IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0220957.html
   My bibliography  Save this article

Modeling of linear programming and extended TOPSIS in decision making problem under the framework of picture fuzzy sets

Author

Listed:
  • M Sarwar Sindhu
  • Tabasam Rashid
  • Agha Kashif

Abstract

Picture fuzzy sets (PFSs) are comparatively a new extension of fuzzy sets which describe the human opinions that has more answers like acceptance, rejection, neutral and desist, which cannot be correctly presented in fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). The PFSs are categorized by three objects, the degree of belonging, the degree of neutral belonging and the degree of non- belonging such that the total of these three degrees must not be more than one. So far, there is no such work presented in the literature which deals with unknown weights of criteria based on PFSs. In the present work, we have developed a linear programming (LP) model to find the exact weights from the given constraints of weights for the criteria and construct a modified distance based on similarity measure between picture fuzzy sets. Then we have utilized this similarity measure to achieve the best option in the multiple criteria decision making (MCDM) problem. Lastly, two practical examples for the selection of alternatives are presented to compare the obtained results with the existing similarity measures.

Suggested Citation

  • M Sarwar Sindhu & Tabasam Rashid & Agha Kashif, 2019. "Modeling of linear programming and extended TOPSIS in decision making problem under the framework of picture fuzzy sets," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-13, August.
  • Handle: RePEc:plo:pone00:0220957
    DOI: 10.1371/journal.pone.0220957
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0220957
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0220957&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0220957?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
    ---><---

    References listed on IDEAS

    as
    1. Kuo, Ting, 2017. "A modified TOPSIS with a different ranking index," European Journal of Operational Research, Elsevier, vol. 260(1), pages 152-160.
    2. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    3. Ishizaka, Alessio & Siraj, Sajid, 2018. "Are multi-criteria decision-making tools useful? An experimental comparative study of three methods," European Journal of Operational Research, Elsevier, vol. 264(2), pages 462-471.
    4. He, Peijun & Ng, Tsan Sheng & Su, Bin, 2015. "Energy import resilience with input–output linear programming models," Energy Economics, Elsevier, vol. 50(C), pages 215-226.
    5. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
    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. Muhammad Sarwar Sindhu & Muhammad Ahsan & Khalil Ahmad & Imran Ameen Khan, 2024. "Modeling of Decision-Making Based on Hesitant Fuzzy Sets," Bulletin of Business and Economics (BBE), Research Foundation for Humanity (RFH), vol. 13(1), pages 720-729.

    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. Fancello, Giovanna & Tsoukiàs, Alexis, 2021. "Learning urban capabilities from behaviours. A focus on visitors values for urban planning," Socio-Economic Planning Sciences, Elsevier, vol. 76(C).
    2. Bana e Costa, Carlos A. & Oliveira, Carlos S. & Vieira, Victor, 2008. "Prioritization of bridges and tunnels in earthquake risk mitigation using multicriteria decision analysis: Application to Lisbon," Omega, Elsevier, vol. 36(3), pages 442-450, June.
    3. Pishchulov, Grigory & Trautrims, Alexander & Chesney, Thomas & Gold, Stefan & Schwab, Leila, 2019. "The Voting Analytic Hierarchy Process revisited: A revised method with application to sustainable supplier selection," International Journal of Production Economics, Elsevier, vol. 211(C), pages 166-179.
    4. Denys Yemshanov & Frank H. Koch & Yakov Ben‐Haim & Marla Downing & Frank Sapio & Marty Siltanen, 2013. "A New Multicriteria Risk Mapping Approach Based on a Multiattribute Frontier Concept," Risk Analysis, John Wiley & Sons, vol. 33(9), pages 1694-1709, September.
    5. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    6. Comino, E. & Ferretti, V., 2016. "Indicators-based spatial SWOT analysis: supporting the strategic planning and management of complex territorial systems," LSE Research Online Documents on Economics 64142, London School of Economics and Political Science, LSE Library.
    7. Kaveh Madani & Laura Read & Laleh Shalikarian, 2014. "Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1839-1856, May.
    8. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    9. He, Peijun & Ng, Tsan Sheng & Su, Bin, 2019. "Energy-economic resilience with multi-region input–output linear programming models," Energy Economics, Elsevier, vol. 84(C).
    10. Haurant, P. & Oberti, P. & Muselli, M., 2011. "Multicriteria selection aiding related to photovoltaic plants on farming fields on Corsica island: A real case study using the ELECTRE outranking framework," Energy Policy, Elsevier, vol. 39(2), pages 676-688, February.
    11. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    12. Faure, Corinne & Guetlein, Marie-Charlotte & Schleich, Joachim & Tu, Gengyang & Whitmarsh, Lorraine & Whittle, Colin, 2022. "Household acceptability of energy efficiency policies in the European Union: Policy characteristics trade-offs and the role of trust in government and environmental identity," Ecological Economics, Elsevier, vol. 192(C).
    13. José M. Merigó & Anna M. Gil-Lafuente & Daniel Palacios-Marqués, 2014. "A new method for fuzzy decision making under risk and uncertainty," International Journal of Business Continuity and Risk Management, Inderscience Enterprises Ltd, vol. 5(1), pages 29-42.
    14. Franceschini, Fiorenzo & Maisano, Domenico, 2015. "Checking the consistency of the solution in ordinal semi-democratic decision-making problems," Omega, Elsevier, vol. 57(PB), pages 188-195.
    15. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    16. Kong, Zhaoyang & Lu, Xi & Jiang, Qingzhe & Dong, Xiucheng & Liu, Guixian & Elbot, Noah & Zhang, Zhonghua & Chen, Shi, 2019. "Assessment of import risks for natural gas and its implication for optimal importing strategies: A case study of China," Energy Policy, Elsevier, vol. 127(C), pages 11-18.
    17. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    18. Pablo Aragonés‐Beltrán & Mª. Carmen González‐Cruz & Astrid León‐Camargo & Rosario Viñoles‐Cebolla, 2023. "Assessment of regional development needs according to criteria based on the Sustainable Development Goals in the Meta Region (Colombia)," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(2), pages 1101-1121, April.
    19. Boris Yatsalo & Sergey Gritsyuk & Terry Sullivan & Benjamin Trump & Igor Linkov, 2016. "Multi-criteria risk management with the use of DecernsMCDA: methods and case studies," Environment Systems and Decisions, Springer, vol. 36(3), pages 266-276, September.
    20. Juliana Martins Ruzante & Valerie J. Davidson & Julie Caswell & Aamir Fazil & John A. L. Cranfield & Spencer J. Henson & Sven M. Anders & Claudia Schmidt & Jeffrey M. Farber, 2010. "A Multifactorial Risk Prioritization Framework for Foodborne Pathogens," Risk Analysis, John Wiley & Sons, vol. 30(5), pages 724-742, May.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0220957. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.