Medium mathematics systems: Review and prospect

Medium mathematics systems (MMS) are the new systems that extend precise quantity objects to fuzzy ones in mathematical foundation. MMS have had important influence to the researches on the logical foundation of mathematics and set theory. Most of the contents in this paper fall into one of the following three aspects: research background of MMS; fundamental contents in MMS and the relation between MMS and classical mathematics systems, in which medium concepts, medium principle, medium logic systems (ML), medium axiom set theory (MS) and current situation of MMS are included; the academic disputation about ML, especially quoting the pros and cons whether or not ML is a new logic. In addition, the application prospect of MMS has been viewed.