Research goals: development and theoretical study of new models in the socio-economic, political and financial fields, as well as the application of the developed models to a number of applied problems of decision making.
Methodology: numerical and combinatorial methods, statistical methods of data analysis and clustering, optimization models, methods of probability theory and fuzzy-sets theory.
For applied studies internet-data and database of open source was used.
The following results have been obtained:
‒ mathematical models for finding optimal volumes of electricity production by base load electricity plants of regional electrical grids and optimal volumes of electricity to be stored were developed in the form of games of several players on polyhedral sets of player strategies for all groups of customers, electricity generators, and a transmission company, and verifiable sufficient conditions for Nash equilibrium points in the these games were established;
‒ a new mathematical model for finding an optimal strategy of moving empty railcars of a company possessing these cars was developed under uncertainty of the demand for the railcars from the potential cargo owners;
‒ an advanced model for finding an optimal schedule of moving cargo trains along single-track parts of a railroad was developed, along with a mathematical model for optimization the functioning of a yard of a railroad, and both problems were mathematically formulated as Boolean programming problems;
‒ a new game-theoretic model was developed for finding competitive tariffs for using railcars of a number (more than three) railcar owners in moving cargoes by cargo owners, and verifiable sufficient conditions for Nash equilibrium points in this game were found;
‒ a game-theoretic model of the co-authorship sharing problem is developed; the equal weights to measure of coauthorship sharing is justified by showing equivalence with the Shapley value approach for sharing co-authors performance in specific games;
‒ efficient algorithms for evaluation of power indices taking into account agents’ preferences in collective decision-making bodies with rules satisfying anonymity were developed;
‒ in the framework of theoretical and experimental studies on cluster analysis and automatic text interpretation: a) series of experiments were conducted to compare string and text similarity measure, used to automate categorization of research papers; it was shown that the annotated suffix tree similarity meausure is more efficient than others; b) the development of the lifting method based on the maximum likelihood principle was continued; c) the development of the method for estimating a scientists’ contribution according to the domain taxonomy was continued (some results for data analysis field were achieved;
‒ the alternative methods of aggregation of basic variables of the Competitive Industrial Performance (CIP) index have been considered. Instead of using a cardinal aggregation function, ordinal ranking methods borrowed from social choice theory have been applied. It has been demonstrated that the ranking is robust, and some of the new aggregate rankings represent the set of criteria better than the original ranking based on the CIP;
‒ different approaches (stochastic, fuzzy-set-theoretic, optimizational and some others) to the problem of defining an order on a set of histograms have been analysed; a ranking of the universities has been computed based on histograms of accepted applicants’ national test scores; the conditions of preservation of sign of binary comparisons of distorted histograms has been analysed;
‒ the set of experiments with the agent-based model of the stock exchange where agents are small and medium sized price-takers has been conducted; the agent-based model of the stock exchange with agents being price makers and internal price mechanism has been designed;
‒ the decision rule for groups of criteria of equal importance was investigated and generalized;
‒ a problem of evaluating coalitional manipulability of voting rules with infinite number of voters was analytically solved for popular positional voting rules; a computational complexity was investigated for different problems and algorithms of manipulability of voting rules;
‒ the comparative analysis of two polarization indices in special cases was conducted; the comparison of these indices with standard deviation of group values from the mean position was performed; the stability of these indices to small perturbations was investigated;
‒ the 28 known and 190 two-stage choice procedures were analyzed in terms of satisfying to given normative conditions ‒ rationality condition, monotonicity condition, strict monotonicity condition, and non-compensatory condition; a complexity of two-stage choice procedures as well as its runtime on real data were evaluated.
The area of application: of obtained results includes organizational structures and tariff policies in the energy and transport sectors, bibliometric analysis, the analysis of polarization of social groups, analysis of the influence of groups in elected bodies, multicriteria decision making, analysis of texts and internet data, the ranking of alternatives and the development of the aggregated ratings, stock analysis.
1) Prof. Yusufcan Masatlioglu, Ph.D, University of Michigan, Ann Arbor, USA; Sabanci University, Turkey, http://www-personal.umich.edu/~yusufcan/
2) Prof. Dennis C. Mueller, Ph.D, University of Vienna, Austria, http://homepage.univie.ac.at/dennis.mueller/
3) Prof. Efe Ok, Ph.D, New York University, USA, https://files.nyu.edu/eo1/public/
4) Prof. Ulle Endriss, Ph.D, ILLC, University of Amsterdam, http://staff.science.uva.nl/~ulle/
5) Prof. Sergiy Butenko, Ph.D, Texas A&M University, USA, http://ise.tamu.edu/people/faculty/butenko/
6) Prof. Hannu Nurmi, Ph.D, University of Turku, Finland, http://users.utu.fi/hnurmi/homepage/index2.html
7) Prof. Agnieszka Rusinowska, Ph.D, Université Paris I Panthéon-Sorbonne, France, http://ces.univ-paris1.fr/membre/Rusinowska/
8) Prof. Michel Grabish, Ph.D, Université Paris I Panthéon-Sorbonne, France, http://ces.univ-paris1.fr/membre/Grabisch/