‎intuitionistic fuzzy modular spaces

‎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.