Axiomatic Fuzzy Set Theory and Its Applications
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 2009
Springer Berlin (Verlag)
978-3-642-10146-5 (ISBN)
Springer Berlin (Verlag)
978-3-642-10146-5 (ISBN)
This volume examines Axiomatic Fuzzy Sets (AFS), in which fuzzy sets and probability are treated in a unified and coherent fashion. It presents AFS as a rigorous mathematical theory as well as a flexible methodology for the development of intelligent systems.
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.
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.
Required Preliminary Mathematical Knowledge.- Fundamentals.- Lattices.- Methodology and Mathematical Framework of AFS Theory.- Boolean Matrices and Binary Relations.- AFS Logic, AFS Structure and Coherence Membership Functions.- AFS Algebras and Their Representations of Membership Degrees.- Applications of AFS Theory.- AFS Fuzzy Rough Sets.- AFS Topology and Its Applications.- AFS Formal Concept and AFS Fuzzy Formal Concept Analysis.- AFS Fuzzy Clustering Analysis.- AFS Fuzzy Classifiers.
| Erscheint lt. Verlag | 21.10.2010 |
|---|---|
| Reihe/Serie | Studies in Fuzziness and Soft Computing |
| Zusatzinfo | XVIII, 514 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 793 g |
| Themenwelt | Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik | |
| Schlagworte | AFS Theory • Algebra • Applications of AFS Theory • Axiomatic Fuzzy Set Theory • Fuzziness • fuzzy • Intelligent Systems • Knowledge • Mathematica |
| ISBN-10 | 3-642-10146-1 / 3642101461 |
| ISBN-13 | 978-3-642-10146-5 / 9783642101465 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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