The “Number” and “Form” are two of the earliest meta-elements in mathematics, generating two disciplines respectively, Algebra and Geometry. In the 17th century, the words “Variables” and “Deformations” were obtained by adding a “Bian (in Chinese language)” in front of both, then the Calculus emerged as the mathematical symbol of the industrial revolution, through the combination of Cartesian Coordinates. The revolution of information is an even greater era, but what is the new mathematical symbol in this era?

Factor is the perspective from which information can be extracted to describe the entity and it’s also a meta-element of mathematics required by the information revolution. A factor is a set of attributes’ values, for instance, the factor “color” is a set containing “red, orange, yellow, green, blue, indigo and violet”. Factor is to “command” or represent attributes. It’s more significant than attributes and lies in a more advanced perspective, without which attributes are like broken pearls spreading all over the place. Human brain is a highly-efficient information processor with sensory nerve cells organized by factors in different zones, slices or layers. Mendel, a well-known biologist, was so impressed by the complexity of biological properties that he proposed the concept of Gene. Each gene “commands” a set of biological properties while its earliest name was Factor, that has been narrowed down to Gene later. Therefore, Factor is the broader version of Gene while gene unlocked the gates of life sciences, factor would open the doors of intelligence and data science. Factor is the new mathematical symbol of this era.

In 1982, I initiated the theory of “Factor Space” with Prof. M. Sugeno. Formulated by factors, Factor Space is a universal framework for the description of things and intelligence, also a mathematical foundation theory for intelligent science and data science. Based on the theory of Factor Space, researchers like Hongxing Li, Hongmin Zhang and I have formulated the theories of Fuzzy Shadow and Factorial Control, promoted the theoretical applications of fuzzy sets, and further made significant progress in developing fuzzy inference machines and computers of new generations, under the guidance of Prof. Xuesen Qian. In 2012, the Factor Space theory infiltrated into data mining and resulted in new breakthroughs of addressing the challenges in big data. In 2016, the Factor Space has been combined with Unified Intelligence, implementing unified mechanisms of intelligence generation into Chinese medicine, fault diagnosis and evidence-based systems. Now it’s also reaching out to multiple industries, like an intelligent incubation program in China for all people titled “Goddess Luo Engineering”, in order to provide more contributions to the digital economy and the society.

The eleven articles selected in this issue show a representative demonstration of Factor Space and its strong connections with related areas like fuzzy set, rough set, decision making and production management. Among those, the two articles of “Intuitionistic Fuzzy Soft Rough Approximation Operators” and “A Fuzzy Multi Objective Inventory Model” are typical cases of the concept “Factor”, that probably could provide you a further understanding of Factor Space.