A Comprehensive Exploration of Hellwig’s Taxonomic Measure of Development and Its Modifications—A Systematic Review of Algorithms and Applications
Source abstract
Abstract
This paper presents an original and comprehensive investigation into the Taxonomic Measure of Development (TMD), introduced by Hellwig in 1968, enriching both its theoretical foundations and practical applications. It provides an overview of various variants of the Hellwig method, including their extensions and applications, while also exploring recent trends across multiple research domains. Primarily developed as a method for multidimensional analysis, TMD has evolved into a pivotal tool in multi-criteria decision-making. It is widely used for evaluating and ranking alternatives, particularly in the analysis of complex socio-economic phenomena and decision-making scenarios involving multiple criteria. This study systematically reviews the original algorithm and its subsequent extensions and modifications, including adaptations for fuzzy sets, intuitionistic fuzzy sets, and interval-valued fuzzy sets. Furthermore, it explores an integrated multi-criteria approach based on Hellwig’s method and its practical applications across various domains. This paper introduces an original approach by conducting a detailed, step-by-step analysis of the TMD framework. This process-oriented analysis is a novel contribution that sets this study apart from typical reviews based on statistical or bibliometric data. By examining key steps in the TMD framework—such as data collection, criterion weighting, data normalization, ideal value determination, distance calculation, and normalization factor—this paper highlights the method’s versatility in addressing complex, real-world decision-making problems. Although similar to the widely used Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method in its reliance on distance to evaluate alternatives, Hellwig’s approach is unique in focusing exclusively on proximity to an ideal solution, without considering distance from a negative ideal. This distinctive emphasis has led to numerous adaptations and extensions that address specific issues such as criterion dependencies, uncertainty, and rank reversal. The findings underscore the continued relevance of the Hellwig method, its recent extensions, and its growing international recognition.
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Research context
OpenAlex topics: Income, Poverty, and Inequality
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
Funding
Bialystok University of Technology and founded by the Ministry of Education and Science
References (100+)
Show source-provided references
1. Multi-Criteria Classification, Sorting, and Clustering: A Bibliometric Review and Research Agenda10.1007/s10479-022-04986-9 ↗
2. Ehrgott, M., and Greco, S. (2005). Multiple Criteria Decision Analysis: State of the Art Surveys, Springer Science.
3. Roy, B. (1996). Multicriteria Methodology for Decision Aiding, Kluwer Academic Publisher.10.1007/978-1-4757-2500-1 ↗
4. Zastosowanie Metody Taksonomicznej Do Typologicznego Podziału Krajów Ze Względu Na Poziom Ich Rozwoju Oraz Zasoby i Strukturę 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]
5. Development of TOPSIS Method to Solve Complicated Decision-Making Problems—An Overview on Developments from 2000 to 201510.1142/S0219622016300019 ↗
6. Wysocki, F. (2010). Metody Taksonomiczne w Rozpoznawaniu Typów Ekonomicznych Rolnictwa i Obszarów Wiejskich [Taxonomic Methods in Recognizing Economic Types of Agriculture and Rural Areas], Uniwersytetu Przyrodniczego w Poznaniu.
