On vague algebraic structures

ABSTRACT ON VAGUE ALGEBRAIC STRUCTURES Sevda SEZER Ph. D. Thesis in Mathematics Adviser: Prof. Dr. Doğan ÇÖKER June 2003, 78 Pages In this thesis work about applications of fuzzy sets on algebra, first a general information about fuzzy sets and then the concepts of fuzzy equality, fuzzy function, vague binary operation, vague group, vague subgroup and vague homomorphism (Demirci 1999-a, 1999-b) are given. In the following chapters, a new concept of vague subgroup is introduced by using the definition of vague group, and some fundamental properties of this vague sub group are investigated. Furthermore, the concepts of vague normal subgroup, vague ring, vague subring, vague ideal, vague prime ideal, vague maximal ideal, vague field, vague integer domain, vague isomorphism are defined and some fundamental properties of these concepts are investigated. KEY WORDS: Fuzzy set, fuzzy equality, fuzzy function, vague binary oper ation, vague group, vague normal subgroup, vague ring, vague ideal, vague field, vague integer domain, vague isomorphism. COMMITTEE : Prof. Dr. Doğan ÇÖKER Prof. Dr. H. Ibrahim KARAKAŞ Prof. Dr. Timur KARAÇAY Prof. Dr. Haydar Eş Prof. Dr. Zeki ASLAN Assoc. Prof. Dr. İlham ALİYEV ii