A Generalized Measure of Riskiness

Are Risk Averters Averse to Risky Gambles?∗

This paper defines local aversion to a risk index. I show that the local aversion to the Aumann and Serrano [2008] index of riskiness coincides with absolute risk aversion, and that the same applies for the Foster and Hart [2009] measure of riskiness. Using this “local consistency” I offer a new approach for axiomatizing the Aumann and Serrano index of riskiness and present other applications o...

Ranking of generalized fuzzy numbers using distance measure and similarity measure

A Reserve-Based Axiomatization of the Measure of Riskiness

We provide an axiomatic characterization of the measure of riskiness of “gambles” (risky assets) that was introduced by Foster and Hart (2007). The axioms are based on the concept of “reserve.” A gamble—or “risky asset”—is a real-valued random variable g having some negative values—losses are possible—and positive expectation, i.e., P[g < 0] > 0 and E[g] > 0. For simplicity we assume that each ...

An improved similarity measure of generalized trapezoidal fuzzy numbers and its application in multi-attribute group decision making

Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric...

Generalized Aggregate Uncertainty Measure 2 for Uncertainty Evaluation of a Dezert-Smarandache Theory based Localization Problem

In this paper, Generalized Aggregated Uncertainty measure 2 (GAU2), as a newuncertainty measure, is considered to evaluate uncertainty in a localization problem in which cameras’images are used. The theory that is applied to a hierarchical structure for a decision making to combinecameras’ images is Dezert-Smarandache theory. To evaluate decisions, an analysis of uncertainty isexecuted at every...