The Fuzzy-Stochastic Entropy and the Concept of a Hybrid Measures of Uncertainty

Abstract

This chapter is devoted to presenting the development of the theory of fuzzy-stochastic entropy through the construct of hybrid measures of general uncertainty from the possibility and probability spaces. It builds the epistemic frame from the discussions on the differences and similarities of possibility and probability spaces and their relationships to the certainty-uncertainty and necessity-freedom dualities with relational continuum and unity within the quality-quantity duality. The necessity is related to necessary conditions of knowing while the freedom is related to sufficient conditions of knowing. The discussions are extended to the construction of the possibility set and the probability set with analytical tools of indicator functions under a specific paradigm of thought as applicable to information conditions within the exact-inexact duality.