{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T20:07:04Z","timestamp":1760731624643,"version":"build-2065373602"},"reference-count":65,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,6]],"date-time":"2024-01-06T00:00:00Z","timestamp":1704499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bialystok University of Technology","award":["WZ\/WI-IIT\/2\/22"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/22"]}]},{"name":"Ministry of Education and Science","award":["WZ\/WI-IIT\/2\/22"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Hellwig\u2019s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig\u2019s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig\u2019s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig\u2019s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable tool for decision-makers in real-life situations. It enables the evaluation of alternatives by considering interactions between criteria, providing a more comprehensive perspective for decision-making.<\/jats:p>","DOI":"10.3390\/sym16010077","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T07:59:20Z","timestamp":1704700760000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Modifying Hellwig\u2019s Method for Multi-Criteria Decision-Making with Mahalanobis Distance for Addressing Asymmetrical Relationships"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2249-7217","authenticated-orcid":false,"given":"Ewa","family":"Roszkowska","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,6]]},"reference":[{"key":"ref_1","unstructured":"Ehrgott, M., and Greco, S. (2005). Multiple Criteria Decision Analysis: State of the Art Surveys, Springer Science + Business Media."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Roy, B. (1996). Multicriteria Methodology for Decision Aiding, Kluwer Academic Publisher.","DOI":"10.1007\/978-1-4757-2500-1"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bas\u00edlio, M.P., Pereira, V., Costa, H.G., Santos, M., and Ghosh, A. (2022). A Systematic Review of the Applications of Multi-Criteria Decision Aid Methods (1977\u20132022). Electronics, 11.","DOI":"10.3390\/electronics11111720"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"121193","DOI":"10.1016\/j.techfore.2021.121193","article-title":"The Use of Multi-Criteria Decision-Making Methods in Business Analytics: A Comprehensive Literature Review","volume":"174","author":"Yalcin","year":"2022","journal-title":"Technol. Forecast. Soc. Change"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.3390\/eng4020088","article-title":"Integrating Multi-Criteria Decision-Making Methods with Sustainable Engineering: A Comprehensive Review of Current Practices","volume":"4","year":"2023","journal-title":"Eng"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10669-017-9642-9","article-title":"Trends and Applications of Multi-Criteria Decision Analysis in Environmental Sciences: Literature Review","volume":"37","author":"Cegan","year":"2017","journal-title":"Environ. Syst. Decis."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.ejor.2016.08.075","article-title":"Measuring Systems Sustainability with Multi-Criteria Methods: A Critical Review","volume":"258","author":"Romero","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.esr.2019.03.003","article-title":"A Comprehensive Review of Fuzzy Multi Criteria Decision Making Methodologies for Energy Policy Making","volume":"24","author":"Kaya","year":"2019","journal-title":"Energy Strategy Rev."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hwang, C.-L., and Yoon, K. (1981). Methods for Multiple Attribute Decision Making, Springer. Lecture Notes in Economics and Mathematical Systems.","DOI":"10.1007\/978-3-642-48318-9"},{"key":"ref_10","first-page":"307","article-title":"Zastosowanie Metody Taksonomicznej Do Typologicznego Podzia\u0142u Kraj\u00f3w Ze Wzgl\u0119du Na Poziom Ich Rozwoju Oraz Zasoby i Struktur\u0119 Wykwalifikowanych Kadr [Application of the Taxonomic Method to the Typological Division of Countries According to the Level of Their Development and the Resources and Structure of Qualified Personnel]","volume":"4","author":"Hellwig","year":"1968","journal-title":"Przegl\u0105d Statystyczny"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0377-2217(03)00020-1","article-title":"Compromise Solution by MCDM Methods: A Comparative Analysis of VIKOR and TOPSIS","volume":"156","author":"Opricovic","year":"2004","journal-title":"Eur. J. Oper. Res."},{"key":"ref_12","first-page":"77","article-title":"Using Individual and Common Reference Points to Measure the Performance of Alternatives in Multiple Criteria Evaluation","volume":"30","author":"Roszkowska","year":"2020","journal-title":"Oper. Res. Decis."