Zur Gleichwertigkeit zweier Arten der Randomisierung

For the choice of a mathematical model describing randomized decisions it is important to make sure that given a ‘behavioral decision rule’ there exists an equivalent ‘randomized decision function’ (cf. [2], p. 24–26). This fact seems to be known only in some special cases (cf. [1], Th. 8.3.1 and [3]). Here we give a simple proof for the general case.     

Total absolute curvature of polyhedral manifolds with boundary in E n

N. H. Kuiper has generalized the notion of total absolute curvature for compact polyhedra in euclidean space by considering the critical points of all height functions (cf. [12]). On the other hand in the case of compact smooth manifolds with boundary in E ⁿ there is a certain relation between the total absolute curvatures of the total space, the interior and the boundary (cf. [9]). In this note we show an analogous relation in the case of compact polyhedral manifolds with boundary leading to theorems of the Chern/Lashof type (cf. [3], [7]).     

Zur Einbettung von Inzidenzräumen und angeordneten Räumen

We characterize subsets of incidence spaces, which are locally complete resp. bundletrue (bündeltreu). Then we specify necessary and sufficient conditions to extend the embedding of a subset of a space into another space to an embedding of the complete space. Using these results we show that every ordered space (not necesserily fulfilling (O3), cf. §4) can be embedded into a projective space. The last result is a generalization of former results using the additional assumption (O3) (cf. [2,9,10]).     

A separation theorem for the hyperext

Summary We introduce, on the hyperext spaces associated to complexes of sheaves with coherent cohomology on an analytic space, a natural topology that extends the natural topology defined by Verdier on the hypercohomology (cf. [13]). For a holomorphically convex space we prove that this topology is separated, which generalizes a result of Ramis [10].

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Riassunto Si introduce, sugli spazi iperext associati ai complessi di fasci a coomologia coerente su uno spazio analitico, una topologia naturale che estende la topologia naturale definita da Verdier sull'ipercoomologia (cf. [13]). Per uno spazio olomorficamente convesso si dimostra che questa topologia è separata e generalizza un risultato di Ramis [10].

     

Supporting complex group decisions: A probabilistic multi-dimensional scaling approach

Groups often face complex decisions; decisions in which the decision alternatives are not clearly defined and the criteria for choosing an alternative are subject to dispute within the group. We present a Group Decision Support System that will use judgments from the group to visualize the decision problem in a probabilistic geometric space. In this geometric representation, actual decision alternatives and an ideal alternative—an artificial alternative that identifies the ideal solution to the group's decision dilemma—are portrayed as distributions in a multi-dimensional space. Dispersions of the distributions measure the uncertainties of the decision process. The psychometric theory used to develop the probabilistic geometric representation is described. Preliminary research is presented which demonstrates that geometric representations of this type help groups both to understand better the decision they face and to find better solutions.     

Zur algebraischen Darstellung fastaffiner Räume

Ten years ago J. ANDRÉ introduced the concept of nearaffine space. He described desarguesian semi-regular nearaffine spaces as spaces over nearfields (cf. [3]). We show that this is also possible, if the nearaffine space is not necessaryly semi-regular.     

A measurable selection theorem for compact-valued maps

The main theorem of this paper establishes the existence of measurable selections for compact-valued multifunctions whose range space is a regular Hausdorff space which need neither be metrizable nor satisfy any restriction on its weight. It is shown that the selection theorems of Sion [16], Hasumi [10], and one of the author (cf. [8]) are immediate consequences of this general result. Moreover some new results concerning Borel and Baire property selections for upper semi-continuous compact-valued maps are deduced.     

The Baire Category Property and Some Notions of Compactness

We work in set theory without the axiom of choice: ZF. We showthat the axiom BC: Compact Hausdorff spaces are Baire, is equivalentto the following axiom: Every tree has a subtree whose levelsare finite, which was introduced by Blass (cf. [4]). This settlesa question raised by Brunner (cf. [9, p. 438]). We also showthat the axiom of Dependent Choices is equivalent to the axiom:In a Hausdorff locally convex topological vector space, convex-compactconvex sets are Baire. Here convex-compact is the notion whichwas introduced by Luxemburg (cf. [16]).     

