{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:06:18Z","timestamp":1778706378603,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T00:00:00Z","timestamp":1580083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>The Delphi method is one of the basic tools for forecasting values in various types of issues. It uses the knowledge of experts, which is properly aggregated (e.g., in the form of descriptive statistics measures) and returns to the previous group of experts again, thus starting the next round of forecasting. The multi-stage prediction under the Delphi method allows for better stabilization of the results, which is extremely important in the process of forecasting. Experts in the forecasting process often have access to time series forecasting software but do not necessarily use it. Therefore, it seems advisable to add to the aggregate the value obtained using forecasting software. The advantage of this approach is in saving the time and costs of obtaining a forecast. That should be understood as a smaller burden on data analysts and the value of their work. According to the above mentioned key factors, the main contribution of the article is the use of a virtual expert in the form of a computer-enhanced mathematical tool, i.e., a programming library for a forecasting time series. The chosen software tool is the Prophet library\u2014a Facebook tool that can be used in Python or R programming languages.<\/jats:p>","DOI":"10.3390\/info11020065","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T11:41:57Z","timestamp":1580125317000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Delphi Method Supported by Forecasting Software"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0235-0878","authenticated-orcid":false,"given":"Marcin","family":"Lawnik","sequence":"first","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4267-2783","authenticated-orcid":false,"given":"Arkadiusz","family":"Banasik","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1016\/j.energy.2018.10.032","article-title":"A novel hybridization of nonlinear grey model and linear ARIMA residual correction for forecasting U.S. shale oil production","volume":"165","author":"Wang","year":"2018","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huang, M., Bao, Q., Zhang, Y., and Feng, W. (2019). A Hybrid Algorithm for Forecasting Financial Time Series Data Based on DBSCAN and SVR. Information, 10.","DOI":"10.3390\/info10030103"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, G., Ma, X., and Yang, H. (2018). A Hybrid Model for Monthly Precipitation Time Series Forecasting Based on Variational Mode Decomposition with Extreme Learning Machine. Information, 9.","DOI":"10.3390\/info9070177"},{"key":"ref_4","unstructured":"Armstrong, J.S. (2001). Expert Opinions in Forecasting: The Role of the Delphi Technique. Principles of Forecasting: A Handbook for Researchers and Practitioners, Springer."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1287\/mnsc.9.3.458","article-title":"An Experimental Application of the DELPHI Method to the Use of Experts","volume":"9","author":"Dalkey","year":"1963","journal-title":"Manag. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.eswa.2009.05.068","article-title":"The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative technology selection","volume":"37","author":"Hsu","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"305","DOI":"10.28945\/3561","article-title":"Delphi panels: Research design, procedures, advantages, and challenges","volume":"11","author":"Avella","year":"2016","journal-title":"Int. J. Doctoral Stud."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1080\/19325037.2012.10599216","article-title":"Advantages and Limitations of the e-Delphi Technique","volume":"43","author":"Donohoe","year":"2012","journal-title":"Am. J. Health"},{"key":"ref_9","unstructured":"(2019, September 30). Prophet. Available online: https:\/\/facebook.github.io\/prophet\/."},{"key":"ref_10","unstructured":"Sackman, H. (2020, January 25). Delphi Assessment: Expert Opinion, Forecasting, and Group Process. Available online: https:\/\/apps.dtic.mil\/dtic\/tr\/fulltext\/u2\/786878.pdf."},{"key":"ref_11","unstructured":"Linstone, H., Turoff, L., and Turoff, M. (2020, January 25). The Delphi Method: Techniques and Applications. Available online: http:\/\/202.91.10.51:8080\/xmlui\/handle\/123456789\/162."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Boulkedid, R., Abdoul, H., Loustau, M., and Alberti, O.S.C. (2011). Using and Reporting the Delphi Method for Selecting Healthcare Quality Indicators: A Systematic Review. J. Pone.","DOI":"10.1371\/journal.pone.0020476"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.futures.2017.11.007","article-title":"Scenario development in transport studies: Methodological considerations and reflections on delphi studies","volume":"96","author":"Melander","year":"2018","journal-title":"Futures"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.techfore.2005.09.002","article-title":"Current validity of the Delphi method in social sciences","volume":"73","author":"Landeta","year":"2006","journal-title":"Technol. Forecast. Soc. Chang."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Brady, S.R. (2015). Utilizing and Adapting the Delphi Method for Use in Qualitative Research. Int. J. Qual. Methods.","DOI":"10.1177\/1609406915621381"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ijnurstu.2016.04.015","article-title":"The use of Delphi and Nominal Group Technique in nursing education: A review","volume":"60","author":"Foth","year":"2016","journal-title":"Int. J. Nurs. Stud."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Banasik, A., and Kapczy\u0144ski, A. (2009, January 21\u201323). Fuzzy logic applied in databases for investors. Proceedings of the 2009 IEEE International Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, Rende, Italy.","DOI":"10.1109\/IDAACS.2009.5342904"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Banasik, A., and Kapczy\u0144ski, A. (2011, January 15\u201317). Fuzzy evaluation of biometric authentication systems. Proceedings of the 6th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems, Prague, Czech Republic.","DOI":"10.1109\/IDAACS.2011.6072881"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/s40092-014-0066-6","article-title":"The application of fuzzy Delphi and fuzzy inference system in supplier ranking and selection","volume":"10","author":"Tahriri","year":"2014","journal-title":"J. Ind. Eng. