Fuzzy Logic

An Introductory Course for Engineering Students

verfasst von: Enric Trillas, Luka Eciolaza

Verlag: Springer International Publishing

Buchreihe : Studies in Fuzziness and Soft Computing

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

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Über dieses Buch

This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.

Inhaltsverzeichnis

Frontmatter

Chapter 1. On the Roots of Fuzzy Sets

Abstract

As fuzzy sets were introduced by Zadeh in 1965, they were born closely linked with imprecise predicates, that is, with names of non-precisely defined classes of objects. Even more, most of the applications of Zadeh’s ideas are made with properties the objects do verify in some degree between the two classical extremes 0 and 1, respectively. Because of that, it is not at all odd to introduce fuzzy sets from some considerations on how predicates are used in language. We will follow Wittgenstein’s statement “The meaning of a word is its use in language”.

Enric Trillas, Luka Eciolaza

Chapter 2. Algebras of Fuzzy Sets

Abstract

From now on it will be only considered the case in which \((L,\leqslant )=([0,1],\leqslant )\), that is, of Zadeh’s fuzzy sets, with predicates \(P\) in \(X\) known through a degree \(\mu _P:X\rightarrow [0,1]\), and without knowing, necessarily, its primary use \(\leqslant _P\).

Enric Trillas, Luka Eciolaza

Chapter 3. Reasoning and Fuzzy Logic

Abstract

The question is, in fact, a philosophical one whose discussion does not correspond to this text, and that received a lot of comments and discussions by philosophers. Instead of such question, there is the more particular,what is a logic?, that can be answered not philosophicaly but in terms of the mathematical definition of what is a consequence’s operator. A definition that corresponds to an abstraction of the term “deduction”.

Enric Trillas, Luka Eciolaza

Chapter 4. Fuzzy Relations

Abstract

A predicate \(R\) on a cartesian product \(X_1\times \ldots \times X_n\) is called a relational (n-ary) predicate.

Enric Trillas, Luka Eciolaza

Chapter 5. T-Preorders and T-Indistinguishabilities

Abstract

To characterize the T-Preorder and the T-indistinguishability relations by means of particular classes of them, and showing ways of constructing T-preorders and T-indistinguishabilities.

Enric Trillas, Luka Eciolaza

Chapter 6. Fuzzy Arithmetic

Abstract

As it was explained before, any operation.

Enric Trillas, Luka Eciolaza

Chapter 7. Fuzzy Measures

Abstract

Fuzzy sets not only appear by representing imprecise predicates, but also partial or incomplete information.

Enric Trillas, Luka Eciolaza

Chapter 8. An Introduction to Fuzzy Control

Abstract

Probably one of the most successful developments of fuzzy reasoning, from the industrial point of view, is the design of fuzzy control systems, also called linguistic control systems, or simpler, the applications of fuzzy controllers.

Enric Trillas, Luka Eciolaza

Backmatter

Titel: Fuzzy Logic
verfasst von: Enric Trillas
Luka Eciolaza
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-14203-6
Print ISBN: 978-3-319-14202-9
DOI: https://doi.org/10.1007/978-3-319-14203-6