PurposeThe purpose of this paper is to present the scientific background from which grey systems theory came into being, the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.Design/methodology/approachThe grey uncertainty is compared with other kinds of uncertainty such as stochastic uncertainty, unascertainty, fuzzy and rough uncertainty.FindingsThe advances in grey systems theory and its various successful applications are introduced individually by algorithms of grey numbers and grey algebraic systems, grey dynamic models and grey predictions, grey optimization analysis for decision making, grey control models.Research limitations/implicationsMany scientific theories require the unremitting efforts of several generations of people and have gone through hundreds of years before reaching maturity and perfection. Grey systems theory is still in its growth period. So, it is unavoidable that there exist immature and imperfect parts in the theory.Originality/valueGrey systems theory is a new method for studying problems of uncertainty with few data points and poor information. This new theory studies small samples and systems with poor information, which have partial information known, partial information unknown. It describes adequately and monitors effectively systems' operations and evolutions through extracting valuable information from the little known information. Grey systems theory comes into being along with the development of modern systems science and uncertainty systems theories and methods. It is also a result of deepened perceptivity about uncertain systems.

Purpose – To present the concept of inverse transfer of the internal structures of a dynamical system to the perception it has of its environment and itself.Design/methodology/approach – We use the formalism of mathematical operators acting on functional spaces.Findings – The concept of inverse transfer clarifies many aspects of the subjectivity of perception (epistemological or praxiological). The decisions taken according to this perception modifies both the environment and the system, generating a feedback loop and showing that the co‐evolution of the system and its environment is a fixed point of an adequate operator.Originality/value – Our research shows the importance of a synthesis of observation and decision in the understanding of perception, giving rise to an epistemo‐praxiology.