7. The Implementation of the Taxonomic Spatial Measure of Development in the Analysis of Convergence in the Standard of Living
8. Visualization of Linear Ordering Results for Metric Data with the Application of Multidimensional Scaling
9. Measuring Sustainable Development Using an Extended Hellwig Method: A Case Study of Education10.1007/s11205-020-02491-9 ↗
10. Zastosowanie Rozmytych Metod Porządkowania Liniowego w Ustalaniu Hierarchii Ważności Cech Usługi Związanych z Jakością
11. Łuczak, A., and Kalinowski, S. (2023). The Measurement of Subjective Household Poverty: Concepts and Application. Res. Sq.10.21203/rs.3.rs-3159844/v1 ↗
12. Jefmański, B., Roszkowska, E., and Kusterka-Jefmańska, M. (2021). Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data. Entropy, 23.10.3390/e23121636 ↗
13. The Intuitionistic Fuzzy Framework for Evaluation and Rank Ordering the Negotiation Offers
14. Roszkowska, E., Jefmański, B., and Kusterka-Jefmańska, M. (2022). On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights. Entropy, 24.10.3390/e24081081 ↗
15. The Intuitionistic Fuzzy Synthetic Measure in a Dynamic Analysis of the Subjective Quality of Life of Citizens of European Cities
16. Roszkowska, E., and Jefmański, B. (2021). Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig’s Approach in the Analysis of Survey Data. Mathematics, 9.10.3390/math9030201 ↗
17. Roszkowska, E., Wachowicz, T., Filipowicz-Chomko, M., and Łyczkowska-Hanćkowiak, A. (2022). The Extended Linguistic Hellwig’s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers. Entropy, 24.10.3390/e24111617 ↗
18. Fuzzy Multiple Criteria Decision-Making Techniques and Applications–Two Decades Review from 1994 to 201410.1016/j.eswa.2015.01.003 ↗
19. Triantaphyllou, E. (2000). Multi-Criteria Decision Making Methods: A Comparative Study, Applied Optimization, Springer.10.1007/978-1-4757-3157-6 ↗
20. Kahraman, C. (2008). Fuzzy Multi-Criteria Decision Making: Theory and Applications with Recent Developments, Springer Science.10.1007/978-0-387-76813-7 ↗
21. Multi-Criteria Decision-Making Methods Based on Intuitionistic Fuzzy Sets10.1016/j.ejor.2006.04.009 ↗
22. A Literature Review of Interval-Valued Intuitionistic Fuzzy Multi-Criteria Decision-Making Methodologies
23. Linguistic Decision Analysis: Steps for Solving Decision Problems under Linguistic Information10.1016/S0165-0114(99)00024-X ↗
24. A Fuzzy Linguistic Methodology to Deal with Unbalanced Linguistic Term Sets10.1109/TFUZZ.2007.896353 ↗
25. Basílio, 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 (1977–2022). Electronics, 11.10.3390/electronics11111720 ↗
26. The Use of Multi-Criteria Decision-Making Methods in Business Analytics: A Comprehensive Literature Review10.1016/j.techfore.2021.121193 ↗
27. Integrating Multi-Criteria Decision-Making Methods with Sustainable Engineering: A Comprehensive Review of Current Practices10.3390/eng4020088 ↗
28. Trends and Applications of Multi-Criteria Decision Analysis in Environmental Sciences: Literature Review10.1007/s10669-017-9642-9 ↗
29. Multiple Criteria Decision Making (MCDM) Methods in Economics: An Overview10.3846/20294913.2011.593291 ↗
30. A Systemic Review for Measuring Circular Economy with Multi-Criteria Methods10.1007/s11356-022-18580-w ↗
31. Multiple Criteria Decision Aiding for Finance: An Updated Bibliographic Survey10.1016/j.ejor.2015.05.032 ↗
32. Application of Multiple-Criteria Decision-Making Techniques and Approaches to Evaluating of Service Quality: A Systematic Review of the Literature10.3846/16111699.2015.1095233 ↗
33. Multicriteria Decision Making for Sustainable Development: A Systematic Review10.1002/mcda.1682 ↗
34. Measuring Systems Sustainability with Multi-Criteria Methods: A Critical Review10.1016/j.ejor.2016.08.075 ↗
35. A Review of Multi-Criteria Decision-Making Methods for Bioenergy Systems10.1016/j.energy.2012.03.074 ↗
36. A Comprehensive and Systematic Review of Multi-Criteria Decision-Making Methods and Applications in Healthcare10.1016/j.health.2023.100232 ↗
37. Multi-Criteria Decision Making-Based Waste Management: A Bibliometric Analysis10.1016/j.heliyon.2023.e21261 ↗
38. Literature Review: Multi-Criteria Decision-Making Method Application for Sustainable Deep-Sea Mining Transport Plans10.1016/j.ecolind.2022.109049 ↗
39. Axiomatization Utility Decision-Rule of Utility, Outranking and Decision Preferen Cemodels Formultiple-Criteria Classification Problems under Partial Inconsistent with the Dominance Principle
40. Keeney, R.L., and Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley.
41. Social Utilities
42. An Approximate Measure of Value
43. Hwang, C.-L., and Yoon, K. (1981). Methods for Multiple Attribute Decision Making. Lecture Notes in Economics and Mathematical Systems, Springer.10.1007/978-3-642-48318-9 ↗
44. Decision Support Systems in Action: Integrated Application in a Multicriteria Decision Aid Process10.1016/S0377-2217(98)00219-7 ↗
45. Decision Making with the Analytic Hierarchy Process
46. Roy, B., and Bouyssou, D. (1993). Aide Multicritère à La Décision: Méthodes et Cas, Economica.
47. Brans, J.-P. (1982). L’ingénierie de La Décision: L’élaboration d’instruments d’aide a La Décision, Université Laval, Faculté des Sciences de l’administration.
