A construction of a fuzzy valued measure based on minimum T-norm

In this paper we generalize the well known construction of "classic" measure theory to the fuzzy case. We consider such T-norm based classes of fuzzy sets as T-semirings and T-tribes (T - sigmaalgebras), such fuzzy valued functions as elementary T-measures, exterior T-measures and T-measures, find we suggest the construction of a T(M)-measure by extension of an elementary T(M)-measure on a T(M)-semiring to a T(M)-measure on a T(M)-tribe in the case of the minimum T-norm T(M).