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This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems.The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value.

fuzzy set theory --- fuzzy semigroups --- nilpotent fuzzy groups, fuzzy topological spaces --- fuzzy decision making --- pattern classi.cation --- intuitionistic fuzzy sets --- neutrosophic fuzzy sets --- credibility measure --- fuzzy linear systems --- lattice isomorphism --- possibilistic models, fuzzy BCK/BCI algebras, hypergraphs, N-hyper sets