AbstractWhat is soft computing? What is fuzzy computing? What is the relationship between them? This paper intends to provide clear answers to these questions. We focus on exploring the notions of the fuzzy coordinate system and the related transformations between qualitative and quantitative information. These notions are considered to be the core ideas of fuzzy computing. Then the three novel theories of fuzzy computing and soft computing developed by the first author of this paper, namely, the Falling Shadow Representation of fuzzy theory, the Factors Space theory and the Truth Value Flow Inference theory are introduced.