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Porównanie metod agregacji kryteriów lokalnych podczas optymalizacji oraz podejmowania decyzji

Dymava L., Sevastsyanau P.

Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie

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2014

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Nr 1(7)

1--11

PL

Celem pracy jest przedstawienie i porównanie zasadności użycia opracowanych metod agregacji kryteriów lokalnych w kryteria globalne, na podstawie których podejmowane są decyzje, gdyż jak wiadomo, formułowanie ich nie jest sprawą prostą i prowadzi do kontrowersyjnych wyników. Porównanie przeprowadzono zarówno dla przypadku równoważnych, jak i nierównoważnych kryteriów lokalnych. Skupiono się na najczęściej stosowanych metodach agregacji. Zaproponowano także nowy sposób stworzenia pewnego kryterium „idealnego”, który może być traktowany jako kompromisowy sposób agregacji. Całość pracy dopełniają ilustracje, które w sposób jednoznaczny ukazują różnice między porównywanymi metodami agregacji kryteriów lokalnych

EN

The aim of paper is the presentation and comparison of validity of known methods for aggregation of local criteria into generalized one, which is used for the decision making, since it is known that their formulation is not a simple task and can provide controversial results. The comparison is made for the case of local criteria of the same importance as well as for the case of different ranks of local criteria. The most frequently used methods of aggregation are considered. A new method for creating of some “ideal” criterion, which can be treated as a compromising aggregation is proposed. The paper includes some illustrations, which show the difference between compared methods of aggregation of local criteria.

2

Decision Support under Risk by Optimization of Scenario Importance Weighted OWA Aggregations

Ogryczak W., Śliwiński T.

Journal of Telecommunications and Information Technology

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2009

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nr 3

5-13

EN

The problem of evaluation outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e., to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective functions related to decisions under risk. Linear programming formulations are introduced for optimization of theWOWA objective representing risk averse preferences. Their computational efficiency is demonstrated.

3

Reference Point Method with Importance Weighted Partial Achievements

Ogryczak W.

Journal of Telecommunications and Information Technology

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2008

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nr 4

17-25

EN

The reference point method (RPM) is based on the so-called augmented max-min aggregation where the worst individual achievement maximization process is additionally regularized with the average achievement. In order to avoid inconsistencies caused by the regularization, we replace it with the ordered weighted average (OWA) which combines all the individual achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further following the concept of the weighted OWA (WOWA) we incorporate the importance weighting of several achievements into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows us to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities.