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.

References in corpus (3)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Generalized entropies and the transformation group of superstatistics
• When do generalized entropies apply? How phase space volume determines entropy

Cited by in corpus (5)

• Generalized Shannon-Khinchin Axioms and Uniqueness Theorem for Pseudo-additive Entropies
• An overview of generalized entropic forms
• Shannon Entropy Reinterpreted
• On the equivalence between four versions of thermostatistics based on strongly pseudo-additive entropies
• Comments on "On q-non-extensive statistics with non-Tsallisian entropy"