Perception-based granular probabilities in risk modeling and decision making

Our focus is on the issue of decision making in risky situations. We discuss the need for using decision functions to aid in capturing the decision maker's preference among these types of uncertain alternatives. The use of fuzzy rule based formulations to model these functions is investigated. We discuss the role of perception based granular probability distributions as a means of modeling the uncertainty profiles of the alternatives. Various properties of this method of describing uncertainty are provided. Tools for evaluating rule based decision functions in the face of perception based uncertainty profiles are presented. Consideration is given to the situation in which our uncertainty profiles are expressed in terms of a cumulative distribution function. We introduce the idea of a perception based granular cumulative distribution and describe its representation in terms of a fuzzy rule-based model