Bøger i Theory and Decision Library B serien

Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures.

Econometrics as an applied discipline attempts to use information in a most efficient manner, yet the information theory and entropy approach developed by Shannon and others has not played much of a role in applied econometrics.

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis.

Beliefs, Interactions and Preferences in Decision Making mixes a selection of papers, presented at the Eighth Foundations and Applications of Utility and Risk Theory (`FUR VIII') conference in Mons, Belgium, together with a few solicited papers from well-known authors in the field.

Aggregation of individual opinions into a social decision is a problem widely observed in everyday life.

Beliefs, Interactions and Preferences in Decision Making mixes a selection of papers, presented at the Eighth Foundations and Applications of Utility and Risk Theory (`FUR VIII') conference in Mons, Belgium, together with a few solicited papers from well-known authors in the field.

After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975).

It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision.

Making use of different frameworks of approximate reasoning and reasoning under uncertainty, notably probabilistic and fuzzy set-based techniques, this book develops formal models of the above inference principle, which is fundamental to CBR.

A Course in Mathematical and Statistical Ecology

Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.

An investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis.

Points out gaps in the way data fusion problems are conceptually treated and addresses this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic way. This book offers research progress on data fusion and serves as an introduction to powerful techniques.

Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Normative decision theory is much more formalized than descriptive theory.

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis.

But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions.

Models and Experiments in Risk and Rationality presents original contributions to the areas of individual choice, experimental economics, operations and analysis, multiple criteria decision making, market uncertainty, game theory and social choice.

Econometrics as an applied discipline attempts to use information in a most efficient manner, yet the information theory and entropy approach developed by Shannon and others has not played much of a role in applied econometrics.

Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application.

Multivariate Statistical Analysis

Use and misuse of statistics seems to be the signum temporis of past decades. In Part One we present the consecutive stages of formalization of statistical problems, i.e., the description of the experiment, the presentation of the aim of the investigation, and of the constraints put upon the decision rules.

Methods of ap plied stochastic control using stochastic processes have now reached an exciti~g phase, where several disciplines like systems engineering, operations research and natural reso- ces interact along with the conventional fields such as mathematical economics, finance and control systems.

The basic model of a decision in classical normative decision theory has very little in common with real decision making: It portrays a decision as a clear-cut act of choice, performed by one individual decision maker and in which states of nature, possible actions, results and preferences are well and crisply defined.

This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme;

A note on numbering of statements and references: The numbering of Lemmata, Propositions, Theorems, Corollaries and (separately) formulae starts anew in each section. If quoted in another section, the section number is added, e.g.

Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Normative decision theory is much more formalized than descriptive theory.

This volume contains most of the invited and contributed papers presented at the Conference on Robustness of Statistical Methods and Nonparametric Statistics held in the castle oj'Schwerin, Mai 29 - June 4 1983. This conference was organized by the Mathematical Society of the GDR in cooperation with the Society of Physical and Mathematical Biology of the GDR, the GDR-Region of the International Biometric Society and the Academy of Agricultural Sciences of the GDR. All papers included were thoroughly reviewed by scientist listed under the heading "Editorial Collabora­ tories·'. Some contributions, we are sorry to report, were not recommended for publi­ cation by the rf'vif'wers and do not appear in these proceedings. The editors thank the reviewers for their valuable comments and suggestions. The conference was organizf'd bv a Programme Committee, its chairman was Prof. Dr. Dieter Rasch (Research Centre of Animal Production, Dummerstorf-Rostock). The members of the Programme Committee were Prof. Dr. ,Johannes Adam (Martin-Luther-University Halle) Prof. Dr. Heinz Ahrens (Academy of Sciences of the GDR, Berlin) Doz. Dr. Jana Jureckova (Charles University Praha) Prof. Dr. Moti Lal Tiku (McMaster University, Hamilton, Ontario) The aim of the conference was to discuss several aspects of robustness but mainly to present new results regarding the robustness of classical statistical methods especially tests, confidence estimations, and selection procedures, and to compare their perfor­ mance with nonparametric procedures. Robustness in this sens~ is understood as intensivity against. violation of the normal assumption.