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.omega.2014.11.009","article-title":"Best-Worst Multi-Criteria Decision-Making Method","volume":"53","author":"Rezaei","year":"2015","journal-title":"Omega"},{"key":"ref_14","unstructured":"Konarzewska-Guba\u0142a, E. (1989). Bipolar: Multiple Criteria Decision Aid Using Bipolar Refernce System. LAMSADE Cashier Doc., 56."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.matdes.2014.09.022","article-title":"A State-of-the-Art Survey on the Influence of Normalization Techniques in Ranking: Improving the Materials Selection Process in Engineering Design","volume":"65","author":"Jahan","year":"2014","journal-title":"Mater. Des."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"185","DOI":"10.15388\/Informatica.2014.10","article-title":"Comparative Analysis of Normalization Procedures in TOPSIS Method: With an Application to Turkish Deposit Banking Market","volume":"25","year":"2014","journal-title":"Informatica"},{"key":"ref_17","first-page":"102","article-title":"A Simulation Based Comparative Study of Normalization Procedures in Multiattribute Decision Making","volume":"Volume 6","author":"Chakraborty","year":"2007","journal-title":"Proceedings of the 6th Conference on 6th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Chakraborty, S., and Yeh, C.-H. (2009, January 6\u20139). A Simulation Comparison of Normalization Procedures for TOPSIS. Proceedings of the 2009 International Conference on Computers and Industrial Engineering (CIE39), Troyes, France.","DOI":"10.1109\/ICCIE.2009.5223811"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1007\/s00158-004-0473-1","article-title":"The Effect of Normalization Norms in Multiple Attribute Decision Making Models: A Case Study in Gear Material Selection","volume":"29","author":"Milani","year":"2005","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1016\/j.procs.2019.09.378","article-title":"Influence of Various Normalization Methods in PROMETHEE II: An Empirical Study on the Selection of the Airport Location","volume":"159","author":"Palczewski","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_21","first-page":"251","article-title":"Normalization Affects the Results of MADM Methods","volume":"11","year":"2001","journal-title":"Yugosl. J. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Camarinha-Matos, L.M., Falc\u00e3o, A.J., Vafaei, N., and Najdi, S. (2016). Technological Innovation for Cyber-Physical Systems, Proceedings of the 7th IFIP 5.5\/SOCOLNET Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2016, Costa de Caparica, Portugal, 11\u201313 April 2016, Springer International Publishing.","DOI":"10.1007\/978-3-319-31165-4"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"601","DOI":"10.15388\/Informatica.2006.158","article-title":"Evaluation of Ranking Accuracy in Multi-Criteria Decisions","volume":"17","author":"Zavadskas","year":"2006","journal-title":"Informatica"},{"key":"ref_24","first-page":"49","article-title":"On the Generalised Distance in Statistics","volume":"2","author":"Mahalanobis","year":"1936","journal-title":"Proc. Natl. Inst. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ghojogh, B., Ghodsi, A., Karray, F., and Crowley, M. (2022). Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey. arXiv.","DOI":"10.1007\/978-3-031-10602-6_11"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.jclepro.2019.04.406","article-title":"A Resilience Evaluation Method for a Combined Regional Agricultural Water and Soil Resource System Based on Weighted Mahalanobis Distance and a Gray-TOPSIS Model","volume":"229","author":"Liu","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ponce, R.V., and Alcaraz, J.L.G. (2013). Evaluation of Technology Using TOPSIS in Presence of Multi-Collinearity in Attributes: Why Use the Mahalanobis Distance?. Rev. Fac. Ing. Univ. Antioq., 31\u201342.","DOI":"10.17533\/udea.redin.16308"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"109","DOI":"10.3846\/tede.2010.07","article-title":"Multiple Criteria Construction Management Decisions Considering Relations between Criteria","volume":"16","author":"Zavadskas","year":"2010","journal-title":"Technol. Econ. Dev. Econ."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, Z.-X., Li, D.-D., and Zheng, H.