Theory of copulass and aggregation operators
We have developed new results formulated in the frame of the theory of aggregation operators and their specific instance, theory of copulas. Main attention was focused on the algebraic properties of copulas, especially regarding their additivity, and on the parametric characterization of aggregation operators. The modern quantitative methods of the processing of realistic data contaminated by uncertainty or vagueness display evident trends of development aiming to modern and advanced mathematical methods of data representation and data processing under uncertainty, with special stress on the economic ones. Namely the copulas theory and triangular-norms theory closely related to it appear to represent the basic tools for handling those problems. Moreover, the analysis of copulas and triangular norms is widely developed in many countries (Italy, Austria, Slovakia, Ireland, Spain, France, Netherland, China, and others), and the successful results achieved by our team motivated wide and intensive international cooperation with partners from those countries.
Management of uncertainty in cooperation and communication
Parallely with the investigation of the general models widely covering the field of potential methods of modern quantitative economy, some more applied problems of econometric modeling were intensively investigated. Namely, special attention was paid to two areas of interest. First of them is the modeling of cooperative behavior and its stability in optimization problems where the expected pay-offs are only vague. The study of these problems is a continuation of the research activities realized in the previous periods, and extends the results achieved in their frame. Qualitatively new topic of interest is represented by the analysis of the vague information sources and information with hardly identifiable alphabets and symbols. The fuzzy information theoretical analysis of the fuzzy information source aims to the applicable methods of analysis of such economic and econometric concepts like “expectation” and “Expected values” of some parameters entering, especially into prospective economic models.
Mathematics, Informatics and Cybernetics: Tools and Applications
Milan Mareš, key project of the Academy of Sciences of the Czech Republic No. K 1019101.
Size an Value of Information in the Optimization over Incomplete Data
Milan Mareš, grant No. 402/08/0618 of the Grant Agency of the Czech Academy of Science.
Aggregation Principles in the Models of Mathematical Economy
Milan Mareš, grant No. 402/04/1294 of the Czech Science Foundation.
2005–2009–2011 (prolonged). M. Mareš – principal investigator.
Centre of Applied Research DAR (Data-Algorithms-Decision Making) supported by the Government of CR, 1M0572. (Members: ÚTIA, West-Bohemian University in Plzeň, University of Technology in Brno, Ostrava University, Empo Praha, Compureg Plzeň, ELTODO Praha, OASA Computers Ostrava, Deltax Praha). Since 2010 also Škoda-auto, Mladá Boleslav. .
2005–2010 M. Mareš – principal investigator till 2007.
Research plan of UTIA No. AV0Z10750506 Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech.(Advanced methods in retrieval, processing, and applications of knowledge and information in complex and non-deterministic systems).
2004–2006 M. Mareš – principal investigator, R. Mesiar - investigator.
Grant Agency of the Czech Republic, Grant No. 402/04/1026. Aggregation Principles in Economic-Mathematical Models.
2008–2009 M. Mareš – principal investigator, R. Mesiar - investigator.
Grant Agency of the Czech Republic, Grant No. 402/08/0618. Size an value of information in the optimization over incomplete data
2011–2013 M. Mareš – principal investigator, R. Mesiar - investigator.
Grant Agency of the Czech Republic, Grant No. P402/11/0378.
Aggregation of knowledge and expectations in the models of mathematical economics.