DEVELOPMENT OF TECHNIQUE FOR DETERMINING THE MEMBERSHIP FUNCTION VALUES ON THE BASIS OF GROUP EXPERT ASSESSMENT IN FUZZY DECISION TREE METHOD
DOI:
https://doi.org/10.15588/1607-3274-2024-2-11Keywords:
the theory of plausible and paradoxical reasoning, fuzzy decision trees, proportional conflict redistribution ruleAbstract
Context. Recently, fuzzy decision trees have become widely used in solving the classification problem. In the absence of objective information to construct the membership function that shows the degrees of belongingness of elements to tree nodes, the only way to obtain information is to involve experts. In the case of group decision making, the task of aggregation of experts’ preferences in order to synthesize a group decision arises. The object of the study is group expert preferences of the degree of belonging (membership function) of an element to a given class, attribute, which require structuring and aggregation in the process of construction and analysis of a fuzzy decision tree.
Objective. The purpose of the article is to develop a methodology for determining the membership degree of elements to a given class (attribute) based on the group expert assessment in the process of construction and analysis of fuzzy decision trees.
Method. The research methodology is based on the complex application of the mathematical apparatus of the theory of plausible and paradoxical reasoning and methods of fuzzy logic to solve the problem of aggregating fuzzy judgments of the classification attribute values in the process of construction and analysis of a fuzzy decision tree. The proposed approach uses the mechanism of combination of expert evidences (judgments), formed within the framework of the Dezert-Smarandache hybrid model, based on the PCR5 proportional conflict redistribution rule to construct a group solution.
Results. The issues of structuring fuzzy expert judgments are considered and the method of synthesis of group expert judgments regarding the values of membership degree of elements to classification attributes in the process of construction and analysis of fuzzy decision trees has been proposed.
Conclusions. The models and methods of structuring and synthesis of group decisions based on fuzzy expert information were further developed. In contrast to the existing expert methods for the construction of membership function in context of group decision making, the proposed approach allows synthesizing a group decision taking into account the varying degree of conflict mass in the process of combination of original expert evidenced. This approach allows to correctly aggregate both agreed and contradictory (conflicting) expert judgments.
References
Páez-Quinde C., Llerena-Llerena W., Zúñiga-Vásquez F., Silva M. P. Ranganathan G., EL Allioui Y., Piramuthu S. (eds), Decision trees as a predictive model in digital marketing, Soft Computing for Security Applications. ICSCS 2023. Advances in Intelligent Systems and Computing. Springer, Singapore, 2023, Vol. 1449, pp 403–414. DOI: 10.1007/978-981-99-3608-3_28
Navada A., Ansari A. N., Patil S., Sonkamble B. A. Overview of use of decision tree algorithms in machine learning, Control and System Graduate Research Colloquium (ICSGRC 2011) : Graduate Research Colloquium, Shah Alam, Malaysia, 27–28 June 2011: proceedings. Shah Alam, IEEE, 2011, pp. 37–42. DOI: 10.1109/ICSGRC.2011.5991826.
Rokach L., Maimon O. Data mining with decision trees. Theory and Applications. London, World Scientific Publishing Co, 2008, 264 p. DOI: 10.1142/9097.9
Bramer M. Avoiding overfitting of decision trees. In: Principles of data mining, Undergraduate topics in computer science. London, Springer, 2013, pp. 121–136. DOI: 10.1007/978-1-4471-4884-5_9
Levashenko V., Hrkut P., Kovalenko A., Kurmasheva L. Fuzzy decision trees in medical decision making support system, Modern technologies of biomedical engineering: the 1st Internationals scientific and technical conference, Odesa, Ukraine, 25−27 May 2022, рroceedings. Odesa, 2022, pp. 190–198.
Ludwig S. A., Picek S., Jakobovic D., Kahraman C., Topcu Y. I. (eds) Classification of cancer data: analyzing gene expression data using a fuzzy decision tree algorithm. Operations research applications in health care management. Cham, Springer, 2018, Vol. 262, pp. 327–347. DOI: 10.1007/978-3-319-65455-3_13
Zhang Z. Applications of the decision tree in business field, Economic Management and Cultural Industry (ICEMCI 2021): the 3rd International Conference, Guangzhou, China, 22–24 October 2021: proceedings. Atlantis Press International B. V., 2011. pp. 926–929. DOI: 10.2991/assehr.k.211209.151
Gofman E. A., Oliinyk A. A., Subbotin S. A. Evolutionary method of decision trees synthesis, Artificial Intelligence, 2011, №2, pp. 6–14.
