident. There are 9 attributes that are retained with 59 432 records.
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Places: This table describes the location where the accident occurred. There are also 9 attributes that are retained with 59 432 places described.
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Vehicles: The table describes the vehicles involved in the accident. There are also 8 attributes that are used for this table and we have 101 924 vehicles recorded.
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Users: This table gives all the information on the users involved in the accidents, a user can be a driver or a pedestrian. This table contains 12 attributes with 133 422 users registered.
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Step 3: Application of Apriori algorithm for exaction of all association rules
Confidence threshold | Support threshold | Number of rules extracted | Execution time (in seconds) |
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0.5 | 0.5 | 324 | 0.54 |
0.5 | 0.6 | 66 | 0.51 |
0.5 | 0.7 | 10 | 0.45 |
0.5 | 0.8 | 0 | 0.36 |
0.5 | 0.9 | 0 | 0.32 |
0.6 | 0.5 | 321 | 0.5 |
0.6 | 0.6 | 66 | 0.57 |
0.6 | 0.7 | 10 | 0.45 |
0.6 | 0.8 | 0 | 0.37 |
0.6 | 0.9 | 0 | 0.33 |
0.7 | 0.5 | 290 | 0.56 |
0.7 | 0.6 | 63 | 0.49 |
0.7 | 0.7 | 10 | 0.43 |
0.7 | 0.8 | 0 | 0.35 |
0.7 | 0.9 | 0 | 0.36 |
0.8 | 0.5 | 185 | 0.69 |
0.8 | 0.6 | 46 | 0.51 |
0.8 | 0.7 | 9 | 0.51 |
0.8 | 0.8 | 0 | 0.37 |
0.8 | 0.9 | 0 | 0.28 |
0.9 | 0.5 | 77 | 0.5 |
0.9 | 0.6 | 20 | 0.49 |
0.9 | 0.7 | 5 | 0.44 |
0.9 | 0.8 | 0 | 0.39 |
0.9 | 0.9 | 0 | 0.31 |
1 | 0.5 | 0 | 0.53 |
1 | 0.6 | 0 | 0.5 |
1 | 0.7 | 0 | 0.49 |
1 | 0.8 | 0 | 0.36 |
1 | 0.9 | 0 | 0.31 |
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Step 4: Application of ELECTRE II for the selection of the most relevant association rules
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A consistent F family of criteria, which are in our application: F = {g1:support, g2: confidence, g3:lift}
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A set of alternatives, which are A = Set of association rules obtained by the Apriori algorithm.
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The concordance thresholds c1 > c2 > 0.5
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The discordance thresholds for each criterion gj: 0 < d1j < d2j.
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The weight wj of each criterion gj, for: 1 ≤ j ≤ 3.
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Step 5: Recommendation of the final solution
Discussion and evaluation
Software | Node environment |
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The database management system Database Oracle XE IDE RStudio MCDA- Ulaval version 0.6.1 | ProBook i5-6200U Single station PC |
Building the transactions table T
Application of the Apriori algorithm
Premise (LHS) | Conclusion (RHS) | Support | Confidence | Lift | |
