Distance Measures for Well-Distributed Sets
نویسندگان
چکیده
منابع مشابه
On distance measures for well-distributed sets
In this paper we investigate the Erdös/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been classically used to study this problem. We conjecture that a majorant for the spherical means suffices to prove the distance conjecture(s) in this setting. For a ...
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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 ...
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Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX may be if X contains a well-distributed set whose distance set ∆ satisfies the estimate |∆ ∩ [0, N ]| ≤ CN3/2− . We also give a necessary and sufficient condition for the existence of a well-distributed set with |∆ ∩ [0, N ]| ≤ CN .
متن کاملDistance Sets of Well-Distributed Planar Point Sets
We prove that a well-distributed subset of R2 can have a distance set ∆ with #(∆ ∩ [0, N ]) ≤ CN3/2− only if the distance is induced by a polygon K. Furthermore, if the above estimate holds with = 1/2, then K can have only finitely many sides.
متن کاملSeveral new results based on the study of distance measures of intuitionistic fuzzy sets
It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-1316-9