Integration Of Fuzzy Logic And Chaos Theory
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Integration of Fuzzy Logic and Chaos Theory
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 fundamental concepts, theories, as well as technologies. In particular, fuzzy systems technology has achieved its maturity with widespread applications in many industrial, commercial, and technical ?elds, ranging from control, automation, and arti?cial intelligence to image/signal processing,patternrecognition,andelectroniccommerce.Chaos,ontheother hand,wasconsideredoneofthethreemonumentaldiscoveriesofthetwentieth century together with the theory of relativity and quantum mechanics. As a very special nonlinear dynamical phenomenon, chaos has reached its current outstanding status from being merely a scienti?c curiosity in the mid-1960s to an applicable technology in the late 1990s. Finding the intrinsic relation between fuzzy logic and chaos theory is certainlyofsigni?cantinterestandofpotentialimportance.Thepast20years have indeed witnessed some serious explorations of the interactions between fuzzylogicandchaostheory,leadingtosuchresearchtopicsasfuzzymodeling of chaotic systems using Takagi–Sugeno models, linguistic descriptions of chaotic systems, fuzzy control of chaos, and a combination of fuzzy control technology and chaos theory for various engineering practices.
Advances in Chaos Theory and Intelligent Control
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate students, researchers, and practitioners in the areas of chaos theory and intelligent control.
Fuzzy Logic
In order to properly characterize the content of this book, it is important to clarify ?rst the intended meaning of its title Fuzzy Logic. This clari?cation is needed since the term “fuzzy logic,” as currently used in the literature, is viewed either in a narrow sense or in a broad sense. In the narrow sense, fuzzy logic is viewed as an area devoted to the formal development, in a u- ?ed way, of the various logical systems of many-valued logic. It is concerned withformalizingsyntactic aspects(basedonthenotionofproof)andsemantic aspects (based on the notion oftruth) of the variouslogical calculi. In order to be acceptable, each of these logical calculi must be sound (provability implies truth) and complete (truth implies provability). The most representativep- lication of fuzzy logic in this sense is, in my opinion, the classic book by Peter Hajek [1]. When the term “fuzzy logic” is viewed in the broad sense, it refers to an extensive agenda whose primary aim is to utilize the apparatus of fuzzy set theoryfordevelopingsoundconcepts,principles,andmethodsforrepresenting and dealing with knowledge expressed by statements in natural language. Although workin fuzzy logicin the broadsense is not directly concernedwith the issues that are investigated under fuzzy logic in the narrow sense, the importance of the latter is that it provides the former with solid theoretical foundations. After examining the content of this book, it is easy to conclude that its title,FuzzyLogic, referstofuzzylogicinthebroadsense. Thisisconsistent,by and large, with the usual meaning of the term “fuzzy logic” in the literature.