Bøger i Theory and Decision Library B serien

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.

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.

This book is devoted to presenting theoretical fundamentals for the methods of multiple criteria decision making (MCDM) in the social sciences with particular intent to their applicability to real-world decision making.

Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their (too) categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

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.

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.

This dichotomous structure of methods very often forced the modeller to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real prob lems.

This dichotomous structure of methods very often forced the modeller to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real prob lems.

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.

The areas covered included topics in the analysis of repeated measurements, cluster analysis, discriminant analysis, canonical cor relations, distribution theory and testing, bivariate densi ty estimation, factor analysis, principle component analysis, multidimensional scaling, multivariate linear models, nonparametric regression, etc.

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.

In this volume we present some of the papers delivered at FUR-IV - the Fourth International Conference on Founda tions and Applications of Utility, Risk and Decision Theory in Budapest, June 1988.

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;

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.

The reader will find here thirty~nine selected papers which were given at FUR-III, the third international confe rence on the Foundations and applications of Utility, Risk and decision theories, held in Aix-en-Provence in June 1986.

Quantitative Methods for Portfolio Analysis provides practical models and methods for the quantitative analysis of financial asset prices, construction of various portfolios, and computer-assisted trading systems.

Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their (too) categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

As desired, the infonnation demand correspondence is single valued at equilibrium prices. P (F *), almost every a E A demands a unique combined infonnation structure (although traders may be indifferent among partial infonnation sales from different information allocations, etc.

In the Russian edition published in 1989, this book was called "Minimax Algorithms in Problems of Numerical Analysis". Thus, the computation model is the epicenter of any structure studied in the book. This approach leads to the concept of sequentially optimal algorithms, which play the central role in the book.

In this way classical analytical mechanics was able to establish some general results, gaining insight through explicit solution of some simple cases and developing various methods of approximation for handling more complicated ones.

Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common.

Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets.

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.