Theory of Fuzzy Computation

verfasst von: Apostolos Syropoulos

Verlag: Springer New York

Buchreihe : IFSR International Series in Systems Science and Systems Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. Ideas for future research and explorations are also provided. Students and researchers in computer science and mathematics will benefit from this work.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The fusion of computability theory (CP) with fuzzy set theory (FST) demands a good knowledge of both theories. Thus, this introductory chapter tries to familiarize readers with a number of concepts and ideas that are necessary for the rest of this book. In particular, I start with a review of the events that lead to what is now known as computer science and then I give an overview of FST. The chapter concludes with a description of what the fusion of CP with FST is about and what to expect from it.

Apostolos Syropoulos

Chapter 2. A Précis of Classical Computability Theory

Abstract

Turing machines form the core of computability theory, or recursion theory as it is also known. This chapter introduces basic notions and results and readers already familiar with them can safely skip it. The exposition is based on standard references [18, 39, 67, 83, 109]. In the discussion that follows, the symbol ℕ will stand for the set of positive integer numbers including zero and ℚ will stand for the set of rational numbers.

Apostolos Syropoulos

Chapter 3. Elements of Fuzzy Set Theory

Abstract

The notion of fuzziness lies at the core of fuzzy computability theory. Thus, one should have a basic understanding of the ideas involved. This chapter serves both as a crash course in fuzzy set theory, for those readers that have no previous knowledge of the concepts involved, and as a précis of fuzzy set theory, for those readers familiar with the relevant notions. The exposition that follows is based on [75], while the material for Sect. 3.1 is borrowed from [49, 137].

Apostolos Syropoulos

Chapter 4. On Fuzzy Turing Machines

Abstract

The Turing machine is the archetypal conceptual computing device and as such it is almost always used to define new models of computations by augmenting the functionality of the machine. For example, as was explained in Sect. 2.2.2, a probabilistic model of computation is defined by introducing a probabilistic version of the Turing machine, that is, a machine that operates nondeterministically. Therefore, it was quite expected to see the emergence of fuzzy Turing machines as models of fuzzy computation, that is, computation that encompasses vagueness in the form of fuzziness as a basic ingredient of computation.

Apostolos Syropoulos

Chapter 5. Other Fuzzy Models of Computation

Abstract

Fuzzy Turing machines are not the only way to perform computation in a vague environment. Other models of fuzzy computation are inspired by biological phenomena or, more generally, by natural phenomena. Fuzzy P systems and the fuzzy chemical abstract machine are such models of computation. Some of these models have been studied in some detail while others are just emerging proposals.

Apostolos Syropoulos

Backmatter

Titel: Theory of Fuzzy Computation
verfasst von: Apostolos Syropoulos
Verlag: Springer New York
Electronic ISBN: 978-1-4614-8379-3
Print ISBN: 978-1-4614-8378-6
DOI: https://doi.org/10.1007/978-1-4614-8379-3

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Chapter 2. A Précis of Classical Computability Theory

Chapter 3. Elements of Fuzzy Set Theory

Chapter 4. On Fuzzy Turing Machines

Chapter 5. Other Fuzzy Models of Computation

Backmatter

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