On some properties of distance measures

NEW RESULTS ON THE EXISTING FUZZY DISTANCE MEASURES

In this paper, we investigate the properties of some recently pro-posed fuzzy distance measures. We find out some shortcomings for these dis-tances and then the obtained results are illustrated by solving several examplesand compared with the other fuzzy distances.

Information Measures via Copula Functions

In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability d...

Several 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...

A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers

Fuzzy measures are suitable in analyzing human subjective evaluation processes. Several different strategies have been proposed for distance of fuzzy numbers. The distances introduced for fuzzy numbers can be categorized in two groups:\1. The crisp distances which explain crisp values for the distance between two fuzzy numbers.\2. The fuzzy distance which introduce a fuzzy distance for normal f...

New distance and similarity measures for hesitant fuzzy soft sets

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 ...

Some properties of a new fuzzy distance measure