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Orders: Description and Roles
Orders: Description and Roles
Knowledge Spaces
Knowledge Spaces offers a rigorous mathematical foundation for various practical systems of knowledge assessment, applied to real and simulated data. The systematic presentation extends research results to new situations, as well as describing how to build the knowledge structure in practice. The book also contains numerous examples and exercises and an extensive bibliography. This interdisciplinary representation of the theory of knowledge spaces will be of interest to mathematically oriented readers in computer science and combinatorics.
Aiding Decisions with Multiple Criteria
Aiding Decisions With Multiple Criteria: Essays in Honor of Bernard Roy is organized around two broad themes: Graph Theory with path-breaking contributions on the theory of flows in networks and project scheduling, Multiple Criteria Decision Aiding with the invention of the family of ELECTRE methods and methodological contribution to decision-aiding which lead to the creation of Multi-Criteria Decision Analysis (MCDA). Professor Bernard Roy has had considerable influence on the development of these two broad areas. £/LIST£ Part one contains papers by Jacques Lesourne, and Dominique de Werra & Pierre Hansen related to the early career of Bernard Roy when he developed many new techniques and...
The Mathematics of Preference, Choice and Order
Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.
Handbook of Computational Social Choice
A comprehensive survey of computational aspects of collective decisions for graduate students, researchers, and professionals in computer science and economics.
Learning Spaces
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of ALEKS is an artificial intelligence engine that assesses each student individually and continously. The book is of interest to mathematically oriented readers in education, computer science, engineering, and combinatorics at research and graduate levels. Numerous examples and exercises are included, together with an extensive bibliography.
Mathematical Analyses of Decisions, Voting and Games
This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.
Social Choice, Welfare, and Ethics
Parts three and four are devoted to algebraic and combinatorial aspects of social choice theory, including analyses of Arrow's Theorem, consensus functions, and the role of geometry. Part five deals with the application of cooperative game theory to social choice.
Non-Conventional Preference Relations in Decision Making
The important issue of how to overcome rigidness, inadequacy and human inconsistency regarding conventional assumptions on preferences in decision making (for example, regarding yes/no crispness or transitivity) is discussed by well-known experts in this volume. In the introductory articles, analyses of those conventional assumptions are given and the need for reconsiderations and changes as to preference-related aspects is advocated. The following contributions are mainly concerned with issues related to valued (including fuzzy) preference relations, such as analysis of their properties and their use in various decision making and choice problems and in group decision making.
