IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v271y2018i2p632-643.html
   My bibliography  Save this article

Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance

Author

Listed:
  • Jiang, Yanping
  • Liang, Xia
  • Liang, Haiming
  • Yang, Ningman

Abstract

A novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making (SMCDM) problem with interval stochastic variables is proposed. By analyzing the uncertainty of interval stochastic variables, we propose the method of determining cumulative distribution function of interval stochastic variables. Then, three types of interval stochastic dominance (ISD) rules are investigated, the definition of interval stochastic dominance degree (ISDD) is presented and some interesting properties of ISD and ISDD are proved. With respect to the SMCDM problem with interval stochastic variables, to begin with, interval cumulative distribution functions of alternative criterion values are determined. Then, the ISD relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on ISD rules and the ISDD matrix on each criterion is calculated. Further, based on PROMETHEE-Ⅱ method, the net flows of each alternative are derived so as to obtain the ranking result. Consequently, examples are presented to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Jiang, Yanping & Liang, Xia & Liang, Haiming & Yang, Ningman, 2018. "Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance," European Journal of Operational Research, Elsevier, vol. 271(2), pages 632-643.
    • Handle: RePEc:eee:ejores:v:271:y:2018:i:2:p:632-643
    DOI: 10.1016/j.ejor.2018.05.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171830482X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.05.063?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.

