Classifying efficient alternatives in SMAA using cross confidence factors

Risto Lahdelma, Pekka Salminen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative; the central weight vectors represent the typical preferences favouring each alternative; and the confidence factors measure whether the criteria data are sufficiently accurate for making an informed decision. In some cases, when the problem involves a large number of efficient alternatives, the analysis may fail to discriminate between them. This situation is revealed by low confidence factors. In this paper we develop cross confidence factors, which are based on computing confidence factors for alternatives using each other's central weight vectors. The cross confidence factors can be used for classifying efficient alternatives into sets of similar and competing alternatives. These sets are related to the concept of reference sets in Data Envelopment Analysis (DEA), but generalized for stochastic models. Forming these sets is useful when trying to identify one or more most preferred alternatives, or suitable compromise alternatives. The reference sets can also be used for evaluating whether criteria need to be measured more accurately, and at which alternatives the measurements should be focused. This may cause considerable savings in measurement costs. We demonstrate the use of the cross confidence factors and reference sets using a real-life example.

Original languageEnglish
Pages (from-to)228-240
Number of pages13
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 1 Apr 2006
MoE publication typeA1 Journal article-refereed


  • Cross confidence factor
  • Helsinki harbor
  • Multicriteria decision support
  • Stochastic multicriteria acceptability analysis


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