Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principl...

Uncertainty theory is a new branch of axiomatic mathematics for studying the subjective uncertainty. In uncertain theory, uncertain variable is a fundamental concept, which is used to represent imprecise quantities (unknown constants and unsharp concepts). Entropy of uncertain variable is an important concept in calculating uncertainty associated with imprecise quantities. This paper introduces...

Uncertainty reduction has a major role in communication theory of relational development. Two competing theories, Berger and Calabrese’s (1975) uncertainty reduction theory (URT) and Sunnafrank’s (1986) predicted outcome value (POV), provide different perspectives on the uncertainty reduction process during initial interactions. Research suggests that when forming a first impression, negative i...

A novel survey dataset on computed tomography (CT) machine acquisition is used to explore which theories best answer two questions from the decision making literature. First, what determines how much uncertainty a firm has when investing in updated technology? Second, what determines the value of the acquisition? In answering these questions, two theoretical comparisons are conducted. In the fi...

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he de…ned them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of r...

Sustainable management of the natural systems is essential in the presence of anthropogenic and natural disasters. Fisher information based measure and hypothesis have been proposed to quantify the sustainability of natural systems, which are used in this work to formulate management objectives. Since uncertainty is omnipresent in natural systems, its consideration is important. Real options th...

As an extension of the classical set theory, rough set theory plays a crucial role in uncertainty measurement. In this paper, concepts of information entropy and mutual information-based uncertainty measures are presented in both complete and incomplete information/decision systems. Then, some important properties of these measures are investigated, relationships among them are established, and...

This paper compares Evidence Theory (ET) and Bayesian Theory (BT) for uncertainty modeling and decision under uncertainty, when the evidence about uncertainty is imprecise. The basic concepts of ET and BT are introduced and the ways these theories model uncertainties, propagate them through systems and assess the safety of these systems are presented. ET and BT approaches are demonstrated and c...

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the Rényi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed pheno...