    References listed on IDEAS

    as
    1. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    2. Lahdelma, Risto & Salminen, Pekka, 2009. "Prospect theory and stochastic multicriteria acceptability analysis (SMAA)," Omega, Elsevier, vol. 37(5), pages 961-971, October.
    3. Montes, Ignacio & Miranda, Enrique & Montes, Susana, 2014. "Stochastic dominance with imprecise information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 868-886.
    4. Lahdelma, Risto & Hokkanen, Joonas & Salminen, Pekka, 1998. "SMAA - Stochastic multiobjective acceptability analysis," European Journal of Operational Research, Elsevier, vol. 106(1), pages 137-143, April.
    5. S. Meysam Mousavi & Fariborz Jolai & Reza Tavakkoli-Moghaddam, 2013. "A Fuzzy Stochastic Multi-Attribute Group Decision-Making Approach for Selection Problems," Group Decision and Negotiation, Springer, vol. 22(2), pages 207-233, March.
    6. Zaras, Kazimierz, 2001. "Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems," European Journal of Operational Research, Elsevier, vol. 130(2), pages 305-314, April.
    7. Zaras, Kazimierz, 2004. "Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems," European Journal of Operational Research, Elsevier, vol. 159(1), pages 196-206, November.
    8. Fan, Zhi-Ping & Liu, Yang & Feng, Bo, 2010. "A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations," European Journal of Operational Research, Elsevier, vol. 207(2), pages 906-915, December.
    9. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2003. "Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)," European Journal of Operational Research, Elsevier, vol. 147(1), pages 117-127, May.
    10. J. P. Brans & Ph. Vincke, 1985. "Note---A Preference Ranking Organisation Method," Management Science, INFORMS, vol. 31(6), pages 647-656, June.
    11. Bruni, Renato & Cesarone, Francesco & Scozzari, Andrea & Tardella, Fabio, 2017. "On exact and approximate stochastic dominance strategies for portfolio selection," European Journal of Operational Research, Elsevier, vol. 259(1), pages 322-329.
    12. Risto Lahdelma & Pekka Salminen, 2001. "SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making," Operations Research, INFORMS, vol. 49(3), pages 444-454, June.
    13. Montes, Ignacio & Miranda, Enrique & Montes, Susana, 2014. "Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance," European Journal of Operational Research, Elsevier, vol. 234(1), pages 209-220.
    14. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    15. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    16. D'Avignon, G. R. & Vincke, Ph., 1988. "An outranking method under uncertainty," European Journal of Operational Research, Elsevier, vol. 36(3), pages 311-321, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sarnataro, Michele & Barbati, Maria & Greco, Salvatore, 2021. "A portfolio approach for the selection and the timing of urban planning projects," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    2. Montes, Ignacio & Rademaker, Michael & Pérez-Fernández, Raúl & De Baets, Bernard, 2020. "A correspondence between voting procedures and stochastic orderings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 977-987.
    3. Su-min Yu & Zhi-jiao Du & Xu-dong Lin & Han-yang Luo & Jian-qiang Wang, 2020. "A Stochastic Dominance-Based Approach for Hotel Selection under Probabilistic Linguistic Environment," Mathematics, MDPI, vol. 8(9), pages 1-25, September.
    4. Yan Sun & Xinya Li & Xia Liang & Cevin Zhang, 2019. "A Bi-Objective Fuzzy Credibilistic Chance-Constrained Programming Approach for the Hazardous Materials Road-Rail Multimodal Routing Problem under Uncertainty and Sustainability," Sustainability, MDPI, vol. 11(9), pages 1-27, May.
    5. Barbati, Maria & Corrente, Salvatore & Greco, Salvatore, 2020. "A general space-time model for combinatorial optimization problems (and not only)," Omega, Elsevier, vol. 96(C).
    6. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fan, Zhi-Ping & Liu, Yang & Feng, Bo, 2010. "A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations," European Journal of Operational Research, Elsevier, vol. 207(2), pages 906-915, December.
    2. Yan-Ping Jiang & Hai-Ming Liang & Minghe Sun, 2014. "A method based on the ideal and nadir solutions for stochastic MADM problems," Working Papers 0178mss, College of Business, University of Texas at San Antonio.
    3. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    4. Su-min Yu & Zhi-jiao Du & Xu-dong Lin & Han-yang Luo & Jian-qiang Wang, 2020. "A Stochastic Dominance-Based Approach for Hotel Selection under Probabilistic Linguistic Environment," Mathematics, MDPI, vol. 8(9), pages 1-25, September.
    5. Durbach, Ian N., 2014. "Outranking under uncertainty using scenarios," European Journal of Operational Research, Elsevier, vol. 232(1), pages 98-108.
    6. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    7. Lahdelma, Risto & Makkonen, Simo & Salminen, Pekka, 2009. "Two ways to handle dependent uncertainties in multi-criteria decision problems," Omega, Elsevier, vol. 37(1), pages 79-92, February.
    8. Wang, Guangchao & Jia, Ning & Ma, Shoufeng & Qi, Hang, 2014. "A rank-dependent bi-criterion equilibrium model for stochastic transportation environment," European Journal of Operational Research, Elsevier, vol. 235(3), pages 511-529.
    9. Maciej Nowak & Tadeusz Trzaskalik, 2013. "Interactive procedure for a multiobjective stochastic discrete dynamic problem," Journal of Global Optimization, Springer, vol. 57(2), pages 315-330, October.
    10. Nowak, Maciej, 2006. "INSDECM--an interactive procedure for stochastic multicriteria decision problems," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1413-1430, December.
    11. Lahdelma, Risto & Makkonen, Simo & Salminen, Pekka, 2006. "Multivariate Gaussian criteria in SMAA," European Journal of Operational Research, Elsevier, vol. 170(3), pages 957-970, May.
    12. Menou, Abdellah & Benallou, Abdelhanine & Lahdelma, Risto & Salminen, Pekka, 2010. "Decision support for centralizing cargo at a Moroccan airport hub using stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 204(3), pages 621-629, August.
    13. Song, Lianlian & Fu, Yelin & Zhou, Peng & Lai, Kin Keung, 2017. "Measuring national energy performance via Energy Trilemma Index: A Stochastic Multicriteria Acceptability Analysis," Energy Economics, Elsevier, vol. 66(C), pages 313-319.
    14. Angilella, Silvia & Corrente, Salvatore & Greco, Salvatore, 2015. "Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem," European Journal of Operational Research, Elsevier, vol. 240(1), pages 172-182.
    15. R. Pelissari & M. C. Oliveira & S. Ben Amor & A. Kandakoglu & A. L. Helleno, 2020. "SMAA methods and their applications: a literature review and future research directions," Annals of Operations Research, Springer, vol. 293(2), pages 433-493, October.
    16. Song, Shiling & Yang, Feng & Yu, Pingxiang & Xie, Jianhui, 2021. "Stochastic multi-attribute acceptability analysis with numerous alternatives," European Journal of Operational Research, Elsevier, vol. 295(2), pages 621-633.
    17. Antonio Jiménez-Martín & Eduardo Gallego & Alfonso Mateos & Juan A. Fernández Pozo, 2017. "Restoring a Radionuclide Contaminated Aquatic Ecosystem: A Group Decision Making Problem with Incomplete Information within MAUT Accounting for Veto," Group Decision and Negotiation, Springer, vol. 26(4), pages 653-675, July.
    18. García-Cáceres, Rafael Guillermo, 2020. "Stochastic Multicriteria Acceptability Analysis – Matching (SMAA-M)," Operations Research Perspectives, Elsevier, vol. 7(C).
    19. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2018. "σ-µ efficiency analysis: A new methodology for evaluating units through composite indices," MPRA Paper 83569, University Library of Munich, Germany.
    20. García Cáceres, Rafael Guillermo & Aráoz Durand, Julián Arturo & Gómez, Fernando Palacios, 2009. "Integral analysis method - IAM," European Journal of Operational Research, Elsevier, vol. 192(3), pages 891-903, February.

    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:ejores:v:271:y:2018:i:2:p:632-643. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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/locate/eor .

    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.