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R1 | {Mobile_obstacle_struck = Vehicle} | {Pedestrian_action = Moving unspecified} | 0.62 | 1.00 | 1.09 |
R2 | {Category_of_vehicle = VLonly} | {Pedestrian_action = Moving unspecified} | 0.60 | 0.91 | 0.99 |
R3 | {Light = Fullday} | {Pedestrian_action = Moving unspecified} | 0.63 | 0.91 | 1.00 |
R4 | {Intersection = Out of intersection} | {Pedestrian_action = Moving unspecified} | 0.64 | 0.91 | 1.00 |
R5 | {User_gender = M} | {Pedestrian_action = Moving unspecified} | 0.65 | 0.93 | 1.02 |
R6 | {Category_of_user = Driver} | {Pedestrian_action = Moving unspecified} | 0.74 | 1.00 | 1.09 |
R7 | {Pedestrian_action = Moving unspecified} | {Category_of_user = Driver} | 0.74 | 0.81 | 1.09 |
R8 | {declivity_of_the_road = Dish} | {Drawing_in_plan = Straight part} | 0.62 | 0.84 | 1.11 |
R9 | {Drawing_in_plan = Straight part} | {declivity_of_the_road = Dish} | 0.62 | 0.82 | 1.11 |
R10 | {declivity_of_the_road = Dish} | {Atmospheric_condition = Normal ATM} | 0.60 | 0.81 | 1.01 |
R11 | {declivity_of_the_road = Dish} | {Accident_Situation = On the pavement} | 0.65 | 0.87 | 1.02 |
R12 | {declivity_of_the_road = Dish} | {Pedestrian_action = Moving unspecified} | 0.67 | 0.91 | 0.99 |
R13 | {State_of_surface = Normal surface} | {Drawing_in_plan = Straight part} | 0.61 | 0.80 | 1.06 |
R14 | {State_of_surface = Normal surface} | {Atmospheric_condition = Normal ATM} | 0.72 | 0.95 | 1.18 |
R15 | {Atmospheric_condition = Normal ATM} | {State_of_surface = Normal surface} | 0.72 | 0.89 | 1.18 |
R16 | {State_of_surface = Normal surface} | {Accident_Situation = On the pavement} | 0.65 | 0.87 | 1.02 |
R17 | {State_of_surface = Normal surface} | {Pedestrian_action = Moving unspecified} | 0.69 | 0.91 | 1.00 |
R18 | {Drawing_in_plan = Straight part} | {Atmospheric_condition = Normal ATM} | 0.62 | 0.82 | 1.01 |
R19 | {Drawing_in_plan = Straight part} | {Accident_Situation = On the pavement} | 0.67 | 0.88 | 1.04 |
R20 | {Drawing_in_plan = Straight part} | {Pedestrian_action = Moving unspecified} | 0.69 | 0.91 | 0.99 |
R21 | {indicator_of_origin = Metropole} | {Atmospheric_condition = Normal ATM} | 0.62 | 0.80 | 1.00 |
R22 | {indicator_of_origin = Metropole} | {Accident_Situation = On the pavement} | 0.65 | 0.84 | 0.99 |
R23 | {indicator_of_origin = Metropole} | {Pedestrian_action = Moving unspecified} | 0.71 | 0.92 | 1.00 |
R24 | {Atmospheric_condition = Normal ATM} | {Accident_Situation = On the pavement} | 0.69 | 0.85 | 1.00 |
R25 | {Accident_Situation = On the pavement} | {Atmospheric_condition = Normal ATM} | 0.69 | 0.81 | 1.00 |
R26 | {Atmospheric_condition = Normal ATM} | {Pedestrian_action = Moving unspecified} | 0.74 | 0.91 | 1.00 |
R27 | {Pedestrian_action = Moving unspecified} | {Atmospheric_condition = Normal ATM} | 0.74 | 0.81 | 1.00 |
R28 | {Accident_Situation = On the pavement} | {Pedestrian_action = Moving unspecified} | 0.78 | 0.91 | 1.00 |
R29 | {Pedestrian_action = Moving unspecified} | {Accident_Situation = On the pavement} | 0.78 | 0.85 | 1.00 |
