Probabilistic-valued decomposable set functions with respect to triangle functions

In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $τ$ in an appropriate probabilistic metric space as natural candidates for the "addition", leading to the concept of $τ$-decomposable measures. Several set functions, among them the classical (sub)measures, previously defined $τ_T$-submeasures, $τ_{L,A}$-submeasures as well as recently introduced Shen's (sub)measures are described and investigated in a unified way. Basic properties and characterizations of $τ$-decomposable (sub)measures are also studied and numerous extensions of results from the above mentioned papers are provided.

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