Intuitionistic Fuzzy Partial Metric Spaces

Abstract

Fuzzy logic is a theory used as an alternative to classical structures in both application and algebraic fields. In particular, there are fuzzy structures in metric spaces and partial metric spaces. The most widely used of these structures are 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.

Fuzzy logic is a theory used as an alternative to classical structures in both application and algebraic fields. In particular, there are fuzzy structures in metric spaces and partial metric spaces. The most widely used of these structures are 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.