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Introduction to fuzzy arithmetic: Theory and applications (Van Nostrand Reinhold electrical/computer science and engineering series), by A
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Here's how to use fuzzy logic to overcome design challenges of designing and analyzing complex processes in order to make televisions, camcorders, washing machines, and other products run more efficiently.
- Sales Rank: #3092179 in Books
- Published on: 1985
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 351 pages
Most helpful customer reviews
7 of 7 people found the following review helpful.
Outstanding - a book that opens many doors.
By wiredweird
I've had this book for years, and keep coming back to it. Many books define fuzzy numbers in various ways, and hint at combining them with some kind of arithmetic. Kaufmann and Gupta actually carry out those operations. Since fuzzy addition is a kind of convolution, they also show why fuzzy subtraction does not reverse the operation - deconvolution does. If you want to use fuzzy arithmetic for constraint propagation, this changes the basic nature of backwards propagation.
I just wish the author's clarity had extended a little farther into the mechanics of the various kinds of convolution. They handle discrete cases only, and offer about the least readable presentation of convolution that I've ever seen.
I'm not a theoretician, so I appreciate the book's clarity and examples. It is so clear and thorough that I refer to it for ideas quite unrelated to fuzzy arithmetic. If a sign of a great book is the number of unrelated topics that it clarifies, then this title is very good indeed.
This title may not suit the beginner and may not suit the expert. For us in the middle, though, it is incredibly helpful.
3 of 3 people found the following review helpful.
Too many errors, not enough content
By Aaron Turner
Although the intent of this text is laudable - to introduce the concepts of fuzzy arithmetic to engineers, and provide certainty in understanding through examples - the execution of the work is terrible. Only the most fundamental of the concepts is communicated with clarity, due to a general sloppiness in writing style, poor mathematical presentation, and lack of logic in some of the "proofs" that are presented.
The technical content of the book could have been presented in less than 20 pages out of the 315. The rest is overstuffed with repetitive and rather trivial examples presented in unnecessarily drawn out detail. The real demise of this work, however, is in the unfathomable number of typographical errors that occur throughout the book. I would estimate there are at least 2 or 3 such errors PER PAGE. This renders the usefulness of the excruciatingly detailed examples very questionable.
The presentation of the mathematical concepts is poorly done, often through a stumbling writing style. In more than one instance, a "theorem" is given "proof" by simply re-stating the theorem and declaring that it has been proven. I understand that this is not meant to be a "theoretical" book, in which case I would have accepted a statement of the theorem without proof, but a non-proof should not have been included.
In a few instances (introductions to chapters) the authors attain moments of clarity using a more verbose writing style. Particularly in trying to explain the nature of fuzzy numbers and their difference from random numbers it is clear that the authors are communicating something of importance. Unfortunately, once past the introductions, these themes are not further developed.
Did I learn from reading this book? Yes, I did learn a good deal about fuzzy arithmetic despite the nature of the work, and yes, I can see that portions of the book can be used as future reference to understand details in the arithmetic operations on fuzzy numbers. However, I think any novice student is going to be at a loss to obtain a firm understanding of the subject from this presentation.
3 of 3 people found the following review helpful.
Steal this book!
By Douglas A. Lefelhocz
The style of this book is excellent in that it gives you plenty of examples of how fuzzy arithmetic works. Honestly, I doubt there exists a more comprehensive book on fuzzy arithmetic around.
You'll find information on fuzzy numbers and their basic arithmetic, how alpha cuts work in fuzzy arithemtic, type-two fuzzy numbers, probabilisitic-fuzzy hybrid numbers, fuzzy modular arithmetic, combinatorics with fuzzy numbers, and an application of fuzzy arithmetic to catastrophe theory. And more, of course.
If you can find a copy, get it immediately. The explanations are clear, the reasoning is thorough, and the examples carefully illustrate the ideas. Steal this book!
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