-H. (2018). The External Performance Appraisal of China Energy Regulation: An Empirical Study Using a TOPSIS Method Based on Entropy Weight and Mahalanobis Distance. Int. J. Environ. Res. Public Health, 15.","DOI":"10.3390\/ijerph15020236"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4642","DOI":"10.1016\/j.eswa.2009.12.044","article-title":"Domestic Open-End Equity Mutual Fund Performance Evaluation Using Extended TOPSIS Method with Different Distance Approaches","volume":"37","author":"Chang","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2824","DOI":"10.1016\/j.eswa.2013.10.015","article-title":"Evaluation of the Provincial Competitiveness of the Chinese High-Tech Industry Using an Improved TOPSIS Method","volume":"41","author":"Wang","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/s12046-019-1088-y","article-title":"Logistics Competitiveness of OECD Countries Using an Improved TODIM Method","volume":"44","author":"Ozmen","year":"2019","journal-title":"S\u0101dhan\u0101"},{"key":"ref_33","first-page":"96","article-title":"Multi-Criteria Clustering-Based Recommendation Using Mahalanobis Distance","volume":"12","author":"Wasid","year":"2020","journal-title":"Int. J. Reason. -Based Intell. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Dong, H., Yang, K., and Bai, G. (2022). Evaluation of TPGU Using Entropy\u2014Improved TOPSIS\u2014GRA Method in China. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0260974"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3600","DOI":"10.1016\/j.patcog.2008.05.018","article-title":"Learning a Mahalanobis Distance Metric for Data Clustering and Classification","volume":"41","author":"Xiang","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1111\/1467-8667.t01-1-00311","article-title":"Wavelet-Clustering-Neural Network Model for Freeway Incident Detection","volume":"18","author":"Adeli","year":"2003","journal-title":"Comput. Aided Civ. Infrastruct. Eng."},{"key":"ref_37","unstructured":"Jefma\u0144ski, B. (2019). Clasification and Data Analysis, Proceedings of the Conference of the Section on Classification and Data Analysis of the Polish Statistical Association, Szczecin, Poland, 18\u201320 September 2019, Springer."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Jefma\u0144ski, B., Roszkowska, E., and Kusterka-Jefma\u0144ska, M. (2021). Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data. Entropy, 23.","DOI":"10.3390\/e23121636"},{"key":"ref_39","unstructured":"Kusterka-Jefma\u0144ska, M., Jefma\u0144ski, B., and Roszkowska, E. (2022). Modern Classification and Data Analysis, Proceedings of the Conference of the Section on Classification and Data Analysis of the Polish Statistical Association, Pozna\u0144, Poland, 8\u201310 September 2021, Springer."},{"key":"ref_40","first-page":"58","article-title":"The Intuitionistic Fuzzy Framework for Evaluation and Rank Ordering the Negotiation Offers","volume":"Volume 308","author":"Kahraman","year":"2021","journal-title":"Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation, Proceedings of the International Conference on Intelligent and Fuzzy Systems INFUS 2021, Istanbul, Turkey, 24\u201326 August 2021"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Roszkowska, E., and Jefma\u0144ski, B. (2021). Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig\u2019s Approach in the Analysis of Survey Data. Mathematics, 9.","DOI":"10.3390\/math9030201"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Roszkowska, E., Wachowicz, T., Filipowicz-Chomko, M., and \u0141yczkowska-Han\u0107kowiak, A. (2022). The Extended Linguistic Hellwig\u2019s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers. Entropy, 24.","DOI":"10.3390\/e24111617"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Mazur-Wierzbicka, E. (2021). Towards Circular Economy\u2014A Comparative Analysis of the Countries of the European Union. Resources, 10.","DOI":"10.3390\/resources10050049"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"11","DOI":"10.14254\/2071-789X.2016\/9-2\/1","article-title":"Multiple-Criteria Evaluation of Quality of Human Capital in the European Union Countries","volume":"9","author":"Balcerzak","year":"2016","journal-title":"Econ. Sociol."},{"key":"ref_45","first-page":"330","article-title":"Rozmyta Wielokryterialna Metoda Hellwiga Porz\u0105dkowania Liniowego Obiekt\u00f3w [Fuzzy Multi-Criteria Hellwig\u2019s Method of Linear Ordering of Objects]","volume":"14","author":"Wysocki","year":"2007","journal-title":"Pr. Nauk. Akad. Ekon. We Wroc\u0142awiu Taksonomia"},{"key":"ref_46","first-page":"7","article-title":"A Comparative Analysis of the Socio-Economic Potential of Polish Regions","volume":"30","author":"Golejewska","year":"2016","journal-title":"Stud. Ind. Geogr. Comm. Pol. Geogr. Soc."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Barska, A., J\u0119drzejczak-Gas, J., and Wyrwa, J. (2022). Poland on the Path towards Sustainable Development\u2014A Multidimensional Comparative Analysis of the Socio-Economic Development of Polish Regions. Sustainability, 14.","DOI":"10.3390\/su141610319"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"222","DOI":"10.14207\/ejsd.2019.v8n5p222","article-title":"Assessment of the Economic Development of Polish Regions in the Context of the Implementation of the Concept of Sustainable Development\u2014Taxonomic Analysis","volume":"8","author":"Barska","year":"2019","journal-title":"Eur. J. Sustain. Dev."