
On attempts to characterize facetdefining inequalities of the cone of exact games
Studený, Milan ; Kroupa, Tomáš ; Kratochvíl, Václav
The sets of balanced, totally balanced, exact and supermodular games play an important role in cooperative game theory. These sets of games are known to be polyhedral cones. The (unique) nonredundant description of these cones by means of the socalled facetdefining inequalities is known in cases of balanced games and supermodular games, respectively. The facet description of the cones of exact games and totally balanced games are not known and we present conjectures about what are the facetdefining inequalities for these cones. We introduce the concept of an irreducible minbalanced set system and conjecture that the facetdefining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facetdefining inequalities for this cone are those which correspond to irreducible minbalanced systems on strict subsets of the set of players and their conjugate inequalities. A consequence of the validity of the conjectures would be a novel result saying that a game m is exact if and only if m and its reflection are totally balanced.


Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter
Jiroušek, R. ; Kratochvíl, Václav
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the DempsterShafer theory of evidence. Up to now, there was no direct way to get the expected value of a utility function in DS theory. If eeded, one had to find a probability mass function corresponding to the considered belief function, and then  using this probability mass function  to compute the classical probabilistic expectation. In this paper, we take four different approaches to defining probabilistic representatives of a belief function and compare which one yields to the best approximations of Shenoy’s expected values of various utility functions. The achieved results support our conjecture that there does not exist a probabilistic representative of a belief function that would yield the same expectations as the Shenoy’s new operator.


About Two Consonant Conflicts of Belief Functions
Daniel, M. ; Kratochvíl, Václav
General belief functions usually bear some internal conflict which comes mainly from disjoint focal elements. Analogously, there is often some conflict between two (or more) belief functions. After the recent observation of hidden conflicts (seminar CJS’17 [17]), appearing at belief functions with disjoint focal elements, importance of interest in conflict of belief functions has increased. This theoretical contribution introduces a new approach to conflicts (of belief functions). Conflicts are considered independently of any combination rule and of any distance measure. Consonant conflicts are based on consonant approximations of belief functions in general; two special cases of the consonant approach based on consonant inverse pignistic and consonant inverse plausibility transforms are discussed. Basic properties of the newly defined conflicts are presented, analyzed and briefly compared with our original approaches to conflict (combinational conflict, plausibility conflict and comparative conflict), with the recent conflict based on nonconflicting parts, as well as with W. Liu’s degree of conflict.


Proceedings of the 11th Workshop on Uncertainty Processing
Kratochvíl, Václav ; Vejnarová, Jiřina
The Workshop on Uncertainty Processing, better known under its abbreviation WUPES, celebrates its 30year anniversary this year. In 1988, when the first Workshop took place, Czechoslovakia was still a communist country and a part of the Soviet bloc. Since then, many things have changed. For example, Czechoslovakia no longer exists as a country (because in 1993 it was peacefully split into two independent countries  Czechia and Slovakia). From this perspective, it is hard to believe that we have several participants who have attended most workshops in the the thirtyyear history of WUPES. As of now, the Program Committee has accepted, based on the extended abstracts, 21 papers to be presented at the Workshop, and 19 out of them are to be published in the present Conference Proceedings. These papers cover diverse topics, such as information processing, decision making, and data analysis, but what is common to most of them is that they are related to uncertainty calculus  Bayesian Networks, DempsterShafer Theory, Belief Functions, Probabilistic Logic, Game Theory, etc.


Dynamic Bayesian Networks for the Classification of Sleep Stages
Vomlel, Jiří ; Kratochvíl, Václav
Human sleep is traditionally classified into five (or six) stages. The manual classification is time consuming since it requires knowledge of an extensive set of rules from manuals and experienced experts. Therefore automatic classification methods appear useful for this task. In this paper we extend the approach based on Hidden Markov Models by relating certain features not only to the current time slice but also to the previous one. Dynamic Bayesian Networks that results from this generalization are thus capable of modeling features related to state transitions. Experiments on real data revealed that in this way we are able to increase the prediction accuracy.


Hidden AutoConflict in the Theory of Belief Functions
Daniel, M. ; Kratochvíl, Václav
Hidden conflicts of belief functions in some cases where the sum of all multiples of conflicting belief masses being equal to zero were observed. Relationships of hidden conflicts and autoconflicts of belief functions are pointed out. We are focused on hidden autoconflicts here  on hidden conflicts appearing when three or more numerically same belief functions are combined. Hidden autoconflict is a kind of internal conflict. Degrees of hidden autoconflicts and full nonconflictness are defined and analysed. Finally, computational issues of hidden autoconflicts and nonconflictness are presented.

 

Information Geometry and its Applications IV
Kratochvíl, Václav
The aim of the conference is to highlight recent developments within the field of information geometry and to identify new directions of research. We are confident that we have put together an exciting program consisting of invited talks and contributed poster presentations. All titles and abstracts are included in this book. We thank Václav Kratochvíl for his terrific work with the local organisation! Special thanks go to Antje Vandenberg who managed all the administrative work in Leipzig. We are also grateful for the support that we received from Milan Studený


Influence diagrams for speed profile optimization" computational issues
Vomlel, Jiří ; Kratochvíl, Václav
Influence diagrams were applied to diverse decision problems. However, the general theory is still not sufficiently developed if the variables are continuous or hybrid and the utility functions are nonlinear. In this paper, we study computational problems related to the application of influence diagrams to vehicle speed profile optimization and suggest an approximation of the nonlinear utility functions by piecewise linear functions.


Proceedings of the 10th Workshop on Uncertainty Processing
Kratochvíl, Václav
WUPES 2015 is organized jointly by the Institute of Information Theory and Automation of the Czech Academy of Sciences and by the Faculty of Management, University of Economics, Prague. It is quite natural that such a meeting could not materialize if it were not for the hard work of many our colleagues and friends. This is why we want to express our gratitude to all the members of both the Programme and Organizing Committees. Last but not least, we also want to acknowledge the fact that this workshop is organized, due to the fact that the research of several members of the Organizing Committee is financially supported by grants GA CR no 1500215S and 1320012S.
