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VOLUME 1 OF THIS CLASSIC SIX VOLUME SET OF THE WORKS OF THE BRILLIANT VON NEUMANN. 654 PAGES. ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize triangle inequality of ordinary metric spaces. ... Read more

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There are several books available on Fuzzy Set Theory and Fuzzy Logic, however most of them are written by engineers and scientists with a specialised set of readers in mind. However this book has been written with a general type of reader in mind who, to begin with, does not have any specific applications of the subject in mind while starting to study the subject as a scientific discipline in its own right.

The book presents the basic rudiments of fuzzy set theory and fuzzy logic in a manner in which other topics of basic mathematics, such as set theory, algebra and calculus etc are usually presented. No specialised knowledge of any engineering discipline or other subject is expected of the reader. Effort has been made to tread the middle path, which avoids the extremes of abstract mathematical proofs and the specialised technical details of the areas of application. The author has taught this subject to undergraduate and postgraduate engineering and mathematics students for many years and has also used it in his research work related to the development of computational algorithms for solving real life optimisation problems.

Contents:

1. Introduction
2. Fuzzy Sets
3. Operations on Fuzzy Sets
4. Fuzzy Numbers
5. Fuzzy Relations and Fuzzy Graphs
6. Fuzzy Functions and Calculus of Fuzzy Functions
7. Fuzzy Measures and Measures of Fuzziness
8. Evidence Theory, Possibility Theory and Probability theory
9. Linguistic Variables, Fuzzy Rules and fuzzy Propositions
10. Fuzzy Logic and Approximate Reasoning
11. Construction of Fuzzy Sets and Defuzzification
12. Decision Making in a Fuzzy Environment
13. Fuzzy Rules Based Models and Fuzzy Systems
14. Engineering and Other Applications
Also available:

Modern Mathematical Models, Methods And Algorithms for Real World Systems - ISBN 1904798640
Bayesian Statistics And Its Applications - ISBN 190574000X

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Quantum logic. Mathematical formulation of quantum mechanics, Multi-valued logic, Quasi-set theory, HPO formalism, Quantum field theory, Garrett Birkhoff, John von Neumann, George Mackey, Self-adjoint operator, Boolean algebra (structure). ... Read more

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The author introduces Lawvere and Tierney's concept of topos theory, a striking development in category theory that unites a number of important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic.Topos theory has led to the forging of surprising new links between classical and constructive mathematics. Bell presents toposes as the models of theories--the so-called local set theories--formulated within a typed intuitionistic logic. ... Read more

Customer Reviews (2)

Baffling
I have a maths degree, I've done some Set Theory, and I've had some exposure to Category Theory from a Computer Science perspective. But I really struggled trying to read this!

If you're looking for "Toposes for Dummies" (and I still am!), this isn't it.

57 is Grothendeick's prime
The Bourbaki structuralist approach is said by Amir C, Aczel to be:
"overly formal . too abstract. and much more rigorous than necessary. thus making it unnecessarily difficult to read and understand mathematics."
My immediate reaction / objection to this book is that this level of abstraction removes categories from the 'real world' reference of a new mathematics for ordinary people. For this approach to be effective one must already have had set theory, algebraic theory, symbolic logic and specifically for this book, the theory of topological neighborhoods.
Those qualifications put this approach to category theory above what is taught to graduates in the physical sciences in general and removes it to graduates( or very advanced undergraduates) in mathematics alone.
I don't think this could be what Grothendieck had in mind
when he wanted to put category theory in the place of set theory
as the base of mathematics in teaching.
I'll give an example of the kind this author fails vividly to give!
Category:
mathematics authors
sub categories:
1) humanist
2) antihumanist ( structuralist)
arrows:
1) theoretical examples
2) concrete examples
Now to make a Lewis Carroll ( Charles Dodgson) type sentence using
this:
A mathematics author is an antihumanist if the only examples he gives in his text are theoretical examples.
A mathematics author is an humanist if he gives both theoretical and concrete examples.
I'll let you figure out in which category I think J. L. Bell belongs.


... Read more

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Hardbound. ... Read more

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Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity.The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory. ... Read more

Customer Reviews (1)

By far the BEST book on the development of Cantor's ideas.
This is BY FAR the best and most INTERESTING book available on how Cantor developed his key ideas about transfinite sets, large cardinals, ordinals etc.It contains materials that will be highly relevant to even the most advanced set theorists, while yet managing to be generally accessible to those who, like myself, have only around a B.S. mathematics degree level ofunderstanding of the field.This ability to be of use and interest to readers with such widely varied mathematical preparations is a true tribute to the author's gift for being able to explain even very advanced concepts clearly and directly, something which is evident throughout the text, -- and unfortunately sorely missing in most mathematical texts operating at such a high level of abstraction.To be a bit more precise, I hope, persons with only a basic understanding of set theory -- something around what one should be able to glean from reading, say, Halmos' "Naive Set Theory" -- will indeed find themselves "out at sea" at times, but actually surprisingly FEW times, considering how well the author manages to unpack most of the key concepts and draw you back into the primary narrative.No doubt because this book is so much better than all its competitors, used copies, even the paperbacks, are now selling for a small fortune.[I kid you not, I just saw one listed at over $990!; though a few minutes of searching the main web book seller consolidators -- including the listings here at Amazon -- should still bag you one for under $100, at least if you act reasonably soon.]Clearly the publisher really needs to reissue this work to meet the fully justified demand!When and if they will do so, -- after all, it was last released, in its one and only paperback edition, in 1986! -- is anybody's guess.So, if you are a Cantor scholar, or a serious set theorist of any persuasion, you should probably bite the bullet and buy one now before the price really goes through the roof and you have to rely on marked-up, slowly disappearing library copies, -- until, that is, they all get stolen and resold on the web, which has happened to several classic math works already.One last thing, for those who don't really need the most sophisticated work on Cantor's intellectual development, Joseph Dauben's biography of Cantor is also very good and still widely available at a reasonable price.[His biography of Abraham Robinson is also very good by the way.] ... Read more