48. Rough Sets Theory for Multicriteria Decision Analysis10.1016/S0377-2217(00)00167-3 ↗
49. A Framework Based on Statistical Analysis and Stakeholders’ Preferences to Inform Weighting in Composite Indicators10.1016/j.envsoft.2021.105208 ↗
50. On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness10.1007/s11205-017-1832-9 ↗
51. Compromise Solution by MCDM Methods: A Comparative Analysis of VIKOR and TOPSIS10.1016/S0377-2217(03)00020-1 ↗
52. Using Individual and Common Reference Points to Measure the Performance of Alternatives in Multiple Criteria Evaluation
53. Best-Worst Multi-Criteria Decision-Making Method10.1016/j.omega.2014.11.009 ↗
54. Konarzewska-Gubała, E. (1989). Bipolar: Multiple Criteria Decision Aid Using Bipolar Refernce System. LAMSADE Cashier Et Doc., 56.
55. Pedrycz, W., Ekel, P., and Parreiras, R. (2011). Fuzzy Multicriteria Decision-Making: Models, Methods and Applications, John Wiley & Sons.10.1002/9780470974032 ↗
56. Obtaining Weights: From Objective to Subjective Approaches in View of More Participative Methods in the Construction of Composite Indicators
57. Elicitation of Criteria Weights for Multicriteria Models: Bibliometrics, Typologies, Characteristics and Applications
58. A Weight-Assessing Method with Habitual Domains10.1016/S0377-2217(97)00246-4 ↗
59. 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.10.1007/978-3-319-12586-2 ↗
60. A State-of the-Art Survey of TOPSIS Applications10.1016/j.eswa.2012.05.056 ↗
61. Normalization in TOPSIS-Based Approaches with Data of Different Nature: Application to the Ranking of Mathematical Videos10.1007/s10479-018-2945-5 ↗
62. A State-of-the-Art Survey on the Influence of Normalization Techniques in Ranking: Improving the Materials Selection Process in Engineering Design10.1016/j.matdes.2014.09.022 ↗
63. A Comparison of Various Normalization in Techniques for Order Performance by Similarity to Ideal Solution (TOPSIS)10.20894/IJCOA.101.003.003.023 ↗
64. Hellwig, Z. (1967). Procedure of Evaluating High-Level Manpower Data and Typology of Countries by Means of the Taxonomic Method. COM/WS/91, Warsaw, unpublished UNESCO working paper.
65. Dynamics of Economic Development Measure. Fiftieth Anniversary of Publication of the Article by Prof. Zdzisław Hellwig
66. Pociecha, J. (1990). Wkład Ośrodka Wrocławskiego w Rozwój Teorii i Zastosowań Metod Taksonomicznych [The Contribution of the Center of Wroclaw in the Development of the Theory and Application of Taxonomic Methods]. Taksonomia–Teoria i Zastosowania, Wydawnictwo AE w Krakowie.
67. Nermend, K. (2009). Methodological Dilemma Over Regional Development Analysis. Vector Calculus in Regional Development Analysis: Comparative Regional Analysis Using the Example of Poland, Physica-Verlag HD.10.1007/978-3-7908-2179-6 ↗
68. Pociecha, J. (1990). Wkład Ośrodka Krakowskiego w Rozwój Teorii i Zastosowań Metod Taksonomicznych [The Contribution of the Center of Kraków in the Development of the Theory and Application of Taxonomic Methods]. Taksonomia–Teoria i Zastosowania, Wydawnictwo AE w Krakowie.
