Download or read book Additive and Polynomial Representations written by David H. Krantz and published by Courier Corporation. This book was released on 2006-12-01 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: All of the sciences — physical, biological, and social — have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence. Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures. Volume II extends the subject in the direction of geometrical, threshold, and probabilistic representations, and Volume III examines representation as expressed in axiomatization and invariance.
Download or read book Additive and Polynomial Representations written by David H. Krantz and published by Academic Press. This book was released on 2014-05-12 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.
Download or read book Foundations of measurement written by and published by . This book was released on 1971 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Number Theory of Polynomials Over a Finite Field written by Gove W. Effinger and published by . This book was released on 1991 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps gather the sum of additive number theory.
Download or read book Rings with Polynomial Identities and Finite Dimensional Representations of Algebras written by Eli Aljadeff and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Download or read book Constructing Scalar Valued Objective Functions written by Andranik Tangian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several decades, scholars have developed methods for solving optimization problems which emerge in economics, econometrics, operations research, and other disciplines. A considerable effort has been made to construct equations from which constraints can be derived, but surprisingly little has been done to construct the other part of optimization models: the scalar-valued objective function, the constrained maximum or minimum of which gives the optimal solution. The given volume is intended to attract attention to the problem, to present the major achievements in the field and to stimulate further research and teaching.
Download or read book Multiple Criteria Decision Analysis State of the Art Surveys written by Salvatore Greco and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 1063 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Criteria Decision Analysis: State of the Art Surveys provides survey articles and references of the seminal or state-of-the-art research on MCDA. The material covered ranges from the foundations of MCDA, over various MCDA methodologies (outranking methods, multiattribute utility and value theories, non-classical approaches) to multiobjective mathematical programming, MCDA applications, and software. This vast amount of material is organized in 8 parts, with a total of 25 chapters. More than 2000 references are listed.
Download or read book Mathematical Psychology written by Jean-Paul Doignon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sometime in the late sixties, one of the editors of this volume realized that the mathematica psychologists in Europe-an odd lot mostly concentrated in Germany, the Netherlands, France, England and Belgium-were suffering from an acute sense of isolation. The papers that they presented at meetings of their national or regional societies had to be 'sanitized' to the point of misrepresentation. They were misunderstood. The mood was grim, depression was lurking. He decided that urgent action was required: a European gathering of mathematical psychologists was called in April 1971. Not being foolhardy, however, he took the precaution of choosing Paris as the meeting place. Around thirty mathematical psychologists received an invitation. They all came, justifying at least Paris's reputation. The meeting took place at the 'Maison des Belges' of the Cite Universitaire, Boulevard Jourdan, in front of the Parc Montsouris. As far as everyone remembers, the meeting was a full success. A happy birth had taken place. This editor then irresponsibly accepted a position in a university in the US, leaving an infant to the whims of the passers-by. Fortunately, a godfather came along. The next meeting took place in Nijmegen, in November 1971, under the loving care of Eddy Roskam. A tradition was established. The third meeting was in Oxford (1972); then in Marseilles (1973), Regensburg (1974), Stirling (1975), Stockholm (1976) . . . The infant became a toddler, then a vigorous child. This annual meeting is now an important event in the field.
Download or read book Decision Making Process written by Denis Bouyssou and published by John Wiley & Sons. This book was released on 2013-05-10 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the main methods and results in the formal study of the human decision-making process, as defined in a relatively wide sense. A key aim of the approach contained here is to try to break down barriers between various disciplines encompassed by this field, including psychology, economics and computer science. All these approaches have contributed to progress in this very important and much-studied topic in the past, but none have proved sufficient so far to define a complete understanding of the highly complex processes and outcomes. This book provides the reader with state-of-the-art coverage of the field, essentially forming a roadmap to the field of decision analysis. The first part of the book is devoted to basic concepts and techniques for representing and solving decision problems, ranging from operational research to artificial intelligence. Later chapters provide an extensive overview of the decision-making process under conditions of risk and uncertainty. Finally, there are chapters covering various approaches to multi-criteria decision-making. Each chapter is written by experts in the topic concerned, and contains an extensive bibliography for further reading and reference.
