This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

We define the notion of a random metric space and prove that with probability one such a space is isometric to the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particular, universal) spaces to the properties of distance matrices. We give examples of other categories in which the randomness and u...

Almost all nonbinary codes were designed for the Hamming metric. The Lee metric was defined by Lee in t958. Golomb and Welch (1968) and Berlekamp (1968) have designed codes for the Lee metric. In this paper, we derive all the discrete, memoryless, symmetric channels matched to the Lee metric, and investigate general properties of Lee metric block codes. Finally, a class of cyclic Lee metric cod...

The paper presents a metric that is well suited to evaluate online job schedules for massively parallel processors. We point out the disadvantages of commonly used metrics like makespan or machine utilization. We suggest to use the well known total weighted completion time metric with an appropriate selection of job weights and show that this metric exhibits many properties that are similar to ...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, 1 (2015) 49–79. ...

Representable relation algebras are characterised by a certain property of networks. Representations of relation algebras can be further classiied as homogeneous or universal. These properties are also characterised by properties of networks properties (amalgamation and joint embedding properties). For the homogeneous, universal case a method of constructing interval algebras from point algebra...

This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.

Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and ...