On general standard grey number representation and operations for multi-type uncertain data

Abstract

Most systems in the real life are complex systems. In the study of complex systems, we tend to get highly uncertain information due to the dynamic and complexity of the cases and our knowledge limitations. Moreover, complex systems are compounded of many parts, and the methods of data collection and storage vary considerably. Hence, the data processed by complex systems are associated with multi-type uncertainty, such as randomness, fuzziness and greyness. To solve the problems of limitations in the conventional representation and operations of uncertain data, this paper proposes a new type of method to represent and operate multi-type uncertain data. Firstly, we fully analyze the features of probability numbers, fuzzy numbers, interval valued fuzzy numbers and grey numbers, and study their relation and commonness so as to propose the concept and representation methods of generalized standard grey numbers. Then, we continue to discuss issues such as the basic operations of generalized standard grey numbers, as well as norm models and value comparison, to suggest a new solution to the representation and operations of uncertain data in complex systems.