{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T05:20:24Z","timestamp":1768972824407,"version":"3.49.0"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,6,19]],"date-time":"2021-06-19T00:00:00Z","timestamp":1624060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and\/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents\u2019 attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the proposed method, as well as its possible limitations, are summarized.<\/jats:p>","DOI":"10.3390\/axioms10020124","type":"journal-article","created":{"date-parts":[[2021,6,20]],"date-time":"2021-06-20T22:00:02Z","timestamp":1624226402000},"page":"124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Innovative Grey Approach for Group Multi-Criteria Decision Analysis Based on the Median of Ratings by Using Python"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6846-3074","authenticated-orcid":false,"given":"Dragi\u0161a","family":"Stanujki\u0107","sequence":"first","affiliation":[{"name":"Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210 Bor, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5308-2503","authenticated-orcid":false,"given":"Darjan","family":"Karaba\u0161evi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2652-4860","authenticated-orcid":false,"given":"Gabrijela","family":"Popovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0655-3741","authenticated-orcid":false,"given":"Predrag S.","family":"Stanimirovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Mathematics and Science Division, Gallup Campus, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2577-7927","authenticated-orcid":false,"given":"Muzafer","family":"Sara\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Computer Sciences, University of Novi Pazar, Dimitrija Tucovi\u0107a bb, 36300 Novi Pazar, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8130-1301","authenticated-orcid":false,"given":"Alptekin","family":"Uluta\u015f","sequence":"additional","affiliation":[{"name":"Department of International Trade and Logistics, Faculty of Economics and Administrative Sciences, Sivas Cumhuriyet University, Sivas 58140, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8208-9656","authenticated-orcid":false,"given":"Vasilios N.","family":"Katsikis","sequence":"additional","affiliation":[{"name":"Division of Mathematics and Informatics, Department of Economics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784 Ilissia, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,19]]},"reference":[{"key":"ref_1","first-page":"145","article-title":"Developing of a Novel Integrated MCDM MULTIMOOSRAL Approach for Supplier Selection","volume":"32","author":"Stanujkic","year":"2021","journal-title":"Informatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.35530\/IT.072.01.1841","article-title":"Going green: Strategic evaluation of green ICT adoption in the textile industry by using bipolar fuzzy Multimoora method","volume":"72","author":"Karabasevic","year":"2021","journal-title":"Ind. Text."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jaukovic Jocic, K., Jocic, G., Karabasevic, D., Popovic, G., Stanujkic, D., Zavadskas, E.K., and Thanh Nguyen, P. (2020). A novel integrated piprecia\u2013interval-valued triangular fuzzy aras model: E-learning course selection. Symmetry, 12.","DOI":"10.3390\/sym12060928"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Karaba\u0161evi\u0107, D., Stanujki\u0107, D., Zavadskas, E.K., Stanimirovi\u0107, P., Popovi\u0107, G., Predi\u0107, B., and Uluta\u015f, A. (2020). A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection. Symmetry, 12.","DOI":"10.3390\/sym12081263"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"107287","DOI":"10.1016\/j.cie.2021.107287","article-title":"A novel model for multi-criteria assessment based on BWM and possibilistic chance-constrained programming","volume":"156","author":"Amiri","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"402","DOI":"10.3846\/tede.2021.14433","article-title":"An overview of fuzzy techniques in supply chain management: Bibliometrics, methodologies, applications and future directions","volume":"27","author":"Lu","year":"2021","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_7","first-page":"49","article-title":"Improved OCRA method based on the use of interval grey numbers","volume":"29","author":"Stanujkic","year":"2017","journal-title":"J. Grey Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.landusepol.2019.03.001","article-title":"A multiple-criteria decision-making model for the selection of a hotel location","volume":"84","author":"Popovic","year":"2019","journal-title":"Land Use Policy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1007\/s11269-006-9112-5","article-title":"A review of multiple criteria analysis for water resource planning and management","volume":"21","author":"Hajkowicz","year":"2007","journal-title":"Water Resour. Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.ejor.2006.10.045","article-title":"A comparison of multiple criteria analysis techniques for water resource management","volume":"184","author":"Hajkowicz","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.enbuild.2004.07.005","article-title":"Multivariant design and multiple criteria analysis of building refurbishments","volume":"37","author":"Kaklauskas","year":"2005","journal-title":"Energy Build."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.ejor.2003.06.010","article-title":"Equitable aggregations and multiple criteria analysis","volume":"158","author":"Kostreva","year":"2004","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","first-page":"883","article-title":"Demystifying DEA\u2014A visual interactive approach based on multiple criteria analysis","volume":"44","author":"Belton","year":"1993","journal-title":"J. Oper. Res. