Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information. Key Features: Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data. Describes methods of increasing importance with applications in areas such as environmental statistics and social science. Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples. Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data. This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
Decision making by the aircrafts services of the international airport, which provides for intensive traffic of aircraft and their ground handling, becomes a very topical issue. If earlier it was believed that the intensity is provided only by the number of runways, nowadays a large accumulation of aircraft on the airport platform-field creates equally complex difficulties in comparison with aircraft take-offs and landings. Solving such problems with the use of «crisp methods» of queuing theory gives little. This article deals with modern «fuzzy methods» based on simulation modeling and fuzzy logic.
В книге рассмотрены вопросы практического применения программного продукта Fuzzy For Excel V.1.0, разработанного фирмой ИНЭКС (Украина) для проведения прогнозных коммерческих расчетов в условиях объективной и субъективной неопределенности. Особое вниманиеуделено вопросам влияния неопределенности при прогнозировании на появление рисков коммерческих проектов. Моделирование неопределенности при прогнозировании на появление рисков коммерческих проектов. Моделирование неопределенности реализуется на базе перспективных подходов Fuzzy-технологии, и в частности, при использовании нечетких чисел. рассматривается триада `прогноз-неопределенность-риск`. Приведены практические примеры применения расчетов на Fuzzy For Excel V.1.0 в условиях неопределенности рынка, процентных ставок, курсов валют.
Explains for the first time how «computing with words» can aid in making subjective judgments Lotfi Zadeh, the father of fuzzy logic, coined the phrase «computing with words» (CWW) to describe a methodology in which the objects of computation are words and propositions drawn from a natural language. Perceptual Computing explains how to implement CWW to aid in the important area of making subjective judgments, using a methodology that leads to an interactive device—a «Perceptual Computer»—that propagates random and linguistic uncertainties into the subjective judgment in a way that can be modeled and observed by the judgment maker. This book focuses on the three components of a Perceptual Computer—encoder, CWW engines, and decoder—and then provides detailed applications for each. It uses interval type-2 fuzzy sets (IT2 FSs) and fuzzy logic as the mathematical vehicle for perceptual computing, because such fuzzy sets can model first-order linguistic uncertainties whereas the usual kind of fuzzy sets cannot. Drawing upon the work on subjective judgments that Jerry Mendel and his students completed over the past decade, Perceptual Computing shows readers how to: Map word-data with its inherent uncertainties into an IT2 FS that captures these uncertainties Use uncertainty measures to quantify linguistic uncertainties Compare IT2 FSs by using similarity and rank Compute the subsethood of one IT2 FS in another such set Aggregate disparate data, ranging from numbers to uniformly weighted intervals to nonuniformly weighted intervals to words Aggregate multiple-fired IF-THEN rules so that the integrity of word IT2 FS models is preserved Free MATLAB-based software is also available online so readers can apply the methodology of perceptual computing immediately, and even try to improve upon it. Perceptual Computing is an important go-to for researchers and students in the fields of artificial intelligence and fuzzy logic, as well as for operations researchers, decision makers, psychologists, computer scientists, and computational intelligence experts.
The training system is implemented with the use of the fuzzy classifier that represents fuzzy knowledge base, the input of which receives signals about current state of the traction rolling stock and of the environment. The results of the work allow implementing intelligent DSS in modern locomotives. This will enhance the level of safety and efficiency of driving a train.
Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about: Formal Logic Syllogisms Constructing proofs and refutations Propositional and predicate logic Modal and fuzzy logic Symbolic logic Deductive and inductive reasoning Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.