Some fuzzy ideals over commutative rings

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Thesis Type: Doctorate

Institution Of The Thesis: Yildiz Technical University, Faculty of Arts & Science, Department of Mathemeatics, Turkey

Approval Date: 2020

Thesis Language: Turkish

Student: Deniz SÖNMEZ

Supervisor: Gürsel Yeşilot

Open Archive Collection: AVESIS Open Access Collection

Abstract:

There is a growing need for fuzzy logic in mathematics, engineering, or in various technical fields that allows expression and resolution of uncertainties that are difficult to express or impossible to pour into data. Based on this need, the concept of fuzzy set has been developed and its basic definitions and properties have emerged. Since the study of Zadeh titled "Fuzzy Sets", many studies have been conducted in this field. Although there are studies on prime and prime fuzzy ideals, an important building block of fuzzy ring, which is one of these areas, the expansion of prime and prime fuzzy ideals has not been done yet.In this thesis, fuzzy ideals will be expanded with the help of a function, a new ideal structure will be formed and the properties of this structure will be investigated. Then, the concept of 2-absorbing primary fuzzy ideal which is the generalization of prime fuzzy ideal and primary fuzzy ideal will be introduced and its basic properties will be examined. In the light of all these studies, both concepts will be synthesized and the 2-absorbing delta primary fuzzy ideal concept will be characterized. Our work in fuzzy ring theory will also be investigated in fuzzy module theory and will be covered with all its features.