Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.     

Gender-Based Vicarious Sensitivity to Disempowering Behavior in Organizations: Exploring an Expanded Concept of Hostile Working Environment

The purpose of this study was to explore evidence of gender-based vicarious sensitivity to disempowering behavior in organizations, expanding the concept of hostile working environment beyond the context of sexual harassment. Male and female graduate and undergraduate students viewed 10 video segments of Anita Hill's interview by U.S. senators during the October 1991 confirmation hearings of Supreme Court Justice Nominee, Clarence Thomas. Although no significant relationship was found between the personal attributes of age and ethnicity to perceptions of disempowering behavior, female participants reported seeing significantly more offensive behavior in the video segments than did male participants. The results are discussed in terms of greater female sensitivity to common forms of disempowering behavior in organizations, and having a disparate negative impact and systematically placing women at a disadvantage in today's workforce.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

The Division of Labor Under Homogeneity: A Critique of Mises and Rothbard

A bstract .   Even the most passionate defenders of free trade, such as Mises and Rothbard, claim that trade cannot occur under conditions of strict homogeneity of land, labor, and capital. We show that specialization, trade, and the division of labor can emerge even when resources are initially homogenous, due to "natural heterogeneity," economies of scale, and learning.     

Progressive stress accelerated life tests under finite mixture models

In this paper, progressive stress accelerated life tests are considered when the lifetime of a product under use condition follows a finite mixture of distributions. The experiment is performed when each of the components in the mixture follows a general class of distributions which includes, among others, the Weibull, compound Weibull, power function, Gompertz and compound Gompertz distributions. It is assumed that the scale parameter of each component satisfies the inverse power low, the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the parameters under consideration are obtained. A special attention is paid to a mixture of two Rayleigh components. Simulation results are carried out to study the precision of the MLEs and to obtain confidence intervals for the parameters involved.     

Reconfiguring the innovation policy portfolios for Taiwan's SIP Mall industry

Since the year 2000, silicon intellectual property (SIP), which can minimize the gap in ‘design productivity’ that exists with systems-on-chip (SOC), has become one of the most important factors in the development of integrated circuit (IC) products in the SOC era. Although SIP is very important for IC industry development, complicated business, technical as well as legal issues inside SIP transactions have hindered successful transactions and the integration of SIPs into SOCs. Thus, web-based SIP e-Commerce mechanisms, called SIP Malls, have emerged, aiming to resolve complex SIP issues. To maintain its leading position and competitiveness in the World's IC industry, as well as the value added by SOC products in Taiwanese IC firms, the Taiwanese government has developed SIP Malls, using innovation policy tools. However, the Taiwanese SIP Mall industry remains immature. No existing Taiwanese SIP Malls generate a profit or account for a significant share of worldwide SIP transactions. This research will develop an analytical framework for defining an innovation policy portfolio that aims to develop Taiwan's SIP Mall industry, so that it will enhance the value added of SIP Malls and, thus, the nation's competitiveness in the SIP and IC industries, something which already has become one of the Taiwanese government's major concerns. The industry innovation requirements (IIRs) are summarized using the Delphi method. Meanwhile, the major IIRs identified by Decision Making Trial and Evaluation Laboratory (DEMATEL) are introduced. After the IIRs are derived, the relationships between the IIRs and innovation policy tools are derived by Grey relational analysis (GRA). Then, the innovation policy tools are clustered, based upon the Grey grades derived by GRA. Finally, reconfigured innovation policy portfolios are presented for the Taiwanese government's policy definition. The results demonstrate that developing an innovative policy portfolio that includes scientific, technical, educational, public enterprise, information, legal and regulatory, financial, and taxation policy tools will be the most necessary step towards developing Taiwan's SIP Mall industry.     

Evaluation of dynamic stochastic general equilibrium models based on distributional comparison of simulated and historical data

We take as a starting point the existence of a joint distribution implied by different dynamic stochastic general equilibrium (DSGE) models, all of which are potentially misspecified. Our objective is to compare “true” joint distributions with ones generated by given DSGEs. This is accomplished via comparison of the empirical joint distributions (or confidence intervals) of historical and simulated time series. The tool draws on recent advances in the theory of the bootstrap, Kolmogorov type testing, and other work on the evaluation of DSGEs, aimed at comparing the second order properties of historical and simulated time series. We begin by fixing a given model as the “benchmark” model, against which all “alternative” models are to be compared. We then test whether at least one of the alternative models provides a more “accurate” approximation to the true cumulative distribution than does the benchmark model, where accuracy is measured in terms of distributional square error. Bootstrap critical values are discussed, and an illustrative example is given, in which it is shown that alternative versions of a standard DSGE model in which calibrated parameters are allowed to vary slightly perform equally well. On the other hand, there are stark differences between models when the shocks driving the models are assigned non-plausible variances and/or distributional assumptions.     

The Theory of Socially Embedded Games: Applications and Extensions to Open and Closed Games

An earlier article, drawing on the mathematical theory of rules and rule complexes, extends and generalizes game theory (GGT). The theory has been used to conceptualize and analyze diverse social relationships, roles, and games as particular types of rule complexes.For instance, a social role, as a major basis of a parent's action in a game, consists of at least four key components – which are mathematical objects – in the determination of action: value complex, model of reality (including beliefs and knowledge bases), a repertoire of acts, routines, programs, and strategies, and modality, a role-specific algorithm for determining or generating action in game settings. This article applies and extends GGT in analyses of a market bargaining game (a type of open game) and of the classical game of prisoners' dilemma (a type of closed game). The applications show the concrete effects of social embeddedness on game structuring, game interaction patterns and outcomes, and social equilibria.     

An effective step-down algorithm for the construction and the identification of nonisomorphic orthogonal arrays

In this paper we present an effective algorithm for the construction and the identification of two-level nonisomorphic orthogonal arrays. Using this algorithm, we identify and list a full catalogue of nonisomorphic orthogonal arrays with parameters OA(24,7,2,t), OA(28,6,2,t) and OA(32,6,2,t), t ≥ 2. Some statistical properties of these designs are also considered.     

When haste makes sense: Cracking down on street markets for illicit drugs

This paper presents an analytical approach to the tactical question: ‘What level of enforcement over time allows one to eliminate a street market for illicit drugs while expanding the least possible total effort?’ The analysis is done in the context of Caulkins' model [6] which predicts the rate of change of dealers as a function of enforcement level and several market parameters. Our analysis suggests that the simple strategy of using the maximum available enforcement intensity until the market has been eliminated minimizes the total enforcement effort required.