The ideas of uncertain variables based on uncertain logics have been introduced and developed for a wide class of uncertain systems. The purpose of this mo- graph is to present basic concepts, definitions and results concerning the uncertain variables and their applications to analysis and decision problems in uncertain systems described by traditional mathematical models and by knowledge rep- sentations. I hope that the book can be useful for graduate students, researchers and all readers working in the field of control and information science. Especially for those interested in the problems of uncertain decision support systems and unc- tain control systems. I wish to express my gratitude to my co-workers from the Institute of Control and Systems Engineering of Wroclaw University of Technology, who assisted in the preparation of the manuscript. My special thanks go to Dr L.Siwek for the valuable remarks and for his work concerning the formatting of the text.