Altay A., Cinar D. Fuzzy decision trees. In Kahraman C., Kabak Ö. (eds) Fuzzy statistical decision-making: theory and applications, 2016, Vol. 343, pp. 221–261. DOI: 10.1007/978-3-319-39014-7_13
Janikow C. Z. Fuzzy decision trees: issues and methods, IEEE Transactions on Systems, Man and Cybernetics, 1998, Vol. 28(1), pp. 1–14. DOI: 10.1109/3477.658573
Quinlan J. R. Induction on decision tree, Machine Learning, 1986, Vol. 1, pp. 81–106. DOI: 10.1007/ BF00116251
Kantarci S., Nasibov E. A fuzzy ID3 induction for linguistic data sets, International Journal of Intelligent Systems, 2018, Vol. 33, pp. 858–878. DOI: 10.1002/int.21971.
Quinlan J. R. C4.5: Programs for machine learning. San Mateo, Morgan Kaufmann Publishers, 1993, 312 p.
Breiman L., Friedman J. H., Olsen R. A., Stone C. J. Classification and regression trees. California, Wadsworth & Brooks, 1984. 368 p.
Klir G. J., Yuan B. Fuzzy sets and fuzzy logic: theory and applications. NJ, Prentice Hall; Upper Saddle River, 1995, 592 p.
Peckol J. K. Introduction to fuzzy logic. Hoboken, NJ, Wiley, 2021, 287 p.
Kondratenko Yu., Kondratenko G., Sidenko I. Hesitant fuzzy information processing based on the generalized aggregation of resulting trapezoidal linguistic terms, ICT in Education, Research and Industrial Applications (ICTERI2019): the 15th International Conference, Kherson, Ukraine, 12–15 June 2019: CEUR workshop proceedings. Integration, Harmonization and Knowledge Transfer, 2019, Vol. I. P. 479–484.
Sancho-Royo A., Verdegay J. Methods for the construction of membership functions, International Journal of Intelligent Systems, 1999, Vol. 14, pp. 1213–1230. DOI: 10.1002/(SICI)1098-111X(199912)14:123.0.CO;2-5.
Smarandache F., Dezert J. Advances and applications of DSmT for information fusion. Rehoboth, American Research Press, 2004, Vol. 1, 760 p.
Bhattacharyya A. On a measure of divergence between two statistical populations defined by their probability distribution, Bulletin of the Calcutta Mathematical Society, 1943, Vol. 35, pp. 99–110.
Cuzzolin F. A geometric approach to the theory of evidence, Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 2007, Vol. 38(4), pp. 522–534. DOI: 10.1109/TSMCC.2008.919174
Jousselme A. L., Grenier D., Boss´e E. A new distance between two bodies of evidence, Information Fusion, 2001, Vol. 2, pp. 91–101. DOI: 10.1016/S1566-2535(01)00026-4
Tessem B. Approximations for efficient computation in the theory of evidence, Artificial Intelligence, 1993, Vol. 61, pp. 315–329. DOI: 10.1016/0004-3702(93)90072-J
Beynon M. J., Curry B., Morgan P. The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modeling, Omega, 2000, Vol. 28(1), pp. 37–50.
Sentz K., Ferson S. Combination of evidence in DempsterShafer theory. Technical report SAND 2002-0835. Albuquerque, Sandia National Laboratories, 2002, 94 p.
Dempster A. P. Upper and lower probabilities induced by a multi-valued mapping, Annals of Mathematical Statistics, 1967, Vol. 38(2), pp. 325–339. DOI: 10.1214/aoms/1177698950
Shafer G. A mathematical theory of evidence. Princeton: Princeton University Press, 1976, 297 p.
Davydenko Ye. O., Shved A. V., Honcharova N. V. Development of technique for structuring of group expert assessments under uncertainty and inconcistancy, Radio Electronics, Computer Science, Control, 2023, Vol. 30(4), pp. 30– 38. DOI: 10.15588/1607-3274-2023-4-3
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