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0165-0114(98)00067-0","article-title":"The fuzzy Delphi method via fuzzy statistics and membership function fitting and an application to the human resources","volume":"112","author":"Chang","year":"2000","journal-title":"Fuzzy Sets Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bojadziev, G., and Bojadziev, M. (2007). Fuzzy Logic for Business, Finance and Management, Wiley.","DOI":"10.1142\/6451"},{"key":"ref_23","unstructured":"Lawnik, M., and Banasik, A. (2020, January 25). Fuzzy Delphi Method for Optimal Player\u2019s Position Selection. (In Polish)."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1108\/09556221311300192","article-title":"Application of fuzzy Delphi method (FDM) and fuzzy analytic hierarchy process (FAHP) to criteria weights for fashion design scheme evaluation","volume":"25","author":"Lin","year":"2013","journal-title":"Int. J. Cloth. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"14172","DOI":"10.1016\/j.ijhydene.2011.05.045","article-title":"Fuzzy Delphi method for evaluating hydrogen production technologies","volume":"36","author":"Chang","year":"2011","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, Z., and Huang, Y. (2012, January 25\u201328). A Fuzzy and comprehensive evaluation model for developing teaching evaluation. Proceedings of the 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet), Seoul, Korea.","DOI":"10.1109\/CECNet.2012.6201685"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17485\/ijst\/2015\/v8i32\/92146","article-title":"Applying the Fuzzy Delphi Method to Analyze the user Requirement for user Centred Design Process in Order to Create Learning Applications","volume":"8","author":"Kamarulzaman","year":"2015","journal-title":"Indian J. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Dama\u0161evi\u010dius, R., and Vasiljevien\u0117, G. (2019). Fuzzy Delphi Method with Z-Numbers. Information and Software Technologies, Springer International Publishing.","DOI":"10.1007\/978-3-030-30275-7"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.1016\/j.ins.2011.02.022","article-title":"A Note on Z-numbers","volume":"181","author":"Zadeh","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Xiao, Z. (2014, January 9\u201310). Application of Z-numbers in multi-criteria decision making. Proceedings of the 2014 International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS), Qingdao, China.","DOI":"10.1109\/ICCSS.2014.6961822"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1142\/S0219622016500310","article-title":"Ranking of Z-Numbers and Its Application in Decision Making","volume":"15","author":"Aliev","year":"2016","journal-title":"Int. J. Inf. Technol. & Decis. Mak."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Banasik, A., and Lawnik, M. (, January 18\u201321September). Fuzzy Method with Z-numbers for Choosing Target Group of Users for UX Applications. Proceedings of the 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS), Metz, France.","DOI":"10.1109\/IDAACS.2019.8924237"},{"key":"ref_33","first-page":"1","article-title":"The Delphi technique: Making sense of consensus","volume":"12","author":"Hsu","year":"2007","journal-title":"Pract. Assess. Res. Eval."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1016\/j.techfore.2011.07.008","article-title":"Is diversity in Delphi panelist groups useful? Evidence from a French forecasting exercise on the future of nuclear energy","volume":"78","author":"Hussler","year":"2011","journal-title":"Technol. Forecast. Soc. Chang."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.futures.2018.03.017","article-title":"Who is a Delphi \u2018expert\u2019? Reflections on a bioeconomy expert selection procedure from Ireland","volume":"99","author":"Devaney","year":"2018","journal-title":"Futures"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.techfore.2019.07.002","article-title":"Improving the practical application of the Delphi method in group-based judgment: A six-step prescription for a well-founded and defensible process","volume":"147","author":"Belton","year":"2019","journal-title":"Technol. Forecast. Soc. Chang."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7394","DOI":"10.1016\/j.eswa.2010.04.033","article-title":"The use of a hybrid fuzzy-Delphi-AHP approach to develop global business intelligence for information service firms","volume":"37","author":"Chen","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.tranpol.2014.04.009","article-title":"Choosing optimal bunkering ports for liner shipping companies: A hybrid Fuzzy-Delphi-TOPSIS approach","volume":"35","author":"Wang","year":"2014","journal-title":"Transp. Policy"},{"key":"ref_39","unstructured":"(2019, December 30). Prophet: Forecasting at Scale. Available online: https:\/\/research.fb.com\/blog\/2017\/02\/prophet-forecasting-at-scale\/."},{"key":"ref_40","unstructured":"(2019, December 30). Prophet: Quick Start. Available online: https:\/\/facebook.github.io\/prophet\/docs\/quick_start.html."},{"key":"ref_41","unstructured":"(2019, December 30). Forecasting with Prophet. Available online: https:\/\/towardsdatascience.com\/forecasting-with-prophet-d50bbfe95f91."},{"key":"ref_42","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2020, January 25). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Available online: tensorflow.org."},{"key":"ref_43","unstructured":"(2019, December 30). PyFlux. Available online: https:\/\/github.com\/RJT1990\/pyflux."},{"key":"ref_44","unstructured":"Seabold, S., and Perktold, J. (July, January 28). Statsmodels: Econometric and statistical modeling with python. Proceedings of the 9th Python in Science Conference, Austin, TX, USA."},{"key":"ref_45","unstructured":"(2019, December 30). ECB Reference Exchange Rate, US Dollar\/Euro, 2:15 pm (C.E.T.). Available online: https:\/\/sdw.ecb.europa.eu\/browseSelection.do?org.apache.struts.taglib.html."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/11\/2\/65\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:30:32Z","timestamp":1760362232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/11\/2\/65"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,27]]},"references-count":45,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["info11020065"],"URL":"https:\/\/doi.org\/10.3390\/info11020065","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,27]]}}}