Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random variables

This paper proposes a convergence theorem of fuzzy set-valued random variables under addition which is given by the general triangular normed extension principles. Applying the result with the known results of the various types for strong laws of large numbers of fuzzy set-valued random variables, we obtain a few interesting results of the strong laws of large numbers for triangular norm-based addition of fuzzy set-valued random variables. The finding of Terán [Strong law of large numbers for t-normed arithmetics, Fuzzy Sets and Systems 159 (2008) 343–360] is a special case of our results.