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The book deals with fuzzy graph theory, fuzzy topology, fuzzy geometry, and fuzzy abstract algebra. It presents the concepts of fuzzy mathematics with its applications to engineering, computer science, and mathematics. In this second edition the chap- ter on geometry is expanded and contains results on the degree of adjacency of two regions and the degree of surroundedness of a region by another. Applications to digital polygons and image description are also given. Furthermore, the new edition includes results on image enhancement and thresholding by optimization of fuzzy compactness as well as results concerning a Hausdorff distance between fuzzy subsets. The most current work on the solution of nonlinear systems of fuzzy intersection equati- ons of fuzzy singletons has been added to the chapter on alge- bra. The book is written with engineers and computer scientists in mind, but it can also serve as a research guide to interested mathematicians as it involves current results.
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