A concept of fuzzy transition probabilities

Starting from fuzzy real numbers with an arbitrary lattice of belief and following the extension principle, we develop concepts of fuzzy probabilities, transition probabilities and random variables and of their combinations, and show that these concepts are consistent. We derive some results on fuzzy real numbers, on the expectation of fuzzy random variables and on fuzzy stochastic processes. To sketch the range of applications of fuzzy stochastics, we give two examples that show how real-world problems may be modeled by means of fuzzy probabilities and that give small numerical examples. Moreover, we give a brief outlook for a possible expansion of our theory to fuzzy Markovian decision processes by means of a partial order on the set of all fuzzy real numbers.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

The Mössbauer effect and collective motions in glass-forming liquids and polymeric networks

Glass-forming liquids, synthetic polymers and biopolymers share essential properties. Dynamic processes in these complex systems are characterized by cooperative motions with wide distributions of time scales, which manifest themselves in broad quasielastic lines in the Mössbauer spectrum. In this article, the application of the Mössbauer effect to the study of structural dynamics in complex systems is discussed.     

Stressed states in domain switching of ferroelectric liquid crystal devices

In this paper we show that the director profile of a low pre-tilt surface stabilized ferroelectric liquid crystal passes through quasi-static stressed states during domain switching under direct drive conditions. Using polarized stroboscopic microscopy, we have observed two quasi-static transmission levels during a domain switching transition from dark to light. This is a result of the directors reorienting into stressed profiles both before and after the chevron interface has switched. By modelling the interaction between the elastic forces and the torque from the applied field, we have determined these voltage dependent director profiles and, by calculating their corresponding transmissivities, have shown very good agreement with the experimentally observed values.