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1016\/j.ejor.2020.09.051","article-title":"Combining multiple criteria analysis, mathematical programming and Monte Carlo simulation to tackle uncertainty in Research and Development project portfolio selection: A case study from Greece","volume":"291","author":"Mavrotas","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1080\/13504509.2020.1780646","article-title":"Assessing national energy sustainability using multiple criteria decision analysis","volume":"28","author":"Phillis","year":"2021","journal-title":"Int. J. Sustain. Dev. World Ecol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"143678","DOI":"10.1016\/j.scitotenv.2020.143678","article-title":"Energy consumption analysis and multiple-criteria evaluation of high-speed trains with different marshaled forms in China","volume":"759","author":"Peng","year":"2021","journal-title":"Sci. Total Environ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110298","DOI":"10.1016\/j.rser.2020.110298","article-title":"Acceptability of transport emissions reduction policies: A multi-criteria analysis","volume":"133","author":"Hasan","year":"2020","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"117475","DOI":"10.1016\/j.energy.2020.117475","article-title":"A two-stage multi-criteria analysis method for planning renewable energy use and carbon saving","volume":"199","author":"Ahmed","year":"2020","journal-title":"Energy"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Huang, H., Mommens, K., Lebeau, P., and Macharis, C. (2021). The Multi-Actor Multi-Criteria Analysis (MAMCA) for Mass-Participation Decision Making. International Conference on Decision Support System Technology, Springer International Publishing.","DOI":"10.1007\/978-3-030-73976-8_1"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kilgour, D.M., and Eden, C. (2021). Multicriteria Methods for Group Decision Processes: An Overview. Handbook of Group Decision and Negotiation, Springer Science & Business Media.","DOI":"10.1007\/978-3-030-49629-6"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.ins.2020.12.033","article-title":"A dynamic group MCDM model with intuitionistic fuzzy set: Perspective of alternative queuing method","volume":"555","author":"Tao","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113447","DOI":"10.1016\/j.dss.2020.113447","article-title":"A group decision-making approach for exploring trends in the development of the healthcare industry in Taiwan","volume":"141","author":"Hsu","year":"2021","journal-title":"Decis. Support Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"114542","DOI":"10.1016\/j.eswa.2020.114542","article-title":"An investigation on Wu-Leung multi-scale information systems and multi-expert group decision-making","volume":"170","author":"Zhan","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1002\/int.22329","article-title":"A variable weight-based hybrid approach for multi-attribute group decision making under interval-valued intuitionistic fuzzy sets","volume":"36","author":"Liu","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Biswas, S., and Pamucar, D. (2020). Facility location selection for b-schools in indian context: A multi-criteria group decision based analysis. Axioms, 9.","DOI":"10.3390\/axioms9030077"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1007\/s40815-020-00827-8","article-title":"Grey Absolute Decision Analysis (GADA) Method for multiple criteria group decision-making under uncertainty","volume":"22","author":"Javed","year":"2020","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Carneiro, J., Martinho, D., Alves, P., Concei\u00e7\u00e3o, L., Marreiros, G., and Novais, P. (2020). A multiple criteria decision analysis framework for dispersed group decision-making contexts. Appl. Sci., 10.","DOI":"10.3390\/app10134614"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"36765","DOI":"10.1007\/s11356-020-09700-5","article-title":"Assessing barriers and solutions for Yemen energy crisis to adopt green and sustainable practices: A fuzzy multi-criteria analysis","volume":"27","author":"Fang","year":"2020","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Musaad, O.A.S., Zhuo, Z., Musaad, O.A.O., Ali Siyal, Z., Hashmi, H., and Shah, S.A.A. (2020). A fuzzy multi-criteria analysis of barriers and policy strategies for small and medium enterprises to adopt green innovation. Symmetry, 12.","DOI":"10.3390\/sym12010116"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"34","DOI":"10.31181\/rme200101034c","article-title":"Sustainable supplier selection using combined FUCOM\u2014Rough SAW model","volume":"1","author":"Chatterjee","year":"2020","journal-title":"Rep. Mech. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1080\/13504509.2020.1795005","article-title":"Collaborative decision-making in sustainable mobility: Identifying possible consensuses in the multi-actor multi-criteria analysis based on inverse mixed-integer linear optimization","volume":"28","author":"Huang","year":"2021","journal-title":"Int. J. Sustain. Dev. World Ecol."},{"key":"ref_32","first-page":"1","article-title":"Introduction to Grey System Theory","volume":"1","author":"Deng","year":"1989","journal-title":"J. Grey Syst."},{"key":"ref_33","unstructured":"Liu, S.F., Yang, Y.J., and Forrest, J.Y.L. (2016). Grey Data Analysis: Methods, Models and Applications, Springer."},{"key":"ref_34","unstructured":"Liu, S.F., and Forrest, J.Y.L. (2010). Grey Systems: Theory and Applications, Springer."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1108\/GS-09-2016-0031","article-title":"Explanation of terms of grey numbers and its operations","volume":"6","author":"Liu","year":"2016","journal-title":"Grey Syst. Theory Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"597","DOI":"10.15388\/Informatica.2010.307","article-title":"A novel method for multiple criteria analysis: Grey additive ratio assessment (ARAS-G) method","volume":"21","author":"Turskis","year":"2010","journal-title":"Informatica"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"141","DOI":"10.24846\/v24i2y201502","article-title":"Selecting a Contractor by Using a Novel Method forMultiple Attribute Analysis: Weighted Aggregated SumProduct Assessment with Grey Values (WASPAS-G)","volume":"24","author":"Zavadskas","year":"2015","journal-title":"Stud. Inform. Control."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"858","DOI":"10.3846\/jcem.2019.11309","article-title":"A grey combined compromise solution (COCOSO-G) method for supplier selection in construction management","volume":"25","author":"Yazdani","year":"2019","journal-title":"J. Civ. Eng. Manag."},{"key":"ref_39","unstructured":"Stanujkic, D., Popovic, G., Karabasevic, D., Meidute-Kavaliauskiene, I., and Ulutas, A. (2021). An Integrated Simple Weighted Sum Product Method\u2014WISP. IEEE Trans. Eng. Manag., 1\u201312."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/124\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:19:00Z","timestamp":1760163540000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,19]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020124"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020124","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,19]]}}}