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

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

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).

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)

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

Information about criteria scale Ordinal scale: v(1) < … < v(q) : First ordered metric scale: 1 > 2 >…> q-1 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

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

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:

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

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. http://mcodm.ru/soft/dass

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

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

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

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