Several methods exist for electing committees of representatives and conducting multiple referenda based on approval voting. Recently, a family of rules for approval-based voting using ordered weighted averaging was proposed in [1], ranging from a simple candidate-wise majority (minisum) to egalitarian rule (minimax). Even though the first rule is strategyproof and the second is not, due to its...

We investigate the energy of arrangements of N points on a rectifiable d-dimensional manifold A ⊂ Rd′ that interact through the power law (Riesz) potential V = 1/r, where s > 0 and r is Euclidean distance in R ′ . With Es(A, N) denoting the minimal energy for such N -point configurations, we determine the asymptotic behavior (as N → ∞) of Es(A, N) for each fixed s ≥ d. Moreover, if A has positi...

For surfaces of revolution B in R, we investigate the limit distribution of minimum energy point masses on B that interact according to the logarithmic potential log(1/r), where r is the Euclidean distance between points. We show that such limit distributions are supported only on the “out-most” portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvatu...

In this paper, the cosine similarity measure of neutrosophic refined (multi-) sets is proposed and its properties are studied. The concept of this cosine similarity measure of neutrosophic refined sets is the extension of improved cosine similarity measure of single valued neutrosophic. Finally, using this cosine similarity measure of neutrosophic refined set, the application of medical diagnos...

It is shown that each continuous transformation h from Euclidean m-space (m > 1) into Euclidean n-space that preserves the equality of distances (that is, fulfils the implication |x−y| = |z−w| =⇒ |h(x)−h(y)| = |h(z)−h(w)|) is a similarity map. The case of equal dimensions already follows from the Beckman–Quarles Theorem. Mathematics Subject Classification (2000): primary 51F20, secondary 51F25,...

We propose a matrix completion algorithm for matrices where the columns appear in clusters. The algorithm estimates the similarity between every pair of points using partial distances, computed from the entries of their commonly observed indices. It is shown that the similarity matrix can be reliably estimated from partial distances, and used to aid the recovery process. It is observed that the...

The paper analyses issues leading to errors in graphic object classifiers. Thedistance measures suggested in literature and used as a basis in traditional, fuzzy, andNeuro-Fuzzy classifiers are found to be not suitable for classification of non-stylized orfuzzy objects in which the features of classes are much more difficult to recognize becauseof significant uncertainties in their location and...