## Fuzzy Mathematics: An Introduction for Engineers and ScientistsThe book deals with fuzzy graph theory, fuzzy topology, fuzzy geometry, and fuzzy abstract algebra. It presents the concepts of fuzzy mathematics with applications to engineering, computer science, and mathematics. In this second edition the chapter 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 equations of fuzzy singletons has been added to the chapter on algebra. 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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### Contents

FUZZY SUBSETS | 1 |

FUZZY GRAPHS | 21 |

FUZZY TOPOLOGICAL SPACES | 67 |

Copyright | |

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### Common terms and phrases

A A(Q affine variety algebraic algorithm called a fuzzy commutative ring compact components connected Consider contains contraction map convex fuzzy subsets crisp Define the fuzzy Definition digital topology distance edge element equations Example exists finite free monoid free semigroup function fuzzy disk fuzzy forest fuzzy graph fuzzy ideal fuzzy line fuzzy numbers fuzzy points fuzzy relation Fuzzy Sets fuzzy subgroup fuzzy subset fuzzy topological space fuzzy topology graph G grey level Hankel matrix Hence identity and let intersection interval Lemma Let G level sets maximal medial axis metric space Mordeson neighborhood nonempty partial fuzzy subgraph path perimeter pixels polynomial ring primary ideal Proof properties Proposition r-edge reflexive respect ring with identity Rosenfeld sequence Sets and Systems space and let starshaped subgraph of G subgroup of G submonoid subsemigroup Suppose symmetric Theorem theory topological space values vertex vertices