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Designed as a text for new research students and scholars of Mathematics, this well establish and high successful book provides a comprehensive and systematic treatment of the subject. The purpose of this book is to present an up to date account of fuzzy ideals of semigroups and Bi-semiring. The book concentrates on theoretical aspects and consists of seven chapters. The Chapters two, three, four discuss fuzzy ideals of semigroups and last three Chapters discuss semiring with Bi-semirings.