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Mathematics of Uncertainty
"Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.
Fuzziness and Approximate Reasoning
We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The “degree” of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.
Management of Knowledge Imperfection in Building Intelligent Systems
There are many good AI books. Usually they consecrate at most one or two chapters to the imprecision knowledge processing. To our knowledge this is among the few books to be entirely dedicated to the treatment of knowledge imperfection when bui- ing intelligent systems. We consider that an entire book should be focused on this important aspect of knowledge processing. The expected audience for this book - cludes undergraduate students in computer science, IT&C, mathematics, business, medicine, etc. , graduates, specialists and researchers in these fields. The subjects treated in the book include expert systems, knowledge representation, reasoning under knowledge Imperfection (Probability The...
Towards a New Evolutionary Computation
Estimation of Distribution Algorithms (EDAs) are a set of algorithms in the Evolutionary Computation (EC) field characterized by the use of explicit probability distributions in optimization. Contrarily to other EC techniques such as the broadly known Genetic Algorithms (GAs) in EDAs, the crossover and mutation operators are substituted by the sampling of a distribution previously learnt from the selected individuals. EDAs have experienced a high development that has transformed them into an established discipline within the EC field. This book attracts the interest of new researchers in the EC field as well as in other optimization disciplines, and that it becomes a reference for all of us working on this topic. The twelve chapters of this book can be divided into those that endeavor to set a sound theoretical basis for EDAs, those that broaden the methodology of EDAs and finally those that have an applied objective.
Applying Fuzzy Mathematics to Formal Models in Comparative Politics
This book explores the intersection of fuzzy mathematics and the spatial modeling of preferences in political science. Beginning with a critique of conventional modeling approaches predicated on Cantor set theoretical assumptions, the authors outline the potential benefits of a fuzzy approach to the study of ambiguous or uncertain preference profiles. This is a good text for a graduate seminar in formal modeling. It is also suitable as an introductory text in fuzzy mathematics.
Epistemic Foundations of Fuzziness
This monograph is a treatment on optimal fuzzy rationality as an enveloping of decision-choice rationalities where limited information, vagueness, ambiguities and inexactness are essential characteristics of our knowledge structure and reasoning processes. The volume is devoted to a unified system of epistemic models and theories of decision-choice behavior under total uncertainties composed of fuzzy and stochastic types. The unified epistemic analysis of decision-choice models and theories begins with the question of how best to integrate vagueness, ambiguities, limited information, subjectivity and approximation into the decision-choice process. The answer to the question leads to the shif...
Algorithms for Fuzzy Clustering
Recently many researchers are working on cluster analysis as a main tool for exploratory data analysis and data mining. A notable feature is that specialists in di?erent ?elds of sciences are considering the tool of data clustering to be useful. A major reason is that clustering algorithms and software are ?exible in thesensethatdi?erentmathematicalframeworksareemployedinthealgorithms and a user can select a suitable method according to his application. Moreover clusteringalgorithmshavedi?erentoutputsrangingfromtheolddendrogramsof agglomerativeclustering to more recent self-organizingmaps. Thus, a researcher or user can choose an appropriate output suited to his purpose,which is another ?exi...
Knowledge Representation Techniques
This book contains a cohesive, self-contained collection of theoretical and applied research results that have been achieved in this project which pertain to nonmonotonic and approximate easoning systems developed for an experimental unmanned aerial vehicle system used in the project. This book should be of interest to the theoretician and applied researcher alike and to autonomous system developers and software agent and intelligent system developers.
Innovations in Machine Learning
Machine learning is currently one of the most rapidly growing areas of research in computer science. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. This book covers the three main learning systems; symbolic learning, neural networks and genetic algorithms as well as providing a tutorial on learning casual influences. Each of the nine chapters is self-contained. Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Postgraduate since it shows the direction of current research.
Soft Computing Applications in Business
Soft computing techniques are widely used in most businesses. This book consists of several important papers on the applications of soft computing techniques for the business field. The soft computing techniques used in this book include (or very closely related to): Bayesian networks, biclustering methods, case-based reasoning, data mining, Dempster-Shafer theory, ensemble learning, evolutionary programming, fuzzy decision trees, hidden Markov models, intelligent agents, k-means clustering, maximum likelihood Hebbian learning, neural networks, opportunistic scheduling, probability distributions combined with Monte Carlo methods, rough sets, self organizing maps, support vector machines, unc...
