Counting belongs to the most elementary and frequent mental activities of human beings. Its results are a basis for coming to a decision in a lot of situations and dimensions of our life. This book presents a novel ap...
详细信息
ISBN:
(数字)9783642346859
ISBN:
(纸本)9783642346842;9783642346859
Counting belongs to the most elementary and frequent mental activities of human beings. Its results are a basis for coming to a decision in a lot of situations and dimensions of our life. This book presents a novel approach to the advanced and sophisticated case, called intelligent counting, in which the objects of counting are imprecisely, fuzzily specified. Formally, this collapses to counting in fuzzy sets, interval-valued fuzzy sets or I-fuzzy sets (Atanassov's intuitionistic fuzzy sets). The monograph is the first one showing and emphasizing that the presented methods of intelligent counting are human-consistent: are reflections and formalizations of real, human counting procedures performed under imprecision and, possibly, incompleteness of information. Other applications of intelligent counting in various areas of intelligent systems and decision support will be discussed, too. The whole presentation is self-contained, systematic, and equipped with many examples, figures and tables. Computer and information scientists, researchers, engineers and practitioners, applied mathematicians, and postgraduate students interested in information imprecision are the target readers.
The development of software system with acceptable level of reliability and quality within available time frame and budget becomes a challenging objective. This objective could be achieved to some extent through early...
详细信息
ISBN:
(数字)9788132211761
ISBN:
(纸本)9788132211754;9788132211761
The development of software system with acceptable level of reliability and quality within available time frame and budget becomes a challenging objective. This objective could be achieved to some extent through early prediction of number of faults present in the software, which reduces the cost of development as it provides an opportunity to make early corrections during development process. The book presents an early software reliability prediction model that will help to grow the reliability of the software systems by monitoring it in each development phase, i.e. from requirement phase to testing phase. Different approaches are discussed in this book to tackle this challenging issue. An important approach presented in this book is a model to classify the modules into two categories (a) fault-prone and (b) not fault-prone. The methods presented in this book for assessing expected number of faults present in the software, assessing expected number of faults present at the end of each phase and classification of software modules in fault-prone or no fault-prone category are easy to understand, develop and use for any practitioner. The practitioners are expected to gain more information about their development process and product reliability, which can help to optimize the resources used.
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for m...
ISBN:
(纸本)3642352200;9783642352201
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.
Fuzzy classiers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientic and business applications. Fuzzy classiers use fuzzy rules and do not require ass...
详细信息
ISBN:
(数字)9783642306044
ISBN:
(纸本)9783642306037
Fuzzy classiers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientic and business applications. Fuzzy classiers use fuzzy rules and do not require assumptions common to statistical classication. Rough set theory is useful when data sets are incomplete. It denes a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classication. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a nite set of learning models, usually weak learners. The present book discusses the three aforementioned elds fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed on the possibility to combine fuzzy rules from fuzzy systems being members of classication ensemble. Furthermore, an emphasis is placed on ensembles that can work on incomplete data, thanks to rough set theory. .
The purpose of this book is to presenta methodology for designing and tuning fuzzyexpert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information....
详细信息
ISBN:
(数字)9783642257865
ISBN:
(纸本)9783642257858
The purpose of this book is to presenta methodology for designing and tuning fuzzyexpert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2analyzesdirect fuzzy inference based on fuzzy if-then rules. Chapter 3is devoted to the tuning of fuzzy rulesfor direct inference using genetic algorithms and neural nets. Chapter4presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describesa method for solving fuzzy logic equationsnecessary for the inverse fuzzy inference indiagnostic systems. Chapters6 and 7 aredevoted to inverse fuzzy inferencebased on fuzzy relations andfuzzy rules. Chapter 8presents a method for extracting fuzzy relations from data. Allthe algorithms presented in Chapters 2-8 arevalidated by computer experiments and illustrated bysolving medical and technicalforecasting anddiagnosis problems. Finally, Chapter 9includes applications of the proposed methodology in dynamicand inventory control systems, prediction of results of football games,decisionmaking in road accident investigations, project management and reliability analysis.
In essence, computing with Words (CWW) is a system of computation in which the objects of computation are predominantly words, phrases and propositions drawn from a natural language. CWW is based on fuzzy logic. In sc...
ISBN:
(数字)9783642274732
ISBN:
(纸本)9783642274725
In essence, computing with Words (CWW) is a system of computation in which the objects of computation are predominantly words, phrases and propositions drawn from a natural language. CWW is based on fuzzy logic. In science there is a deep-seated tradition of according muchmore respect to numbers than to words. In a fundamental way, CWW is a challenge to this tradition. What is not widely recognized is that, today, words are used in place of numbers in a wide variety of applications ranging from digital cameras and household appliancesto fraud detection systems, biomedicalinstrumentation and subway trains. CWW offersa unique capabilitythe capability to precisiate natural language. Unprecisiated (raw) natural language cannot be computed with. A key concept which underlies precisiation of meaning is that of the meaning postulate: A proposition, p, is a restriction on the values which a variable, Xa variable which is implicit in pis allowed to take. CWW has an important ramification for mathematics. Addition of the formalism of CWW to mathematics empowers mathematics to construct mathematical solutions of computational problems which are stated in a natural language. Traditional mathematics does not have this capability.
This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the authors previous book on Intuitionistic...
详细信息
ISBN:
(数字)9783642291272
ISBN:
(纸本)9783642291265
This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the authors previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, studies in fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the authors most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.
暂无评论