Comparing representational geometries using whitened unbiased-distance-matrix similarity

Unbiased Matrix Rounding

We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular, statistics. We improve earlier solutions of different authors in two ways. For rounding matrices of size m × n, we reduce the runtime from O((mn)) to O(mn lo...

Ranking of generalized fuzzy numbers using distance measure and similarity measure

A revised Fuzzy - PROMETHEE method , using Fuzzy Distance and Similarity Measures

PROMETHEE refers to a collection of methods of ranking in the field of multi-criteria decision making. These methods are characterized by conceptual simplicity and practical applicability. However, the nature of phenomena involving decision-making in real world leads us to use fuzzy method of preference ranking. The most common criticism on mathematical ranking procedures is that they tend to d...

New distance and similarity measures for hesitant fuzzy soft sets

The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and similarity measures are considered as the important tools in different areas such as ...

Using Accurate Solid Angle Tools when Comparing EDS Detector Geometries

Analysts should strive for the EDS system that provides the highest efficiency for their analytical work. For detectors, that typically means starting with the geometry with the best solid angle (SA) value. Manufacturers should be designing interfaces to maximize the solid angle of the detectors without compromising the integrity of the electron columns. Accurate modeling of the solid angle is ...