العنوان Fuzzy Structures of Some Algebras./ الناشر جامعة عين شمس . كلية التربية . قسم الرياضيات . المؤلف العزب ، ريهام عبدالله عبدالحميد . هيئة الاعداد باحث / ريهام عبدالله عبدالحميد العزب مشرف / عبد العزيز العزب على مشرف / سامى محمد مصطفى مناقش / أمانى محمد عبد الحميد تاريخ النشر 1/1/2016 عدد الصفحات 166 ص ، اللغة الإنجليزية الدرجة الدكتوراه التخصص الرياضيات (المتنوعة) تاريخ الإجازة 1/1/2016 مكان الإجازة جامعة عين شمس - كلية التربية - قسم الرياضيات الفهرس | Only 14 pages are availabe for public view |

AbstractThis thesis has been mainly divided into five chapters. Chapter 1 highlights some basic definitions and results available in the standard literature. In this chapter we collect all the necessary preliminaries which will be useful in our discussions in the main text of the thesis. Chapter 2 consists of two parts: In part (I) the notion of interval–valued fuzzy medial-ideals (briefly i-v fuzzy medial-ideal) in BCI-algebras is introduced. Several theorems are stated and proved. The image and pre-image of interval–valued fuzzy medial-ideals are defined and how the homomorphic images and pre-images of interval–valued fuzzy medial-ideals become interval–valued fuzzy medial -ideals in BCI-algebras is studied as well. In (II) part, we introduce the notion of doubt intuitionistic fuzzy medial ideals, doubt intuitionistic fuzzy magnified translation medial ideals in BCI-algebras and investigate some interesting results. Moreover, some algorithms for medial ideals, fuzzy set and doubt intuitionistic fuzzy medial ideals have been constructed. Chapter 3 consists of two parts: In first part, we introduce the concept of cubic medial-ideal and investigate several properties .Also, we give relations between cubic medial-ideal and cubic BCI-ideal .The image and the pre-image of cubic medial-ideal under homomorphism of BCI-algebras are defined and how the image and the pre-image of cubic medial-ideal under homomorphism of BCI-algebras become cubic medial-ideal are studied. Moreover, the Cartesian product of cubic medial-ideal in Cartesian product BCI-algebras is given. In the second part, we introduce the concept of bipolar fuzzy medial-ideal and investigate several properties. Also, we give relations between bipolar fuzzy medial-ideal and bipolar BCI-ideal. The image and the pre-image of bipolar fuzzy medial-ideal under homomorphism of BCI-algebras are defined and how the image and the pre-image of bipolar fuzzy medial-ideal under homomorphism of BCI-algebras become bipolar fuzzy medial-ideal are studied. Moreover, the Cartesian product of bipolar fuzzy medial-ideal in Cartesian product BCI-algebras is given. Chapter 4 consists of two parts: In first part, the intuitionistic (T,S)-fuzzification of the concept medial ideals are considered. The image (pre-image) of (T,S)-fuzzy medial ideals under homomorphism of BCI-algebras are defined and some of there properties are investigated. The notion of product of intuitionistic (T,S)-fuzzy medial ideals in BCI-algebras are introduced and some related properties investigated. In the second part, the generalization of notions intuitionistic (T,S)- fuzzy medial sub-algebras and intuitionistic fuzzy medial ideals in BCI-algebras by using t-norm T and s-norm S are given .Moreover some interesting results are investigated . Chapter 5 consists of two parts: In first part, we introduce the concept of bipolar (T,S)-fuzzy medial-ideal and investigate several properties. Also, we give relations between bipolar (T,S)-fuzzy medial-ideal and bipolar (T,S)-fuzzy BCI-ideal. The image and the pre-image of bipolar (T,S)- fuzzy medial-ideal under homomorphism of BCI-algebras are defined and how the image and the pre-image of bipolar (T,S)-fuzzy medial-ideal under homomorphism of BCI-algebras become bipolar (T,S)-fuzzy medial-ideal are studied. Moreover, the Cartesian product of bipolar (T,S)-fuzzy medial-ideal in Cartesian product BCI-algebras is given. In the second part, we consider the interval-valued intuitionistic -fuzzification of the concept medial ideals. The image (pre-image) of interval-valued intuitionistic -fuzzy medial ideals under homomorphism of BCI-algebras are defined and investigated some of there properties. We introduce the notion of product of interval-valued intuitionistic -fuzzy medial ideals in BCI-algebras, and investigate some related properties. Key words: BCI-algebras, medial ideals, fuzzy medial ideals, (T,S) norm, interval–valued fuzzy medial-ideals, doubt intuitionistic fuzzy medial ideals, cubic medial-ideals, bipolar fuzzy medial-ideals. |