Intuitionistic Fuzzy Partial Metric Spaces

Öz

Fuzzy logic is a theory that is used as an alternative to classical structures in both application and algebraic fields. The fixed point theorem is a theorem widely used in mathematics, especially in metric spaces and partial metric spaces. The fixed point theorem is used on classical metric structures, but it is also widely used on fuzzy metric spaces, fuzzy partial metric spaces and intuitionistic fuzzy metric spaces. In this paper, intuitionistic fuzzy partial metric spaces are defined, their basic properties and examples are obtained. For it, open ball, convergent sequence, and Cauchy sequence are defined and their basic properties are introduced. Furthermore, the relations between intuitionistic fuzzy partial metric spaces, classical metric spaces, fuzzy metric spaces, fuzzy partial metric spaces, and intuitionistic fuzzy metric spaces are analyzed. As a result of this investigation, it is shown that from each classical metric, classical partial metric, and intuitionistic fuzzy metric, an intuitionistic fuzzy partial metric can be obtained. Moreover, it is achieved that an intuitionistic fuzzy metric is also an intuitionistic fuzzy partial metric space. Thus, a new structure is given by transferring the partial metric structure to intuitionistic fuzzy metric spaces.

Anahtar Kelimeler

• Metric Spaces
• Partial Metric Spaces
• Fuzzy Metric Spaces
• Fuzzy Partial Metric Spaces
• Intuitionistic Fuzzy Metric Spaces
• Intuitionistic Fuzzy Partial Metric Spaces.

Sezgisel Bulanık Kısmi Metrik Uzaylar

Öz

Bulanık mantık, hem uygulama hem de cebirsel alanlarda klasik yapılara alternatif olarak kullanılan bir teoridir. Sabit nokta teoremi, matematikte özellikle metrik uzaylarda ve kısmi metrik uzaylarda yaygın olarak kullanılan bir teoremdir. Sabit nokta teoremi klasik metrik yapılar üzerinde kullanılmakla birlikte, bulanık metrik uzaylar, bulanık kısmi metrik uzaylar ve sezgisel bulanık metrik uzaylar üzerinde de yaygın olarak kullanılmaktadır. Bu çalışmada, sezgisel bulanık kısmi metrik uzaylar tanımlanmış, temel özellikleri ve örnekleri elde edilmiştir. Bunun için açık küre, yakınsak dizi ve Cauchy dizisi tanımlanmış ve temel özellikleri tanıtılmıştır. Ayrıca, sezgisel bulanık kısmi metrik uzaylar, klasik metrik uzaylar, bulanık metrik uzaylar, bulanık kısmi metrik uzaylar ve sezgisel bulanık metrik uzaylar arasındaki ilişkiler incelenmiştir. Bu inceleme sonucunda, her bir klasik metrik, klasik kısmi metrik ve sezgisel bulanık metrikten bir sezgisel bulanık kısmi metrik elde edilebileceği gösterilmiştir. Ayrıca, bir sezgisel bulanık metriğin aynı zamanda bir sezgisel bulanık kısmi metrik uzay olduğu elde edilmiştir. Böylece kısmi metrik yapısı sezgisel bulanık metrik uzaylara aktarılarak yeni bir yapı verilmiştir.

Anahtar Kelimeler

• Kısmi Metrik Uzaylar
• Bulanık Metrik Uzaylar
• Bulanık Kısmi Metrik Uzaylar
• Sezgisel Bulanık Metrik Uzaylar
• Sezgisel Bulanık Kısmi Metrik Uzaylar

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