The tau-additive measure and its connection with the lambda-additive measure

In this paper, we study monotone set functions defined as the composition of an additive measure with a strictly increasing function. This function is unary operator in continuous-valued logic, called tau function, and it generator function-based parametric mapping. We provide necessary sufficient condition for equality two that are induced by different functions. Using its properties, introduce new call tau-additive measure. computationally simple can be viewed upper or lower probability depending on parameter settings present parameter-dependent submodularity supermodularity show how constructed from finite set. procedure analogous to well-known lambda-additive constructed, but our method simpler. demonstrate used approximate Lastly, exploiting these theoretical results, application area human resource management.