This book is an above average history of the conceptualization ,development,and application of fuzzy logic.Fuzzy logic essentially replaces the point estimates of the mathematical laws of probability(addition and multiplication rules for disjunction and conjunction,respectively)with interval estimates using linear programming techniques.The two main protaganists are L. Zadeh and B. Kosko.They certainly should be recognized for independently developing their own particular versions and approaches to interval estimates but they are NOT the originators.The authors of the book overlok that it was George Boole who was the first to come up with interval estimates for probabilities,including non rational numbers, in chapters 16-21 of his 1854 The Laws of Thought.J M Keynes then used modified versions of a number of these problems of Boole's to present a method of approximation using an interval estimate approach in his A Treatise on Probability in chapters 15 and 17.Keynes rejected the purely mathematical laws of probability as a special case and emphasized the notion of " non numerical " probabilities or indeterminate or non comparable probabilities,by which he meant interval estimates.Theodore Hailperin,in 1965 and in full length books in 1976,1986,and 1996,demonstrated that all of the Boole problems could be solved as linear programming problems.Daniel Ellsberg's "ambiguous" probabilities(intervals)are also overlooked in this book.
The authors mix subjectivist Bayesians(Ramsey,De Finetti,and Savage)with Objectivist Bayesians(Jeffreys,Jaynes)without apparently realizing that there are major differences between them.The claim that Boole reduced thinking to "classical logic " and "well bounded symbols " while ignoring " vagueness " on p.71 is false as is the claim that Boole was a supporter of the purely mathematical application of the laws of probability who rejected subjectivism at the top of p.180.He was not.
This is a entertaining book.It is worth buying even though the authors have overlooked the actual originators of the interval estimate approach to decision making based on indeterminate probabilities-George Boole,J M Keynes,Theodore Hailperin,and Daniel Ellsberg.