69. A Comparative Analysis of the Socio-Economic Potential of Polish Regions
70. Regional Disparities in Development Based on Taxonomic Research: A Case of Poland
71. Analiza przestrzennego zróżnicowania poziomu rozwoju społeczno-gospodarczego województw Polski w latach 2005–2017 [Analysis of Spatial Variation in the Level of Socio-Economic Development of Polish Voivodeships in 2005–2017]10.15584/nsawg.2020.1.10 ↗
72. The Level of Socio-Economic Development of Regions in Poland
73. Barska, A., Jędrzejczak-Gas, J., and Wyrwa, J. (2022). Poland on the Path towards Sustainable Development—A Multidimensional Comparative Analysis of the Socio-Economic Development of Polish Regions. Sustainability, 14.10.3390/su141610319 ↗
74. The Level of Socio-Economic Development of Polish Provinces in the Period 2005-2020
75. Ranking of EU Countries in Terms of the Value of Environmental Governance Indicators in 2010 and 2015
76. Multidimensional Comparative Analysis of Demographic Growth of Voivodeships in Poland
77. Application of the Linear Ordering Methods to Analysis of the Agricultural Market in Poland
78. Diversity of Polish Regions in the Level of Technical Infrastructure Development10.22630/ASPE.2020.19.3.30 ↗
79. Katsoni, V., and van Zyl, C. (2021). Conditions for Creating Business Tourism Offers and the Regional Potential in Poland. Culture and Tourism in a Smart, Globalized, and Sustainable World, Proceedings of the 7th International Conference of IACuDiT, Hydra, Greece, 2–4 September 2020, Springer International Publishing.10.1007/978-3-030-72469-6 ↗
80. Poverty in Polish Regions in the Light of European Union Policy10.15584/nsawg.2022.4.3 ↗
81. Pawlewicz, K., and Cieślak, I. (2024). An Analysis of the Relationships between Social Capital Levels and Selected Green Economy Indicators on the Example of Polish Voivodeships. Sustainability, 16.10.3390/su16041459 ↗
82. A Spatial Comparison of Semi-Urban and Rural Gminas in Poland in Terms of Their Level of Socio-Economic Development Using Hellwig’s Method
83. The Diversity of Demographic Potential and Socioeconomic Development of Urban Functional Areas—Evidence from Poland10.1016/j.cities.2021.103516 ↗
84. Variability of the Level of Development of Functional Urban Areas
85. The Socioeconomic Development of Rural Municipalities Representing Various Demographic and Functional Types
86. Assessing the Development of Cultural Institutions in Poland–a Multidimensional Comparative Analysis
87. Evaluation of Theater Activity Using Hellwig’s Method
88. Ziemba, E. (2018). Synthetic Indexes for a Sustainable Information Society: Measuring ICT Adoption and Sustainability in Polish Enterprises. Information Technology for Management. Ongoing Research and Development, Springer International Publishing.10.1007/978-3-319-77721-4_9 ↗
89. An Evaluation of Economic Efficiency of Health Care Entities Using the Taxonomic Measure of Development (TMD)10.1016/j.procs.2022.09.222 ↗
90. Tarczyńska-Łuniewska, M., and Tarczyński, W. (2006). Metody Wielowymiarowej Analizy Porównawczej Na Rynku Kapitałowym [Methods of Multidimensional Comparative Analysis on the Capital Market], Wydawnictwo Naukowe PWN.
91. Węgrzyn, T. (2013). Stock Selection Based on Financial Ratios on the Warsaw Stock Exchange. Analysis between 2001 and 2010. European Financial Systems 2013, Proceedings of the 10th International Scientific Conference, 10–11 June 2013, Telč, Czech Republic, Masarykova Univerzita Nakladatelství.
92. Synthetic Measures of the European Capital Markets Development
93. Does Fundamental Strength of the Company Influence Its Investment Performance?
94. Taxonomic Analysis of the Polish Public Health in Comparison with Selected European Countries10.59170/stattrans-2012-028 ↗
95. Multiple-Criteria Evaluation of Quality of Human Capital in the European Union Countries10.14254/2071-789X.2016/9-2/1 ↗
96. Factors of Tourism’s Competitiveness in European Union Countries
97. Multiple Criteria Analysis of European Union Agriculture10.14254/2071-8330.2016/9-3/5 ↗
98. The Use of Selected Methods of Linear Ordering to Assess the Innovation Performance of the European Union Member States
99. Level of Development of E-Commerce in EU Countries
100. Changes in the Competitive Positıon of the Food Industry in the European Unıon Member States