Fuzzy Vector Metrıc Spaces

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Thesis Type: Doctorate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2018

Student: ŞEHLA EMİNOĞLU

Supervisor: CÜNEYT ÇEVİK

Abstract:

In our fuzzy vector metric spaces focused study were on one hand probabilistic metric spaces and related concepts, on the other hand the theory of fuzzy sets handled. Fuzzy metric spaces which are constructed by associating with the theory of fuzzy sets to the probabilistic metric spaces with t-norms were addressed and related examples were given. Here fuzzy vector metric spaces were rst dened in the literature by considering t which is a positive real number as a vector from Riesz spaces. Then some topological concepts and convergence properities in these spaces were mentioned. Moreover, continuity for fuzzy vector metric spaces was updated with the lattice norm condition. Finally, some important theorems were proved with the help of the concept of defective fuzzy vector diameter.