‎Intuitionistic Fuzzy Modular Spaces

Article Type:
Research/Original Article (بدون رتبه معتبر)
‎After the introduction of the concept of fuzzy sets‎ ‎by Zadeh‎, ‎several researches were conducted on‎ ‎the generalizations of the notion of fuzzy sets‎. ‎There are many viewpoints on the notion of metric space in fuzzy topology‎. ‎One of the most important problems in fuzzy topology is obtaining an appropriate concept of fuzzy metric space‎. ‎This problem has been investigated by many authors from different points of view‎. ‎Atanassov gives the concept of the intuitionistic fuzzy set as a generalization of the fuzzy set‎. ‎Park introduced the notion of intuitionistic fuzzy metric space as a natural generalization of fuzzy metric spaces due to George and Veeramani‎. ‎This paper introduces the concept of intuitionistic fuzzy modular space‎. ‎Afterward‎, ‎a Hausdorff topology induced by a $\delta$-homogeneous intuitionistic fuzzy modular is defined and some related topological properties are also examined‎. ‎After giving the fundamental definitions and the necessary examples‎, ‎we introduce the definitions of intuitionistic fuzzy boundedness‎, ‎intuitionistic fuzzy compactness‎, ‎and intuitionistic fuzzy convergence‎, ‎and obtain several preservation properties and some characterizations concerning them‎. ‎Also‎, ‎we investigate the relationship between an intuitionistic fuzzy modular and an intuitionistic fuzzy metric‎. ‎Finally‎, ‎we prove some known results of metric spaces including Baire’s theorem and the Uniform limit theorem for intuitionistic fuzzy modular spaces‎.
Transactions on Fuzzy Sets and Systems, Volume:2 Issue: 2, Fall - Winter 2023
113 to 126
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