Desarguessche Axiome in fastaffinen Räumen einer Dimension Grösser als zwei

Nearaffine spaces were introduced by J. ANDRé [1] as a generalization of affine spaces. Desarguesian semi-regular nearaffine spaces can be described as spaces over nearfields (cf. [2]). We show that the Desargues-theorems are valid in every nearaffine space, whose dimension is equal to or larger than three.     

A comparison of two approaches for solving unconstrained influence diagrams

Influence diagrams and decision trees represent the two most common frameworks for specifying and solving decision problems. As modeling languages, both of these frameworks require that the decision analyst specifies all possible sequences of observations and decisions (in influence diagrams, this requirement corresponds to the constraint that the decisions should be temporarily linearly ordered). Recently, the unconstrained influence diagram was proposed to address this drawback. In this framework, we may have a partial ordering of the decisions, and a solution to the decision problem therefore consists not only of a decision policy for the various decisions, but also of a conditional specification of what to do next. Relative to the complexity of solving an influence diagram, finding a solution to an unconstrained influence diagram may be computationally very demanding w.r.t. both time and space. Hence, there is a need for efficient algorithms that can deal with (and take advantage of) the idiosyncrasies of the language. In this paper we propose two such solution algorithms. One resembles the variable elimination technique from influence diagrams, whereas the other is based on conditioning and supports any-space inference. Finally, we present an empirical comparison of the proposed methods.     

A Model for Multi-timescaled Sequential Decision-making Processes with Adversary

Extending the multi-timescale model proposed by the author et al. in the context of Markov decision processes, this paper proposes a simple analytical model called M timescale two-person zero-sum Markov Games (MMGs) for hierarchically structured sequential decision-making processes in two players' competitive situations where one player (the minimizer) wishes to minimize their cost that will be paid to the adversary (the maximizer). In this hierarchical model, for each player, decisions in each level in the M-level hierarchy are made in M different discrete timescales and the state space and the control space of each level in the hierarchy are non-overlapping with those of the other levels, respectively, and the hierarchy is structured in a "pyramid" sense such that a decision made at level m (slower timescale) state and/or the state will affect the evolutionary decision making process of the lower-level m+1 (faster timescale) until a new decision is made at the higher level but the lower-level decisions themselves do not affect the transition dynamics of higher levels. The performance produced by the lower-level decisions will affect the higher level decisions for each player. A hierarchical objective function for the minimizer and the maximizer is defined, and from this we define "multi-level equilibrium value function" and derive a "multi-level equilibrium equation". We also discuss how to solve hierarchical games exactly.     

Optimal healthcare decisions: Comparing medical treatments on a cost-effectiveness basis

This paper deals with medical treatments comparison from the cost-effectiveness viewpoint. A decision theory scheme is considered, where the decision space is the set of treatments involved, the space of states of nature consists of the respective net benefits of the treatments, and the utility function is one of two possible candidates. A first candidate is the one typically used in the literature on cost-effectiveness analysis, for which the utility of a decision is proportional to the net benefit gain, and a second one is of the type 0–1, which penalizes the wrong decisions with a fixed quantity. Their associated optimal decision rules, both frequentist and Bayesian, are analyzed and compared via frequentist evaluation of their performance, and the conclusion is that the latter beats the former in the sense of choosing the optimal treatment more often than any other, thus minimizing the proportion of wrong decisions. Illustrations with simulated and real data are provided.     

Cosheaves and distributions on toposes

Distributions on a Grothendieck topos were introduced by Lawvere [12] (cf. also [13]) as a generalization of the classical notion (cf. [20]) of real-valued distributions on a topological space. The cosheaves approach to distributions which is implicit in work of Pitts [19] is used here first, in order to answer affirmatively a question posed in [12] concerning the existence of the symmetric topos and next, in order to prove a structure theorem for categories of distributions on Grothendieck toposes that is similar in spirit to the Joyal-Tierney [11] structure theorem for Grothendieck toposes.Dedicated to the memory of Alan Day.Presented by J. Sichler.     

Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

Geometry of decision making and the vector space formulation of the analytic hierarchy process

We extend the conventional Analytic Hierarchy Process (AHP) to an Euclidean vector space and develop formulations for aggregation of the alternative preferences with the criteria preferences. Relative priorities obtained from such a formulation are almost identical with the ones obtained using conventional AHP. Each decision is represented by a preference vector indicating the orientation of the decision maker's mind in the decision space spanned by the decision alternatives. This adds a geometric meaning to the decision making processes. We utilise the measure of similarity between any two decision makers and apply it for analysing decisions in a homogeneous group. We propose an aggregation scheme for calculating the group preference from individual preferences using a simple vector addition procedure that satisfies Pareto optimality condition. The results agree very well with the ones of conventional AHP.     

On separation axioms in hyperspaces

It is shown that the well-known characterizations of separation axiomsT ₂ andT ₃, respectively of hit-and-miss hyperspace topologies withT ₁ base space (cf. [9], [10]) are valid with no preliminary conditions on the base space.     

Completeness in quasi-uniform spaces

We introduce a theory of completeness (the π-completeness) for quasi-uniform spaces which extends the theories of bicompleteness and half-completeness and prove that every quasi-uniform space has a π-completion. This theory is based on a new notion of a Cauchy pair of nets which makes use of couples of nets. We call them cuts of nets and our inspiration is due to the construction of the τ-cut on a quasi-uniform space (cf. [1], [20]). This new version of completeness coincides with bicompletion, half-completion and D-completion in extended subclasses of the class of quasi-uniform spaces.     

Making decisions in the absence of clear facts

Bennis and O’Toole [Bennis, W.G., O’Toole, J., 2005. How business schools lost their way. Harvard Business Review 83, 96–104] have recently argued that decision makers need guidance in ‘making decisions in the absence of clear facts’. As such, decision makers must be able to resourcefully use whatever limited information is available and advantageously portray its implications. Based on recently published theory which directly addresses this requirement, this paper demonstrates, through a practical example, how decision makers can make systemic decisions in situations characterized by extremely limited information and, furthermore, what form such decisions can take. Evidence is provided, therefore, that operational research can effectively address what appears to be a gap in management training.     

Numerical Analysis of the Stochastic Moving Boundary Problem

We extend and generalize some recent results on complete convergence (cf. Hu, Moricz, and Taylor [14], Gut [11], Wang, Bhaskara Rao, and Yang [26], Kuczmaszewska and Szynal [17], and Sung [23]) for arrays of rowwise independent Banach space valued random elements. In the main result, no assumptions are made concerning the existence of expected values or absolute moments of the random elements and no assumptions are made concerning the geometry of the underlying Banach space. Some well-known results from the literature are obtained easily as corollaries. The corresponding convergence rates are also established     

Correct or incorrect application of CAPM? Correct or incorrect decisions with CAPM?

This paper focuses on inconsistencies arising from the use of NPV and CAPM for capital budgeting. It shows that: (i) CAPM capital budgeting decision-making based on disequilibrium NPV is deductively inferred by the capital asset pricing model, (ii) the use of the disequilibrium NPV is widespread in finance both as a decision rule and as a valuation tool, (iii) the disequilibrium NPV does not guarantee additivity nor consistency with arbitrage pricing, so that it is unreliable for valuation, (iv) Magni’s [Magni, C.A., 2002. Investment decisions in the theory of finance: Some antinomies and inconsistencies. European Journal of Operational Research 137, 206–217; Magni, C.A., 2007a. Project valuation and investment decisions: CAPM versus arbitrage. Applied Financial Economics Letters 3 (2), 137–140] criticism of the NPV criterion refers to the disequilibrium NPV, and De Reyck’s [De Reyck, B., 2005. On investment decisions in the theory of finance: Some antinomies and inconsistencies. European of Operational Research 161, 499–504] project valuation method, on the basis of which Magni’s criticism to NPV is objected, leaves decision makers open to arbitrage losses and incorrect decisions.