A lot of machine learning algorithms, including clustering methods such as K-nearest neighbor (KNN), highly depend on the distance metrics to understand data pattern well and make right decision based data. In recent years, studies show that can significantly improve performance or deep model in clustering, classification, recovery tasks, etc. this article, we provide a survey widely used chall...

On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.

this paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space takagi-sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. lyapunov krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space.

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...

We discuss the computational complexity of special cases of the 3-dimensional (axial) assignment problem where the elements are points in a Cartesian space and where the cost coefficients are the perimeters of the corresponding triangles measured according to a certain norm. (All our results also carry over to the corresponding special cases of the 3-dimensional matching problem.) The minimizat...

We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a seminorm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f . We determine a decomposition formula for this Laurent norm; an expression for the Laurent norm for f in terms of the Laurent norms for each of the irreducibl...

in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.