R30 | {Atmospheric_condition = Normal ATM;Category_of_user = Driver} | {Pedestrian_action = Moving unspecified} | 0.60 | 1.00 | 1.09 |
R31 | {Category_of_user = Driver;Pedestrian_action = Moving unspecified} | {Atmospheric_condition = Normal ATM} | 0.60 | 0.81 | 1.01 |
R32 | {Atmospheric_condition = Normal ATM;Pedestrian_action = Moving unspecified} | {Category_of_user = Driver} | 0.60 | 0.82 | 1.10 |
R33 | {Accident_Situation = On the pavement;Category_of_user = Driver} | {Pedestrian_action = Moving unspecified} | 0.64 | 1.00 | 1.09 |
R34 | {Category_of_user = Driver;Pedestrian_action = Moving unspecified} | {Accident_Situation = On the pavement} | 0.64 | 0.86 | 1.01 |
R35 | {Accident_Situation = On the pavement;Pedestrian_action = Moving unspecified} | {Category_of_user = Driver} | 0.64 | 0.82 | 1.10 |
R36 | {Atmospheric_condition = Normal ATM;State_of_surface = Normal surface} | {Accident_Situation = On the pavement} | 0.62 | 0.87 | 1.02 |
R37 | {State_of_surface = Normal surface;Accident_Situation = On the pavement} | {Atmospheric_condition = Normal ATM} | 0.62 | 0.95 | 1.18 |
R38 | {Atmospheric_condition = Normal ATM;Accident_Situation = On the pavement} | {State_of_surface = Normal surface} | 0.62 | 0.90 | 1.20 |
R39 | {Atmospheric_condition = Normal ATM;State_of_surface = Normal surface} | {Pedestrian_action = Moving unspecified} | 0.65 | 0.91 | 1.00 |
R40 | {State_of_surface = Normal surface;Pedestrian_action = Moving unspecified} | {Atmospheric_condition = Normal ATM} | 0.65 | 0.95 | 1.18 |
R41 | {Atmospheric_condition = Normal ATM;Pedestrian_action = Moving unspecified} | {State_of_surface = Normal surface} | 0.65 | 0.89 | 1.18 |
R42 | {Drawing_in_plan = Straight part;Accident_Situation = On the pavement} | {Pedestrian_action = Moving unspecified} | 0.61 | 0.91 | 0.99 |
R43 | {Drawing_in_plan = Straight part;Pedestrian_action = Moving unspecified} | {Accident_Situation = On the pavement} | 0.61 | 0.88 | 1.04 |
R44 | {Atmospheric_condition = Normal ATM;Accident_Situation = On the pavement} | {Pedestrian_action = Moving unspecified} | 0.63 | 0.92 | 1.00 |
R45 | {Atmospheric_condition = Normal ATM;Pedestrian_action = Moving unspecified} | {Accident_Situation = On the pavement} | 0.63 | 0.85 | 1.00 |
R46 | {Accident_Situation = On the pavement;Pedestrian_action = Moving unspecified} | {Atmospheric_condition = Normal ATM} | 0.63 | 0.81 | 1.00 |
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In this work, it’s a first application of our proposed approach, we intend to apply it to a database on the road circulation spread over several years. In this case the data will have a very varied distribution. This will lead to measures of lift for a better distribution.
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In general, the circular and partially symmetrical rules, do not present any inconvenience in the operation of extraction of knowledge, in fact, this type of rules shows that there is a mutual correlation between the premises and the conclusions of these rules, that leads to a richer relation like the equivalence relation.
