A new weighted metric: the relative metric I

A New Weighted Metric: the Relative Metric I

The M–relative distance, denoted by ρM is a generalization of the p–relative distance, which was introduced in [10]. We establish necessary and sufficient conditions under which ρM is a metric. In two special cases we derive complete characterizations of the metric. We also present a way of extending the results to metrics sensitive to the domain in which they are defined, thus finding some con...

A New Weighted Metric: the Relative Metric II

In the first part of this investigation, [1], we generalized a weighted distance function of [2] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so–called M–relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generaliza...

On The Ranking Fuzzy Numbers Using Weighted Metric

A weighted metric method to optimize multi-response robust problems

In a robust parameter design (RPD) problem, the experimenter is interested to determine the values of con-trol factors such that responses will be robust or insensitive to variability of the noise factors. Response sur-face methodology (RSM) is one of the effective methods that can be employed for this purpose. Since quality of products or processes is usually evaluated through several quality ...

Weighted Hamming Metric Structures

A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the extended binary Hamming code to be perfect codes in the weighted Hamming metric. And, we also give some structures of a 2-perfect code and how to construct ...