Aleksandra Łuczak https://orcid.org/0000-0002-3149-7748 , Małgorzata Just https://orcid.org/0000-0001-7655-6046
ARTICLE

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ABSTRACT

In this paper, the authors propose a new methodological approach to the construction of a synthetic measure, where the objects are described by variables with strong asymmetry and extreme values (outliers). Even a single extreme value (very large or very small) of a variable for the object may significantly affect the attribution of an excessively high or low rank in the final ranking of objects. This dependence is particularly apparent when using the classical TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method. The aim of the study is to present the application potential of the positional MEF-TOPSIS method for the assessment of the level of development of complex economic phenomena for territorial units. In the positional TOPSIS method, the application of the spatial median of Oja, which limits the impact of strong asymmetry, is proposed. In order to weaken the influence of extreme values, the Mean Excess Function (MEF) is used, by means of which it is possible to identify the limits of extreme values and establish model objects. The proposed approach is used to assess the financial self-sufficiency of Polish municipalities in 2016. The study finally compares the results of applications of positional MEF-TOPSIS and the classic and positional TOPSIS methods.

KEYWORDS

synthetic measure, TOPSIS, spatial median of Oja, Mean Excess Function

REFERENCES

AFSORDEGAN, A., SÁNCHEZ, M., AGELL, N., ZAHEDI, S., CREMADESL, L. V., (2016). Decision making under uncertainty using a qualitative TOPSIS method for selecting sustainable energy alternatives, International Journal of Environmental Science and Technology, 13(6), pp. 1419-1432.

BEHZADIAN, M., OTAGHSARA, K. S., YAZDANI, M., IGNATIUS, J., (2012). A state-of the-art survey of TOPSIS applications, Expert Systems with Applications, 39(17), pp. 13051-13069.

CHEN, C.-T., (2000). Extension of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems, 114(1), pp. 1-9.

CHEN, S.-M., LEE, L.-W., (2010). Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method, Expert Systems with Applications, 37(4), pp. 2790-2798.

CHEN, J., LEI, X., ZHANG, L., PENG, B., (2015). Using extreme value theory approaches to forecast the probability of outbreak of highly pathogenic influenza in Zhejian, China, PLOS ONE, 10(2), [online] Available at: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118521 [Accessed 5 February 2019].

CHEN, T.-Y., TSAO, C.-Y., (2008). The interval-valued fuzzy TOPSIS method and experimental analysis, Fuzzy Sets and Systems, 159(11), pp. 1410-1428.

COLES, S., (2001). An Introduction to Statistical Modeling of Extreme Values, Springer, London.

ECHAUST, K., (2014). Ryzyko zdarzeń ekstremalnych na rynku kontraktów futures w Polsce (Risk of extreme events on the futures market in Poland), Poznań University of Economics and Business, Poznan.

FISCHER, D., MÖTTÖNEN, J., NORDHAUSEN, K., VOGEL, D., (2015). Package 'OjaNP'. Multivariate Methods Based on the Oja Median and Related Concepts, Version 0.9-8, [online] Available at: https://cran.r-project.org/web/packages/OjaNP/.

HUBERT, L., LEVIN, J., (1976). A general statistical framework for assessing categorical clustering in free recall, Psychological Bulletin, 83(6), pp. 1072-1080.

HWANG, C. L., LAI, Y. J., LIU, T. Y., (1993). A new approach for multiple objective decision making, Computers and Operational Research, 20, pp. 889-899.

HWANG, C. L., YOON, K., (1981). Multiple attribute decision-making: Methods and applications, Springer, Berlin.

JAHANSHAHLOO, G. R., LOTFI, F. H. IZADIKHAH, M., (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data, Applied Mathematics and Computation, 175(2), pp. 1375-1384.

KOZERA, A., ŁUCZAK, A., WYSOCKI, F., (2016). The application of classical and positional TOPSIS methods to assess financial self-sufficiency levels in local government units, [In:] Palumbo F., Montanari A., Vichi M. (eds.), Data Science. Studies in Classification, Data Analysis, and Knowledge Organization, Springer, Cham, pp. 273-284.

KUSUMAWARDANI, R. P., AGINTIARA, M., (2015). Application of Fuzzy AHPTOPSIS Method for Decision Making in Human Resource Manager Selection Process, Procedia Computer Science, 72, pp. 638-646.

LI, D.-F., (2010). TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems, 18(2), pp. 299-311.

LIRA, J., WYSOCKI, F., WAGNER, W., (2002). Mediana w zagadnieniach porządkowania obiektów wielocechowych (Median in the ordering problems of multi-variable objects), [In:] Paradysz, J. (ed.), Statystyka regionalna w służbie samorządu terytorialnego i biznesu, (Regional statistics in the service of local government and business), Academy of Economics in Poznań, Poznan, pp. 87-99.

