Some concepts and properties of uncertain fields

Uncertain field is virtually an extension of uncertain process with the index space changing from a totally ordered set into a partially ordered one such as time-space or a surface. For describing the uncertain field, this paper introduces several concepts of uncertainty distribution and inverse uncertainty distribution. In addition, a sufficient and necessary condition is proved for the uncertainty distribution of an uncertain field. Then a concept of independence of uncertain fields is introduced and the operational law is derived for a strictly monotone function of independent uncertain fields. Furthermore, another two concepts of uncertain stationary independent increment field and Liu field are proposed, and meanwhile some of their properties are investigated.