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Fuzzy mathematics. An introduction for engineers and scientists. 2nd ed. (English) Zbl 1009.03002
Studies in Fuzziness and Soft Computing. 20. Heidelberg: Physica-Verlag. xiii, 310 p. DM 138.00; sFr. 119.84; £ 48.00; $ 84.00 (2001).
This is a slightly expanded version of the first edition (1998; Zbl 0956.03046), and again it is a nice and valuable presentation of seriously “fuzzified” tools of standard applied mathematics. Chapters 1 to 4 remained unchanged. The other two chapters have been slightly modified and extended. In Chapter 5 on “Fuzzy geometry” the authors now also present results (of A. Rosenfeld and co-workers) from the late 1980s on degrees of adjacency and surroundness, on image enhancement and thresholding via fuzzy compactness, and on Hausdorff distances between fuzzy sets. In Chapter 6 on “Fuzzy abstract algebra” recent results (mainly of the first named author) are added on (local) solutions of nonlinear systems of fuzzy intersection equations of fuzzy singletons.

03-01Textbooks (mathematical logic)
03E72Fuzzy set theory
00A06Mathematics for non-mathematicians
00A05General mathematics
00-01Textbooks (general mathematics)
68U05Computer graphics; computational geometry
68R99Discrete mathematics in relation to computer science
54-01Textbooks (general topology)
68-01Textbooks (computer science)
54A40Fuzzy topology
08A72Fuzzy algebraic structures