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## Ranking probability measures by inclusion indices in the case of unknown utility function.

This paper gives a way of analyzing decisions in the case of unknown utility function, or more precisely, when we know only a linear order on an income space. It is shown that in this situation, decisions and corresponding probability measures are partially ordered, and this order is identical to the inclusion relation of comonotone fuzzy sets. It enables us to use inclusion indices of fuzzy sets to analyze the comparability of decisions. To do this, we introduce an inclusion index having properties, which are close to ones of the classical expected utility.

The paper shows the possibility of applying the tool of non-additive measures and the belief functions theory to solving a number of problems of significance analysis and conflict of the political party positions. The study was performed on a database of online polls of parties in Germany before the elections to the Bundestag in 2013 and the results of these elections. The possibility of finding the most significant groups of issues for voting, evaluating the political heterogeneity of society, assessing the importance of the positions of individual parties for voting, assessing the conflict of the party positions on important issues is shown.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Purpose – The purpose of this paper is to address issues related to organizational design and strategy fit by examining the “strategic stretch” that occurs when there exists a mismatch between an organization’s structure and firm-level strategy. Design/methodology/approach – The paper contains a discussion of relevant issues and a presentation of research that considers the relationship between organizational design, strategy selection, and the competitive environment within which a firm operates. This research includes an analysis of a survey of top managers and an evaluation of organizational design and firm strategy to determine the existence of strategic misfit. Findings – Misfits in strategy and structure exist because of Russian managerial proclivity to maintain direct control through centralization of all strategic formulations and because of high risk-taking behaviors of Russian managers. While organizational inertia is a clear driver of organizational structure, cultural inertia also exists and, in the case of Russian organizational design, societal organizational culture drives strategy misfits. Practical implications – An understanding of strategic misfits is crucial for managers so that they may recognize these disconnects early and make improvements as market or firm conditions changes. The results of the analysis of Russian firms suggest that in designing efficient organizations, greater attention should be placed on the specific impact of societal organizational culture. In addition, practitioners in organizational design consulting positions should make clear, whenever they attempt to eliminate misfits between existing structures and current strategies, the need to develop effective stretch for implementation of intended strategies. Originality/value – The paper provides a unique application of the connection of strategy and organizational design under conditions of extreme uncertainty. This paper also extends the analysis of organizational design and strategy to firms operating in emerging markets. Rapid changes in dynamic, emerging markets provide fertile testing grounds for management theory and practices; this paper examines a unique set of empirical evidence.

This article analyses the capacity of healthy patients for decision making based on the mechanism of the emotional learning (Damasio’s somatic marker hypothesis). The relation of this mechanism to the perception of the emotionally significant situations in real life and the use of emotions in cognitive control is estimated. The dependence of the emotional learning on parameters of the executive functions is considered. The influence of propensity to risk and impulsiveness on the decision making is analyzed. The following methods are used: the International Game Technology (IGT), the Mayer-Salovey-Caruso Emotional Intelligence Test (MSCEIT), the Wisconsin Card Sorting Test (WCST), the D-KEFS Color-Word Interference Test, the Barratt Impulsiveness Scale (BIS-11), the questionnaire “Impulsiveness 7” (I7). 95 people were involved in the study. The connection of the decision making in uncertainty which estimates with the International Game Technology (IGT), with the emotional processes is demonstrated. It is shown that the decrease of the regulatory functions, such as the inhibition of the irrelevant answers and the control of the result of their own actions, is connected to the decreasing of the capacity for decision making in uncertainty. The personal features (the interest to the complex problem solving and the focusing on the future) are connected with better decision making in uncertainty. By the persons with risk propensity the learning occurs later on the basis of emotional experience. High level of the capacity for planning and self-control is connected to the features of the emotional decision making.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.