Last edited by Tojalmaran

Wednesday, January 29, 2020 | History

4 edition of **Cardinalities of fuzzy sets** found in the catalog.

Cardinalities of fuzzy sets

James Tyler Kent

- 176 Want to read
- 40 Currently reading

Published
**2004** by Springer Verlag in Berlin .

Written in English

**Edition Notes**

Statement | Maciej Wygralak. |

Classifications | |
---|---|

LC Classifications | QA76 |

The Physical Object | |

Pagination | xiv, 195 p. ; |

Number of Pages | 195 |

ID Numbers | |

Open Library | OL22535320M |

ISBN 10 | 3540003371 |

Let us mention, for instance, fuzzy sets and derivative concepts, flou sets and twofold fuzzy sets, which have been created for different purposes as well as using distinct formal and informal motivations. Empirical Research in Fuzzy Set Theory. Introduction to Fuzzy Sets. Part Two.

Book News, Inc. In it I show how to use FL in new ways and how to effectively solve problems that are awash in uncertainties. List of Figures. For a possible example of such a set consider the set of your eight closest friends in the set of "tall people" or your "Top Eight" in your MySpace page if you had one a few years ago. Such rule-based fuzzy logic systems FLSsboth type-1 and type-2, are what this book is about. However, such an object can be defined as follows.

At the social level, uncertainty has even strategic uses and it is often created and maintained by people for different purposes privacy, secrecy, propriety. Such sets are said to be equipotent, equipollent, or equinumerous. Such rule-based fuzzy logic systems FLSsboth type-1 and type-2, are what this book is about. One of the best sources for general discussions about uncertainty is the book Uncertainty-Based Information, by Klir and Wierman1. Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their too categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

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Basic Notions and Problems. Empirical Research in Fuzzy Set Theory. Unfortunately, neither fuzzy sets nor the other nonclassical concepts have been equipped with a satisfactory nonclassical cardinality theory.

Faculty must provide a university department mailing address and department telephone number. To get it, one needs a suitable notion of cardinality and, moreover, a possibility to calculate with such cardinalities. In it I show how to use FL in new ways and how to effectively solve problems that are awash in uncertainties.

In my opinion, it actually comes as harder to find real-world sets with natural number cardinalities, but I've almost surely started to digress. Finally, sum all these together, and at least in plenty of cases the set of say red book covers in that room will have a non-natural number for its cardinality.

For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers.

No previous knowledge of fuzzy set theory and fuzzy logic is required for understanding the material covered in the book. Regarding the causes of uncertainty, they state: Uncertainty involved in any problem-solving situation is a result of some information deficiency.

Comparing sets[ edit ] Bijective function from N to the set E of even numbers. Professor Klir and his students for example, Klir and T. Fuzzy Mathematics. One of the best sources for general discussions about uncertainty is the book Uncertainty-Based Information, by Klir and Wierman1.

The Extension Principle and Applications. That the original FLtype-1 FLcannot do this sounds paradoxical because the word fuzzy has the connotation of uncertainty. For the person who is only interested in type-2 fuzzy set theory, read Chapters 3,and Appendices A and B.

Professor Zimmermann's treatise is a major contribution to the literature of fuzzy sets and decision analysis. Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their too categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their too categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc.

Throughout the book, many examples are used to illustrate concepts, methods, and generic applications as they are introduced.

Abundant examples show how the theory can be applied to the solution of realistic problems--and how it can lead to results not obtainable by classical methods. Each chapter is followed by a set of exercises, which are intended to enhance readers' understanding of the material presented in the chapter.

Such sets are said to be equipotent, equipollent, or equinumerous. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over.

For a person who is interested in knowledge mining and wants to get a quick overview of the benefits to modeling uncertainties on judgment making when using rule-based advisors, read Chapters 4 Section 4. Although many applications have been found for type-1 FL, it is its application to rule-based systems that has most significantly demonstrated its importance as a powerful design methodology.

At the empirical level, uncertainty is an inseparable companion of almost any measurement, resulting from a combination of inevitable measurement errors and resolution limits of measuring instruments.

Indeed, Professor Zimmermann, who as a researcher, author, editor and organizer of international meetings has contributed so much for the cause of the fuzzy sets and systems and the fuzzy community, deserves our compliments.

The most common choice is the initial ordinal in that class.

Part 4-Type-2 Fuzzy Logic Systems-which is the heart of the book, contains five chapters, four having to do with different architectures for a FLS and how to handle different kinds of uncertainties within them, and one having to do primarily with four specific applications of type-2 FLSs.

Unfortunately, neither fuzzy sets nor the other nonclassical concepts have been equipped with a satisfactory nonclassical cardinality theory.

Another source for some general discussions about uncertainty is H.For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.

A Fuzzy Patch is de ned by a fuzzy rule: a patch is a mapping of two membership functions, it is a product of two geometrical objects, line segments, triangles, squares etc. In a fuzzy controller, a rule in the rule set of the controller can be visualized as a \device" for.

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well.

vi CONTENTS 6 Fuzzy Relations and Fuzzy Graphs 71 Fuzzy Relations on Sets and Fuzzy Sets 71 Compositions of Fuzzy Relations 76 Properties of the Min-Max Composition 79 Fuzzy Graphs 83 Special Fuzzy Relations 86 7 Fuzzy Analysis 93 Fuzzy Functions on Fuzzy Sets 93 Extrema of Fuzzy Functions 95 Integration of Fuzzy Functions 99 Integration of a Fuzzy.

Fuzzy Sets and Systems 55 () 61 North-Holland The cardinality of fuzzy sets and the continuum hypothes, is Li Hong-xing, Luo Cheng-zhong and Wang Pei-zhuang Department of Mathematics, Beifing Normal University, BeifingChina Received July Revised March Abstract: Up to now, the research of the cardinality of fuzzy sets has hardly advanced since it is Cited by: 6.

In mathematics, fuzzy sets (aka uncertain sets) are somewhat like sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A.

Zadeh and Dieter Klaua [] in as an extension of the classical notion of set.

At the same time, Salii () defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context.