IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v127y2024ics0305048324000604.html
   My bibliography  Save this article

On the sigma-mu stochastic multicriteria analysis: Exact solutions for common particular cases

Author

Listed:
  • Dias, Luis C.

Abstract

The sigma-mu approach is one of the recent innovations in the field of multicriteria decision aiding and composite indicators, extending the stochastic multicriteria acceptability analysis (SMAA) toolbox. The initial stage of this method involves computing the mean (mu) and standard deviation (sigma) for the composite value of the units under evaluation, considering a stochastic distribution on a set of admissible weights. This work develops closed-form formulas to obtain exact values for mu and sigma without needing approximations via Monte-Carlo simulations, which can be applied in some cases that are quite common. In terms of aggregation, these cases are characterized by an additive model, such as a weighted sum, a multiattribute value function, or PROMETHEE II. In terms of stochastic distributions, these cases include uniformly distributed unconstrained vectors of weights, rank-ordered vectors of weights, or lower-bounded weights. The developed formulas are applied to a didactic example and some open problems for future research are suggested.

Suggested Citation

  • Dias, Luis C., 2024. "On the sigma-mu stochastic multicriteria analysis: Exact solutions for common particular cases," Omega, Elsevier, vol. 127(C).
    • Handle: RePEc:eee:jomega:v:127:y:2024:i:c:s0305048324000604
    DOI: 10.1016/j.omega.2024.103093
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048324000604
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2024.103093?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:127:y:2024:i:c:s0305048324000604. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.