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Zbl 0891.90088
Athanassopoulos, A.D.; Podinovski, V.V.
Dominance and potential optimality in multiple criteria decision analysis with imprecise information. (English)
[J] J. Oper. Res. Soc. 48, No.2, 142-150 (1997). ISSN 0160-5682

Summary: This paper discusses multiple criteria models of decision analysis with finite sets of alternatives. A weighted sum of criteria is used to evaluate the performance of alternatives. Information about the weights is assumed to be in the form of arbitrary linear constraints. Conditions for checking dominance and potential optimality of decision alternatives are presented. In the case of testing potential optimality, the proposed approach leads to the consideration of a couple of mutually dual linear programming problems. The analysis of these problems gives valuable information for the decision maker. In particular, if a decision alternative is not potentially optimal, then a mixed alternative dominating it is defined by a solution to one of the LP problems. This statement generalizes similar results known for some special cases. The interpretation of the mixed alternative is discussed and compared to its analogue in a data envelopment analysis context.

MSC 2000:: *90B50 Multiple-criteria decision making
90C29 Multi-objective programming, etc.
91B06 Decision theory

Keywords: dominance; potential optimality; weights restrictions; multiple criteria; decision analysis; mutually dual linear programming problems; data envelopment analysis

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