Download or read book Intelligent Decision Support Systems written by Salvatore Greco and published by Springer Nature. This book was released on 2022-05-31 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of essays written by leading researchers to honor Roman Słowiński’s major scholarly interests and contributions. He is well-known for conducting extensive research on methodologies and techniques for intelligent decision support, where he combines operational research and artificial intelligence. The book reconstructs his main contributions, presents cutting-edge research and provides an outlook on the most promising and advanced domains of computer science and multiple criteria decision aiding. The respective chapters cover a wide range of related research areas, including decision sciences, ordinal data mining, preference learning and multiple criteria decision aiding, modeling of uncertainty and imprecision in decision problems, rough set theory, fuzzy set theory, multi-objective optimization, project scheduling and decision support applications. As such, the book will appeal to researchers and scholars in related fields.
Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.
Download or read book Escaping from Bad Decisions written by Kazuhisa Takemura and published by Academic Press. This book was released on 2021-07-27 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Escaping from Bad Decisions presents a modern conceptual and mathematical framework of the decision-making process. By interpreting ordinal utility theory as normative analysis examined in view of rationality, it shows how decision-making under certainty, risk, and uncertainty can be better understood. It provides a critical examination of psychological models in multi-attribute decision-making, and evaluates the constitutive elements of "good" and "bad" decisions. Multi-attribute decision-making is analysed descriptively, based on the psychological model of decision-making and computer simulations of decision strategies. Finally, prescriptive examinations of multi-attribute decision-making are performed, supporting the argument that decision-making from a pluralistic perspective creates results that can help "escape" from bad decisions. This book will be of particular interest to graduate students and early career researchers in economics, decision-theory, behavioral economics, experimental economics, psychology, cognitive sciences, and decision neurosciences. Provides a comprehensive background to the phenomena of bad decisions, considered in their economic, psychological and cognitive aspects Reinterprets existing theories and phenomena and proposes a new overview of decision behaviors by integrating mathematical and psychological perspectives Adapts model-based techniques, such as mathematical model based functional magnetic resonance imaging (fMRI) using mathematical models of the decision process
Download or read book The Handbook of Rational and Social Choice written by Paul Anand and published by Oxford University Press. This book was released on 2009-01-15 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an overview of issues arising in work on the foundations of decision theory and social choice. The collection will be of particular value to researchers in economics with interests in utility or welfare, but also to any social scientist or philosopher interested in theories of rationality or group decision-making.
Download or read book Information Processing and Management of Uncertainty in Knowledge Based Systems written by Joao Paulo Carvalho and published by Springer. This book was released on 2016-06-10 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set (CCIS 610 and 611) constitute the proceedings of the 16th International Conference on Information processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, held in Eindhoven, The Netherlands, in June 2016. The 127 revised full papers presented together with four invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy measures and integrals; uncertainty quantification with imprecise probability; textual data processing; belief functions theory and its applications; graphical models; fuzzy implications functions; applications in medicine and bioinformatics; real-world applications; soft computing for image processing; clustering; fuzzy logic, formal concept analysis and rough sets; graded and many-valued modal logics; imperfect databases; multiple criteria decision methods; argumentation and belief revision; databases and information systems; conceptual aspects of data aggregation and complex data fusion; fuzzy sets and fuzzy logic; decision support; comparison measures; machine learning; social data processing; temporal data processing; aggregation.
Download or read book Advances in Decision Analysis written by Nadine Meskens and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book fmds its roots in the International Conference on Methods and Applications of Multiple Criteria Decision Making held in Mons in May 1997. A small number of contributions to that conference were selected via a refereeing procedure and retained authors were requested to include in their final version their more recent results. This explains why some papers differ significantly from the original presentation. The introductory paper of Raynaud addresses the long range forecasts in Multiple Criteria Decision Making on the basis of a Delphi process that was run before and during the congress. In a second part, the French author explains how he and some of his partners could find the proof of an important conjecture : the iteration of a strongly monotonic choice function is not a strongly monotonic ranking function. The second part of the book covers methodological aspects of decision theory. The contribution of Bouyssou and Pirlot concerns the reformulation of classical conjoint measurement models that induce a complete and transitive preference binary relation on the set of alternatives which seem to be unrealistic when decision makers are asked to compare objects evaluated on several attributes. The authors propose to consider non transitive, non complete and non additive decomposable conjoint models. They define properties that characterize such models.
Download or read book Finite Fields and Applications written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 2008 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.
Download or read book The Metaphysics of Quantities written by J. E. Wolff and published by Oxford University Press. This book was released on 2020-05-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: What are physical quantities, and in particular, what makes them quantitative? This book articulates and defends an original answer to this important, insufficiently understood question through the novel position of substantival structuralism. This position argues that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces. The book first explores what it means for an attribute to be quantitative, and what metaphysical implications a commitment to quantitative attributes has. It then sets the stage to address the metaphysical and ontological consequences of the existence of quantitative attributes.
