Distribution of decision-making: • The number of criteria:
– One-criteria decision making– Multicriteria decision making
• Methods of measurement criteria:– Nominal– Ordinal– Absolute
Deterministic decision(decision-making under conditions of certainty)
Procedure for multi-criteria decision making:
• It is based on the selection of the most suitable option for two or more interchangeable variants using two or more evaluation criteria.
1. Create a model - in the form of decision matrices.
2. Determining the importance weights (intensity perception) of the individual criteria.
3. Aggregation evaluationAggregation criteria and importance weights
Illustrative Example: - multicriteria selection
options• Ad1. Creating a model
Variant Criterion
K1: power per liter
(kW/l)
acceleration time
(O→200) km/h(s)
Breaking distance
(100→O) km/h(m)
V1: BMW M3 CLS 81,6 16,8 33,3
V2: Porsche 911 GT3
77,8 15,1 37,6
Vz: average 79,7 15,95 35,45
Order Method to determine the importance of the criteria weights
Importance of the criteria using two "experts" E1, E2.
Expert K1 K2 K3 ∑
E1 1 2 3 6
E2 1 3 2 6
Hi nonstandard
weight
2 5 5 12
Vi normalized
weight
2/12 5/12 5/12 12/12=1
Scoring (classification) method Scoring scale:
5,1n
Expert K1 K2 K3 ∑
E1 2 4 5 11
E2 1 5 3 9
Hi nonstandard
weight
3 9 8 20
Vi normalized
weight
3/20 9/20 8/20 20/20=1
The method of paired comparisons:Preferential arrangements such as:E1: K3 > K2 > K1; E2: K2 > K3 > K1
K1 K2 K3 ∑ K1 K2 K3 ∑ Vi
K1 X 0 0 0 K1 X 0 0 0 0
K2 1 X 0 1 K2 1 X 1 2 (1+2) / 6 = 0,5
K3 1 1 X 2 K3 1 0 X 1 (2+1) / 6 = 0,5
Ad3. Aggregation of the evaluation criteria and the importance weights: Determine sequence variants
• The method of sequence functions (aggregation)The method of scoring (aggregation)Method basic (aggregation)
The method of sequence functions (aggregation) weights for these criteria: V1 = 0; V2 = 0,5; V3 = 0,5;
K1 K2 K3 Hi1 ∙ V1 Hi2 ∙ V2 Hi3 ∙ V2 Wt order
V1 2 1 2 0 1,5 1,5
V2 1 2 1 0 1,5 1,5
5,01 5,02
5,02 5,01
inconclusiveresult!
The method of scoring (aggregation)– for the same weight
points K1 (kW/l) K2 (s) K3 (m) Variant K1 K2 K3 Wt order
1 <70 - 75> <18 - 17> <38 -37>
V1 3 2 5 3,5 1.2 (75 - 80> (17 - 16> (37 - 36>
3 (80 - 85> (16 - 15> (36 - 35>
V2 2 3 1 2 2.4 (85 - 90> (15 - 14> (35 - 34>
5 (90 - 95> (14 - 13> (34 - 33>
Basic Method (aggregation)
Variant
↓ coefficients →
h1 = Vi / Vb(Revenues criterion
type (better larger value)
h2 = Vb / Vi(cost type criteria
(better smaller value)
h3 = Vb / Vi(cost type criteria
(better smaller value)
V1 1,0238 0,9494 1,0646
V2 0,9762 1,0563 0,9428
Wt1 = 0 + 0,5 ∙ 0,9494 + 0,5 ∙ 1,0646 = 1,007 … first in the order
Wt2 = 0 + 0,5 ∙ 1,0563 + 0,5 ∙ 0,9428 = 0,9428 … second in the
order
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