Item description for Fuzzy Sets, Fuzzy Logic, Applications (Advances in Fuzzy Systems - Applications and Theory, Vol 5) by George Bojadziev & Maria Bojadziev...
Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics. The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 8.5" Width: 6.1" Height: 0.9" Weight: 1.1 lbs.
Publisher World Scientific Publishing Company
ISBN 9810223889 ISBN13 9789810223885
Reviews - What do customers think about Fuzzy Sets, Fuzzy Logic, Applications (Advances in Fuzzy Systems - Applications and Theory, Vol 5)?
Beautiful Introduction Oct 5, 2005
I find the approach in this book to fuzzy logic interesting, useful, simple, and beautiful. Starting with something like interval numbers is almost certainly the best way to start a fuzzy logic text. It presents a simple example that is very easily understood and allows one to see what differentiates fuzzy logic from other multi-valued logics in an almost intuitive manner. I have not worked through all of this book. But, while working through the truth table exercises in Chapter 8 I thought 'couldn't I do these on a spreadsheet like Microsoft Excel or Microsoft Works?' With Bojadziev's formulations how to produce truth tables on a spread sheet (I used Microsoft Works) came almost immediately. (The only real exception was that I had to treat fractional truth values, as functions. Expressly, in Works you type =1/2 in the cell.) To paraphrase Betrand Russell (correct this if I have the author wrong), 'a good notation has a certain suggestion to it.' Since I did this, I noticed some textual errors. p. 164, (g) reads [~p->(q^~q)]->~p proof by contradiction. This is not a tautology. The tautological form, I think, Bojadziev is looking for is either [p->(q^~q)]->~p, or more likely [~p->(q^~q)]->p. Also, on p. 165 p^(p->q) should not read (1 0 1 0, which is q^(p->q) in context), but 1 0 0 0. Additionally, on p. 267 8.5 (a) for p->~q should read (0 1/2 1 1/2 1 1 1 1 1). Still, Bojadziev's notation is the most helpful I have seen for fuzzy logic texts. The notation helped me to think of simpler ways to deal with truth tables. This also allowed me to check many different forms of tautologies and see if they are tautologies in other than 2-value logics. For instance, modus tollens is only a quasi-tautology in greater than 2-valued logics (I have investigated up to 11-valued logics, and no doubt, this could be proven for all n-valued crisp logics). Modus ponens is a tautology for n-valued logics, where n is greater than 2 (at least up to an 11-valued logic, and no doubt this can be proven). This suggests, on a logical basis, that falsifiability is not as strong a criterion as verification. Without this book, such insights would have not happened or would have been much harder.