1. HSE, ICAD RAS, MERI RAS. Moscow
Methods of criteria importance theory and their software implementation
Podinovski V.V.
Potapov M.A.
Nelyubin A.P.
HSE, ICAD RAS, MERI RAS. Moscow
The 7th International Conference on Network Analysis, June 22 – 24, 2017, Nizhny Novgorod

2. Multicriteria decision making (choice) problems
M = < X, K, Z, R >,
X – set of alternatives (decisions),
K1, … , Km – criteria (objective functions)
with common scale Z0 = {1, …, q}, where q ≥ 2,
Z = Z0m – set of vector estimates y(x) = (K1(x), … , Km (x)),
R – partial preference relation of the decision maker

3. Criteria Importance Theory
Criteria 1 and 2 are equally important (denote as 1 ~ 2) if variants (a, b) and (b, a) are indifferent for decision maker.
Criterion 1 is more important then Criterion 2 (denote as 1  2) if variant (a, b), where a >b, is more preferable than (b, a).

4. Argumentation of the solution
Criteria importance theory
P0 – Pareto relation
12 – the 1st criterion is more important than the 2nd
(5, 3) P12 (3, 5) P0 (3, 4)
Argumentation of the solution
12
(4, 2) P12 (2, 4) P0 (2, 3)

5. Information about importance of criteria
: Qualitative ordering: 1 ≥ 2 ≥ … ≥ m
Ξ: Interval information:
li ≤ i /i+1 ≤ ri, i = 1, …, m  1.
: Exact information:
i, i = 1, …, m

6. Information about criteria scale
Ordinal scale: v(1) < … < v(q)
: First ordered metric scale:
1 > 2 >…> q или 1 < 2 <…< q-1,
где k = v(k +1)  v(k), k = 1, …, q  1.
[V]: First bounded metric scale:
dk ≤ k /k+1 ≤ uk , k = 1, …, q  2
V: Interval scale:
k /k+1 = gk , k = 1, …, q  2

7. Criteria Importance Theory
Information types and decision rules
Criteria importance
Quantitative
Exact information R
R
R[V]
RV
Interval information RΞ
RΞ
RΞ [V]
RΞV
Qualitative
ordering R
R
R[V]
RV
No information
Pareto relation
Information about the DM preferences
Ordinal scale
First ordered metric scale
First bounded metric scale
Interval scale
Criteria scale

8. Decision rules under interval preference information
Interval constraints
determine the set А of possible values of criteria importance coefficients.
Under this inexact information
In case of ordinal scale, optimization decision rule:
Analytic decision rule:

9. Bilinear programming problem
Interval constraints on both parameters of preferences:
Additive value function
Coordinates of vertices of the set A:

10. Software DASS (Decision Analysis Support System)
Implements iterative approach to the analysis of decision making problems: In the beginning, it collects simple, qualitative information about the DM preferences. Than, if it is necessary, the DM specifies more complex, quantitative information in the interval form.

11. Example of the choice problem solution process
Pareto preference relation
Partial preference relation according to qualitative criteria ordering by importance 1234

12. Refinement of the information about the decision maker preferences helps to reduce the number of nondominated alternatives

13. Refinement of quantitative information about criteria importance:
«The 2nd criterion is more than 2 times important than the 3rd criterion»

14. Thank you for your attention