Analysis of the Generalized Thurstone Method and Investigation of Its Applicability in Industrial Environments Using Theoretical and Simulation Methods
Thesis supervisor: Csaba Mihálykó
co-supervisor: Éva Mihálykóné Orbán
Location of studies (in Hungarian): H-8200 Veszprém, Egyetem str. 10., University of Pannonia, Faculty of Information Technology, Department of Mathematics Abbreviation of location of studies: PE
Description of the research topic:
One commonly used method of multi-level decision-making is based on paired comparisons. This procedure can be applied in many areas of life, including, but not limited to, information retrieval, fault detection and analysis, public opinion polling, tender evaluation, marketing, and the evaluation of sports competitions. The information obtained by comparisons in pairs can be evaluated using several methods, one of which is the generalized Thurstone method or Bradley-Terry method. This method has probabilistic background and allows for the ranking of the compared objects, determining their strengths (goodness, reliability, etc.), and estimating probabilities regarding the outcomes of future comparisons. The aims of the research are as follows:
i) to determine the necessary and/or sufficient conditions for the applicability of the method in the presence of an arbitrary number of options and potential advantages;
ii) optimal design of augmentations with epsilon-perturbation in the case of insufficient information;
iii) investigating the consistency of the information set; developing and applying metrics for cases of inconsistency;
iv) determining the graph structures necessary for the optimal operation of the method;
v) demonstrating the applicability of the developed procedures in an industrial environment.
Preliminary results can be found in the following publications:
Orbán-Mihálykó, É. ; Mihálykó, Cs.; Koltay, L.: A generalization of the Thurstone method for multiple choice and incomplete paired comparisons, CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 27 pp. 133-159. , 27 p. (2019)
Orbán-Mihálykó, É. ; Mihálykó, Cs. ; Koltay, L.: Incomplete paired comparisons in case of multiple choice and general log-concave probability density functions, CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 27 : 2 pp. 515-532. , 18 p. (2019)
Kosztyán, Zs. T. ; Orbán-Mihálykó, É. ; Mihálykó, Cs. ; Csányi, V. V. ; Telcs, A. :Analyzing and clustering students' application preferences in higher education, JOURNAL OF APPLIED STATISTICS 47 : 16 pp. 2961-2983. , 23 p. (2020)
Gyarmati, L.; Orbán-Mihálykó, É.; Mihálykó Cs.; Szádoczki, Zs.; Bozóki, S.: The incomplete analytic hierarchy process and Bradley–Terry model: (In)consistency and information retrieval, EXPERT SYSTEMS WITH APPLICATIONS 229, Part B pp. 120522, 13 p. (2023)
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