Application of the ELECTRE II method
Alternatives | Criteria | ||
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Criterion1: support | Criterion2: confidence | Criterion3: lift | |
MAX | MAX | MAX | |
w1 = 1 | w2 = 1 | w3 = 1 | |
R1 | 0.62 | 1.00 | 1.09 |
R2 | 0.60 | 0.91 | 0.99 |
R3 | 0.63 | 0.91 | 1.00 |
R4 | 0.64 | 0.91 | 1.00 |
… | … | … | … |
R46 | 0.63 | 0.81 | 1.00 |
[Alternative] | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 | R13 | R14 | R15 | R16 | R17 | R18 | R19 | R20 … |
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R1 | ~ | 0.67 | 0.33 | 0.33 | 0.33 | 0.33 | 0.33 | 0.67 | 0.67 | 0.67 | 0.33 | 0.33 | 0.67 | 0.33 | 0.33 | 0.33 | 0.33 | 0.67 | 0.33 | 0.33 |
R2 | 0.33 | ~ | 0.67 | 0.67 | 0.33 | 0.33 | 0.67 | 0.67 | 0.67 | 1.00 | 0.67 | 0.67 | 0.67 | 0.33 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
R3 | 0.67 | 0.67 | ~ | 0.33 | 0.33 | 0.33 | 0.67 | 1.00 | 1.00 | 1.00 | 0.67 | 0.33 | 1.00 | 0.33 | 0.67 | 0.67 | 0.67 | 1.00 | 0.67 | 0.33 |
R4 | 0.67 | 1.00 | 1.00 | ~ | 0.33 | 0.33 | 0.67 | 1.00 | 1.00 | 1.00 | 0.67 | 0.67 | 1.00 | 0.33 | 0.67 | 0.67 | 0.67 | 1.00 | 0.67 | 0.67 |
R5 | 0.67 | 0.67 | 0.67 | 0.67 | ~ | 0.33 | 0.67 | 1.00 | 1.00 | 0.67 | 1.00 | 0.33 | 1.00 | 0.33 | 0.67 | 1.00 | 0.33 | 0.67 | 0.67 | 0.33 |
R6 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | ~ | 0.67 | 1.00 | 1.00 | 0.67 | 0.67 | 0.67 | 0.67 | 1.00 | 1.00 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
R7 | 0.67 | 0.33 | 0.33 | 0.33 | 0.33 | 0.67 | ~ | 0.67 | 0.67 | 0.67 | 0.33 | 0.33 | 0.67 | 0.67 | 0.67 | 0.33 | 0.33 | 0.33 | 0.33 | 0.33 |
R8 | 0.67 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | ~ | 1.00 | 0.67 | 0.00 | 0.00 | 0.67 | 0.33 | 0.33 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 |
R9 | 0.67 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.67 | ~ | 0.67 | 0.00 | 0.00 | 0.67 | 0.33 | 0.33 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 |
R10 | 0.33 | 0.33 | 0.00 | 0.00 | 0.33 | 0.33 | 0.67 | 0.33 | 0.33 | ~ | 0.33 | 0.00 | 0.67 | 0.33 | 0.33 | 0.33 | 0.00 | 0.33 | 0.33 | 0.00 |
… |
Criterion 1: support | Criterion 2: confidence | Criterion 3: support | |
---|---|---|---|
Extent = 0.18 | Extent = 0.20 | Extent = 0.21 | |
d1 | 60% × 0.18 = 0.108 | 60% × 0.20 = 0.12 | 60% × 0.21 = 0.126 |
d2 | 80% × 0.18 = 0.144 | 80% × 0.20 = 0.16 | 80% × 0.21 = 0.168 |
Rank | Descendant ranking: V1 | Ascendant ranking: V2 | Median ranking: V |
---|---|---|---|
1 | R6 | R6 | R6 |
2 | R14 | R14 | R14 |
3 | [R7, R15, R23, R28, R33, R38, R40] | R28 | R28 |
4 | [R1, R5, R19, R26, R29, R37, R41] | [R15, R23, R26, R40] | [R15, R23, R40] |
5 | R30 | [R5, R17, R19, R33, R41] | [R26, R33] |
6 | [R8, R11, R16, R17, R27, R35, R43, R44] | R39 | [R5, R19, R41] |
7 | [R9, R20, R24, R34, R36, R39] | [R4, R7, R11, R16, R29, R37, R38, R44] | [R7, R38] |
8 | [R4, R12, R13, R18, R25, R32] | [R1, R3, R8, R20, R24, R27, R34] | [R17, R29, R37] |
