A unified characterization of generalized information and certainty measures

Abstract: In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously considered by numerous authors. We provide the corresponding characterization theorems and define a new generalized measure called the Inforcer, which is the quasi-linear mean of the function associated to the event probability following the general composition law. In particular, we pay attention to the polynomial composition and the corresponding polynomially composable Inforcer measure. The most common measures appearing in literature can be obtained by specific choice of parameters appearing in our generic measures and they are listed in tables.