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This book aims to introduce fuzzy matrix theory as a basic framework forcharacterizing the full scope of the fuzzy sets concept and its relationshipwith the increasingly important concept of information and complexity invarious sciences and professions. The book provides a wide coverage on thetheoretical developments of fuzzy matrices and fuzzy vector spaces, on thetheory of generalized inverses for fuzzy matrices, on fuzzy relations and onpartial orderings on fuzzy matrices. The book also discusses the role of fuzzymatrices in the spectral theory of linear transformations on finitedimensional vector spaces. The concept of fuzzy matrix and its applicationsin document retrieval system, medical diagnosis, database managementsystem, decision making theory and dynamical systems are developediteratively and illustrated with suitable examples wherever necessary. Eachchapter has brief notes and exercises for the benefit of students.