مجموعه ارزشمندفازی مستمر راست فرآیندهای تصادفی با محدودیت چپ

The concept of (d) quasi-left continuous fuzzy set-valued stochastic process is proposed. A (d) cadlag. fuzzy set-valued stochastic process, i.e. (d) right continuous fuzzy set-valued stochastic processes with left limitation, is (d) quasi-left continuous if and only if for each positive predictable time this process is (d) left continuous almost surely on the set on which the predictable time is finite. A (d) cadlag. fuzzy set-valued stochastic process only has accessible jump if and only if for each totally inaccessible time this process is (d) left continuous almost surely on the set on which the totally inaccessible time is finite.

The theory of fuzzy set-valued stochastic process has been studied in [1{3], however, there are still many propertiesoffuzzyset-valuedstochasticprocess to be studied. This paper's purpose is to discuss a kind off uzzyset-valuedstochasticprocess,i.e.the(d) cadlag. fuzzy set-valued stochastic process. We will study the equivalent conditions for it being (d) quasi- left continuous and its other properties. For convenience, in Section 2 we rst introduce some basic denitions and results about fuzzy set- valued random variables which may be found in [1]. AttheendofSection2,wewillgivethemainresults, Theorems1and2.We will prove the two theoremsin Section 3.