},{"key":"ref_49","first-page":"13","article-title":"Ranking of EU Countries in Terms of the Value of Environmental Governance Indicators in 2010 and 2015","volume":"66","year":"2018","journal-title":"Ekon. Sr. Econ. Environ."},{"key":"ref_50","first-page":"24","article-title":"Selection of the Optimal Way of Linear Ordering of Objects: Case of Sustainable Development in EU Countries","volume":"101","year":"2021","journal-title":"Stat. Stat. Econ. J."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"62","DOI":"10.14254\/2071-8330.2016\/9-3\/5","article-title":"Multiple Criteria Analysis of European Union Agriculture","volume":"9","author":"Reiff","year":"2016","journal-title":"J. Int. Stud."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"167","DOI":"10.22630\/MIBE.2019.20.3.16","article-title":"Application of the Linear Ordering Methods to Analysis of the Agricultural Market in Poland","volume":"20","author":"Gostkowski","year":"2019","journal-title":"Metod. Ilo\u015bciowe W Badaniach Ekon."},{"key":"ref_53","unstructured":"Wysocki, F. (2010). Metody Taksonomiczne w Rozpoznawaniu Typ\u00f3w Ekonomicznych Rolnictwa i Obszar\u00f3w Wiejskich [Taxonomic Methods in Recognizing Economic Types of Agriculture and Rural Areas], Wydawnictwo Uniwersytetu Przyrodniczego w Poznaniu."},{"key":"ref_54","unstructured":"Krukowski, A., Nowak, A., and R\u00f3\u017ca\u0144ska-Boczula, M. (2018, January 25\u201326). Evaluation of Agriculture Development in the Member States of the European Union in the Years 2007\u20132015. Proceedings of the 31st International Business Information Management Association Conference, Milan, Italy."},{"key":"ref_55","unstructured":"Di Domizio, M. (2008). The Competitive Balance in the Italian Football League: A Taxonomic Approach, Department of Communication, University of Teramo."},{"key":"ref_56","first-page":"9","article-title":"The Use of Selected Methods of Linear Ordering to Assess the Innovation Performance of the European Union Member States","volume":"19","author":"Grzelak","year":"2019","journal-title":"Econ. Environ. Stud."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Ga\u0142ecka, M., and Smolny, K. (2018). Evaluation of Theater Activity Using Hellwig\u2019s Method. Optim. Econ. Stud., 38\u201350.","DOI":"10.15290\/oes.2018.02.92.04"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"81","DOI":"10.18778\/0208-6018.338.05","article-title":"Comparison of Several Linear Ordering Methods for Selection of Locations in Order-Picking by Means of the Simulation Methods","volume":"5","year":"2018","journal-title":"Acta Univ. Lodz. Folia Oecon."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1016\/j.cor.2006.09.026","article-title":"Comparing Methods for Multiattribute Decision Making with Ordinal Weights","volume":"35","author":"Ahn","year":"2008","journal-title":"Comput. Oper. Res."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Ayan, B., Abac\u0131o\u011flu, S., and Basilio, M.P. (2023). A Comprehensive Review of the Novel Weighting Methods for Multi-Criteria Decision-Making. Information, 14.","DOI":"10.3390\/info14050285"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/S0360-8352(00)00019-X","article-title":"Interpretation of Criteria Weights in Multicriteria Decision Making","volume":"37","author":"Choo","year":"1999","journal-title":"Comput. Ind. Eng."},{"key":"ref_62","first-page":"1","article-title":"Elicitation of Criteria Weights for Multicriteria Models: Bibliometrics, Typologies, Characteristics and Applications","volume":"18","author":"Souza","year":"2021","journal-title":"Braz. J. Oper. Prod. Manag."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"14","DOI":"10.15290\/ose.2013.05.65.02","article-title":"Rank Ordering Criteria Weighting Methods\u2014A Comparative Overview","volume":"5","author":"Roszkowska","year":"2013","journal-title":"Optim. Econ. Stud."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Zardari, N.H., Ahmed, K., Shirazi, S.M., and Yusop, Z.B. (2015). Weighting Methods and Their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management, Springer.","DOI":"10.1007\/978-3-319-12586-2"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/S0377-2217(97)00246-4","article-title":"A Weight-Assessing Method with Habitual Domains","volume":"110","author":"Tzeng","year":"1998","journal-title":"Eur. J. Oper. Res."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:41:28Z","timestamp":1760103688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,6]]},"references-count":65,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010077"],"URL":"https:\/\/doi.org\/10.3390\/sym16010077","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,1,6]]}}}