9 | R3 | [R9, R12, R25, R35, R36, R45] | R1 |
10 | R45 | [R18, R30, R32, R42, R43, R46] | [R11, R16, R39, R44] |
11 | [R10, R22, R31, R42, R46] | [R2, R10, R13, R21, R22, R31] | [R8, R27] |
12 | R21 | [R4, R20, R24, R30, R34, R35] | |
13 | R2 | [R9, R36, R43] | |
14 | [R3, R12, R25] | ||
15 | [R18, R32] | ||
16 | [R13, R45] | ||
17 | [R42, R46] | ||
18 | [R10, R22, R31] | ||
19 | R21 | ||
20 | R2 |
Robustness analysis
Case1a | Case1b | Case1c | Case2a | Case2b | Case1c | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
c1, c0, c2 | 0.6, 0.7, 0.8 | 0.7, 0.8, 0.9 | ||||||||||
d1, d2 Median ranking | 50% | 70% | 60% | 80% | 70% | 90% | 50% | 70% | 60% | 80% | 70% | 90% |
1 | R6 | R6 | R6 | [R6, R14, R28] | [R6, R14, R28] | [R6, R14, R28] | ||||||
2 | R14 | R14 | R14 | [R23, R26, R40] | [R23, R26, R40] | [R23, R26, R40] | ||||||
3 | R28 | R28 | R40 | R15 | R15 | R15 | ||||||
4 | [R15, R23, R40] | [R15, R23, R40] | R28 | [R5, R17, R33, R38] | [R5, R17, R33, R38] | [R5, R17, R33, R38] | ||||||
5 | [R26, R33] | [R26, R33] | [R15, R23] | [R7, R19, R29, R41] | [R7, R19, R29, R41] | [R7, R19, R29, R41] | ||||||
6 | [R5, R19, R41] | [R5, R19, R41] | [R5, R26] | [R37, R39] | [R37, R39] | [R37, R39] | ||||||
7 | [R7, R38] | [R7, R38] | R33 | [R1, R11, R16, R27, R44] | [R1, R11, R16, R27, R44] | [R1, R11, R16, R27, R44] | ||||||
8 | [R17, R29, R37] | [R17, R29, R37] | [R7, R17, R19, R38, R41] | [R4, R8, R20, R24] | [R4, R8, R20, R24] | [R4, R8, R20, R24] | ||||||
9 | R1 | R1 | [R29, R37] | [R34, R35] | [R34, R35] | [R34, R35] | ||||||
10 | [R11, R16, R39, R44] | [R11, R16, R39, R44] | [R1, R11, R16, R39, R44] | [R3, R9, R12, R25, R30, R36, R43] | [R3, R9, R12, R25, R30, R36, R43] | [R3, R9, R12, R25, R30, R36, R43] | ||||||
11 | [R8, R27] | [R8, R27] | [R8, R27] | [R18, R32, R45] | [R18, R32, R45] | [R18, R32, R45] | ||||||
12 | [R4, R20, R24, R30, R34, R35] | [R4, R20, R24, R30, R34, R35] | [R4, R20, R24, R34, R35] | [R13, R22, R42] | [R13, R22, R42] | [R13, R22, R42] | ||||||
13 | [R9, R36, R43] | [R9, R36, R43] | [R9, R30, R36, R43] | [R10, R31, R46] | [R10, R31, R46] | [R10, R31, R46] | ||||||
14 | [R3, R12, R25] | [R3, R12, R25] | [R3, R12, R25] | R2 | R2 | R2 | ||||||
15 | [R18, R32] | [R18, R32] | [R18, R32] | R21 | R21 | R21 | ||||||
16 | [R13, R45] | [R13, R45] | [R13, R45] | [R6, R14, R28] | ||||||||
17 | [R42, R46] | [R42, R46] | [R42, R46] | |||||||||
18 | [R10, R22, R31] | [R10, R22, R31] | [R10, R22, R31] | |||||||||
19 | R21 | R21 | R21 | |||||||||
20 | R2 | R2 | R2 |
Discussion
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R6: {Category_of_user = Driver} → {Pedestrian action = Moving unspecified}
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R14: {State_of_surface = Normal surface} → {Atmospheric_condition = Normal ATM}
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R28: {Accident_Situation = On the pavement} → {Pedestrian_action = Moving unspecified}