By Shoumei Li

After the pioneering works by means of Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was once systematically brought by way of Kendall {1974) and Matheron {1975). it's popular that the idea of set-valued random variables is a normal extension of that of normal real-valued random variables or random vectors. notwithstanding, as a result of the topological constitution of the gap of closed units and designated beneficial properties of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many distinct homes. this provides new meanings for the classical chance concept. as a result of improvement during this quarter long ago greater than 30 years, the speculation of set-valued random variables with many functions has turn into certainly one of new and lively branches in chance concept. In perform additionally, we're frequently confronted with random experiments whose results aren't numbers yet are expressed in inexact linguistic phrases.