Abstract. We introduce the concepts of double bitopological spacesas a generalization of intuitionistic fuzzy topological spaces in Sostak’ssense and Kandil’s fuzzy bitopological spaces. Also we introduce theconcept of (T ;U )-double (r;s)(u;v)-semiopen sets and doublepairwise (r;s)(u;v)-semicontinuous mappings in double bitopologi-cal spaces and investigate some of their characteristic properties. 1. IntroductionChang [2] de ned fuzzy topological spaces. These spaces and itsgeneralizations are later studied by several authors, one of which, devel-oped by Sostak [12], used the idea of degree of openness. This type ofgeneralization of fuzzy topological spaces was later rephrased by Chat-topadhyay, Hazra, and Samanta [3], and by Ramadan [11].As a generalization of fuzzy sets, the concept of intuitionistic fuzzysets was introduced by Atanassov [1]. C˘oker and his colleagues [4, 6,7] introduced intuitionistic fuzzy topological spaces using intuitionisticfuzzy sets. Using the idea of degree of openness and degree of nonopen-ness, C˘oker and M. Demirci [5] de ned intuitionistic fuzzy topologicalspaces in Sostak’s sense as a generalization of smooth fuzzy topologicalspaces and intuitionistic fuzzy topological spaces.Kandil [8] introduced and studied the notion of fuzzy bitopologicalspaces as a natural generalization of fuzzy topological spaces.In this paper, we introduce the concepts of double bitopological spacesas a generalization of intuitionistic fuzzy topological spaces in Sostak’s