Some Compact Classes of Open Sets under Hausdorff Distance and Application to Shape Optimization

Hierarchical Group Compromise Ranking Methodology Based on Euclidean–Hausdorff Distance Measure Under Uncertainty: An Application to Facility Location Selection Problem

Proposing a hierarchical group compromise method can be regarded as a one of major multi-attributes decision-making tool that can be introduced to rank the possible alternatives among conflict criteria. Decision makers’ (DMs’) judgments are considered as imprecise or fuzzy in complex and hesitant situations. In the group decision making, an aggregation of DMs’ judgments and fuzzy group compromi...

A Supervised Modification of the Hausdorff Distance for Visual Shape Classification

Hausdorff distance is a deformation tolerant measure between two sets of points. The main advantage of this measure is that it does not need an explicit correspondence between the points of the two sets. This paper presents the application to automatic face recognition of a novel supervised Hausdorff-based measure. This measure is designed to minimize the distance between sets of the same class...

Probabilistic matching of sets of polygonal curves∗

Analysis and comparison of geometric shapes are of importance in various application areas within computer science, e.g., pattern recognition and computer vision. The general situation in a shape matching problem is that we are given two shapes A and B and a certain class T of allowable transformations and we want to transform B optimally so that the transformed image of B is as close to A as p...

Some separation axioms via modified θ-open sets

Computable Operations on Compact Subsets of Metric Spaces with Applications to Fréchet Distance and Shape Optimization

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces (X, d): thereby generically including computational and optimization problems over higher types, such as the compact ‘hyper’ spaces of (i) nonempty closed subsets of X w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on X . The thus obtained...