Fuzzy Sets And Membership Functions
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Fundamentals of Fuzzy Sets
Author: Didier Dubois
language: en
Publisher: Springer Science & Business Media
Release Date: 2000-01-31
Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.
Axiomatic Fuzzy Set Theory and Its Applications
Author: Xiaodong Liu
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-07
It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.
Advanced Dynamic-System Simulation
A unique, hands-on guide to interactive modeling and simulation of engineering systems This book describes advanced, cutting-edge techniques for dynamic system simulation using the DESIRE modeling/simulation software package. It offers detailed guidance on how to implement the software, providing scientists and engineers with powerful tools for creating simulation scenarios and experiments for such dynamic systems as aerospace vehicles, control systems, or biological systems. Along with two new chapters on neural networks, Advanced Dynamic-System Simulation, Second Edition revamps and updates all the material, clarifying explanations and adding many new examples. A bundled CD contains an industrial-strength version of OPEN DESIRE as well as hundreds of program examples that readers can use in their own experiments. The only book on the market to demonstrate model replication and Monte Carlo simulation of real-world engineering systems, this volume: Presents a newly revised systematic procedure for difference-equation modeling Covers runtime vector compilation for fast model replication on a personal computer Discusses parameter-influence studies, introducing very fast vectorized statistics computation Highlights Monte Carlo studies of the effects of noise and manufacturing tolerances for control-system modeling Demonstrates fast, compact vector models of neural networks for control engineering Features vectorized programs for fuzzy-set controllers, partial differential equations, and agro-ecological modeling Advanced Dynamic-System Simulation, Second Edition is a truly useful resource for researchers and design engineers in control and aerospace engineering, ecology, and agricultural planning. It is also an excellent guide for students using DESIRE.