LIU, S., CHAN, F. T., RAN, W., (2013). Multi-attribute group decision-making with multi-granularity linguistic assessment information: An improved approach based on deviation and TOPSIS, Applied Mathematical Modelling, 37(24), pp. 10129-10140.

LOCAL DATA BANK, (2018). Central Statistical Office, Poland, [online] Available at: www.stat.gov.pl [Accessed 9 July 2018].

ŁUCZAK, A., (2015). Wykorzystanie rozszerzonej interwałowej metody TOPSIS do porządkowania liniowego obiektów (The use of the extended interval TOPSIS methods for linear ordering of objects.), [In:] Jajuga, K., Walesiak, M. (eds.), Taksonomia, 25, Klasyfikacja i analiza danych. Teoria i zastosowania. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, 385, (Taxonomy No. 25, Classification and Data Analysis. Theory and Applications. Research Papers of Wrocław University of Economics No. 385), Wroclaw University of Economics and Business, Wroclaw, pp. 147-155.

ŁUCZAK, A., JUST, M., KOZERA, A., (2018). Application of the positional POTTOPSIS method to the assessment of financial self-sufficiency of local administrative units, [In:] Cermakova, K., Mozayeni, S., Hromada, E. (eds.), Proceedings of the 10th Economics & Finance Conference, Rome, International Institute of Social and Economic Sciences and International Society for Academic Studies, z.s., Prague, pp. 610-621, [online] Available at: http://www.iises.net/proceedings/10th-economics-finance-conferencerome/ table-of-content?cid=69&iid=043&rid=10173 [Accessed 5 February 2019].

MARDANI, A., JUSOH, A., ZAVADSKAS, E. K., (2015). Fuzzy multiple criteria decision-making techniques and applications – Two decades review from 1994 to 2014, Expert Systems with Applications, 42(8), pp. 4126-4148.

MCNEIL, A. J., (1999). Extreme Value Theory for Risk Management, Department Mathematics ETH Zentrum, Zurich.

MŁODAK, A., (2006). Analiza taksonomiczna w statystyce regionalnej (Taxonomic analysis in regional statistics), Difin, Warsaw.

NĂDĂBAN, S., DZITAC, S., IDZITAC, I., (2016). Fuzzy TOPSIS: A General View, Procedia Computer Science, 91, pp. 823-831.

OJA, H., (1983). Descriptive statistics for multivariate distributions, Statistics and Probability Letters, 1, pp. 327-332.

RONKAINEN, T., OJA, H., ORPONEN, P., (2002). Computation of the multivariate Oja median, [In:] Dutter, R., Filzmoser, P., Gather, U., Rousseeuw, P. J. (eds.), Developments in Robust Statistics, Springer, Heidelberg, pp. 344-359.

TALEIZADEH, A. A., NIAKI, S. T. A., ARYANEZHAD, M-B., (2009). A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multiconstraint inventory control systems with random fuzzy replenishments, Mathematical and Computer Modelling, 49(5-6), pp. 1044-1057.

VELASQUEZ, M., HESTER, P. T., (2013). An Analysis of Multi-Criteria Decision Making Methods, International Journal of Operations Research, 10(2), pp. 56-66.

WANG, P., ZHU, Z., WANG, Y., (2016). A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design, Information Sciences, 345, pp. 27-45.

WEBER, A., (1909). Über den Standort der Industrien, Tubingen.

WUERTZ, D., SETZ, T., CHALABI, Y., (2017). Package 'fExtremes'. Rmetrics – Modelling Extreme Events in Finance, Version 3042.82, [online] Available at: https://cran.r-project.org/web//packages/fExtremes/ fExtremes.pdf.

WYSOCKI, F., (2010). Metody taksonomiczne w rozpoznawaniu typów ekonomicznych rolnictwa i obszarów wiejskich (Taxonomic methods in recognizing economic types of agriculture and rural areas), Poznań University of Life Sciences, Poznan.

WYSOCKI, F., ŁUCZAK, A., (2009). An evaluation of the social and economic development of powiats in the Wielkopolskie province using a fuzzy multi-criteria decision making (FMCDM) method, [In:]: Adamus, W. (ed.), The Analytic Hierarchy & Network. Application in Solving Multicriteria Decision Problems, Jagiellonian University Press, Cracow, pp. 319-329.

YOON, K., (1987). A reconciliation among discrete compromise situations, Journal of Operational Research Society, 38, pp. 277-286.

ZAVADSKAS, E. K., MARDANI, A., TURSKIS, Z., JUSOH, A., NOR, K. MD., (2016). Development of TOPSIS Method to Solve Complicated Decision-Making Problems: An Overview on Developments from 2000 to 2015, International Journal of Information Technology & Decision Making, 15(03), pp. 645-682.

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