This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy subgroups of a group. It includes applications to abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are discussed. Construction of free fuzzy subgroups is determined. Numerical invariants of fuzzy subgroups of Abelian groups are developed. The problem in group theory of obtaining conditions under which a group can...
This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy...
This book is devoted to reporting innovative and significant progress in fuzzy system engineering. Given the maturation of fuzzy logic, this book is dedicated to exploring the recent breakthroughs in fuzziness and soft computing in favour of intelligent system engineering. This monograph presents novel developments of the fuzzy theory as well as interesting applications of the fuzzy logic exploiting the theory to engineer intelligent systems.
This book is devoted to reporting innovative and significant progress in fuzzy system engineering. Given the maturation of fuzzy logic, this book i...
Rule-basedevolutionaryonlinelearningsystems, oftenreferredtoasMichig- style learning classi?er systems (LCSs), were proposed nearly thirty years ago (Holland, 1976; Holland, 1977) originally calling them cognitive systems. LCSs combine the strength of reinforcement learning with the generali- tion capabilities of genetic algorithms promising a ?exible, online general- ing, solely reinforcement dependent learning system. However, despite several initial successful applications of LCSs and their interesting relations with a- mal learning and cognition, understanding of the systems remained...
Rule-basedevolutionaryonlinelearningsystems, oftenreferredtoasMichig- style learning classi?er systems (LCSs), were proposed nearly thirty years ago (...
The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot? A. Zadeh were so c- fusing that they were called fuzzy set theory and fuzzy logic; a deterministic system found by E. N. Lorenz to have random behaviours was so unusual that it was lately named a chaotic system. Just like irrational and imaginary numbers, negative energy, anti-matter, etc., fuzzy logic and chaos were gr- ually and eventually accepted by many, if not all, scientists and engineers as...
The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set t...
1. 1 Introduction This book is written in two major parts. The ?rst part includes the int- ductory chapters consisting of Chapters 1 through 6. In part two, Chapters 7-26, we present the applications. This book continues our research into simulating fuzzy systems. We started with investigating simulating discrete event fuzzy systems ( 7], 13], 14]). These systems can usually be described as queuing networks. Items (transactions) arrive at various points in the s- tem and go into a queue waiting for service. The service stations, preceded by a queue, are connected forming a network of queues...
1. 1 Introduction This book is written in two major parts. The ?rst part includes the int- ductory chapters consisting of Chapters 1 through 6. In par...
"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...
"Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variabi...
Genetic algorithms (GAs) are powerful search techniques based on principles of evolution and widely applied to solve problems in many disciplines. However, most GAs employed in practice nowadays are unable to learn genetic linkage and suffer from the linkage problem. The linkage learning genetic algorithm (LLGA) was proposed to tackle the linkage problem with several specially designed mechanisms. While the LLGA performs much better on badly scaled problems than simple GAs, it does not work well on uniformly scaled problems as other competent GAs. Therefore, we need to understand why it is...
Genetic algorithms (GAs) are powerful search techniques based on principles of evolution and widely applied to solve problems in many disciplines. ...
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...
Estimation of Distribution Algorithms (EDAs) are a set of algorithms in the Evolutionary Computation (EC) field characterized by the use of explici...
From a linguistic perspective, it is quanti?cation which makes all the di?- ence between "having no dollars" and "having a lot of dollars." And it is the meaning of the quanti?er "most" which eventually decides if "Most Ame- cans voted Kerry" or "Most Americans voted Bush" (as it stands). Natural language(NL)quanti?erslike"all,""almostall,""many"etc. serveanimp- tant purpose because they permit us to speak about properties of collections, as opposed to describing speci?c individuals only; in technical terms, qu- ti?ers are a 'second-order' construct. Thus the quantifying statement "Most...
From a linguistic perspective, it is quanti?cation which makes all the di?- ence between "having no dollars" and "having a lot of dollars." And it is ...
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...
Machine learning is currently one of the most rapidly growing areas of research in computer science. In compiling this volume we have brought together...
