Weighted averaging filters and nonlinear partial differential equations (PDEs) are two popular concepts for discontinuity-preserving denoising. In this paper we investigate novel relations between these filter classes: We deduce new PDEs as the scaling limit of the spatial step size of discrete weighted averaging methods. In the one-dimensional setting, a simple weighted averaging of both neigh...

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study ...

Model uncertainty remains a challenge to researchers in different applications. When many competing models are available for estimation, and without enough guidance from theory, model averaging represents an alternative to model selection. Despite model averaging approaches have been present in statistics for many years, only recently they are starting to receive attention in applications. The ...

In this paper, we develop a new approach for decision making with Dempster-Shafer theory of evidence by using linguistic information. We suggest the use of different types of linguistic aggregation operators in the model. We then obtain as a result, the belief structure — linguistic ordered weighted averaging (BS-LOWA), the BS — linguistic hybrid averaging (BS-LHA) and a wide range of particula...

in a detection network, the final decision is made by fusing the decisions from local detectors. the objective of that decision is to minimize the final error probability. to implement and optimal fusion rule, the performance of each detector, i.e. its probability of false alarm and its probability of missed detection as well as the a priori probabilities of the hypotheses, must be known. howev...

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysi...

In turbulent flow, the normal procedure has been seeking means u of the fluid velocity u rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of largeand small-length scales in the flow field. The filtered field u denotes the eddies of size O(δ) and larger. Applying local spatial averaging operator with averaging radius δ to the...

The renormalization group approach is used to study the effects of a “canonical” constraint (e.g., a fixed number of occupied bonds) on critical quenched disordered systems. The constraint is found to be always irrelevant, even near the “random” fixed point. This proves that α<0, or that ν>2/d. “Canonical” and “grand canonical” averages thus belong to the same universality class. Related predic...

A b s t r a c t In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.