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In this book we introduce the concepts of a completely closed ideal of a BH-algebra, a completely closed ideal with respect to an element of a BH-algebra, a completely closed filter, a completely closed filter of a BH-algebra and a closed filter with respect to an element of a BH-algebra. We prove many relations and theorems among these notions and some other types of ideals and filters of a BH-algebra. On the other hand, in fuzzy sense, we define the concepts of a fuzzy completely closed ideal, a fuzzy completely closed filter, a fuzzy completely closed ideal with respect to an element of a BH-algebra and a fuzzy closed filter with respect to an element of a BH-algebra. Also we study all these new notions in ordinary and fuzzy senses when BH-algebra is a BG-algebra.

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A Prof. Husein Hadi Abbass is the Dean Assistant post for Scientific Affairs in the Faculty of Computer Science and Mathematics university of Kufa - Iraq. He obtained master´s degree in applied mathematics from the Technology University in Iraq in 1995. He has publications in Algebra, MV-algebra,Image Processing ,Algebraic Statistics,Fuzzy maths

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