Compared with the complex fuzzy set (CFS) and intuitionistic (IFS), (CIFS) can handle two-dimensional uncertain information simultaneously, thus strengthen capability of capturing useful information. In this paper, we consider situation environment, where importance certain is also taken into consideration. To deal these situations, develop ordered weighted distance (CIFOWD) measure investigate...

For two closed curves on a plane (discrete version) and local criteria for similarity of points on the curves one gets a potential, which describes the similarity between curve points. This is the base for a global similarity measure of closed curves (Fréchet distance). I use borderlines of handwritten digits to demonstrate an area of application. I imagine, measuring the similarity of closed c...

This paper deals with the problem of measuring the similarity degree between two normalized possibility distributions encoding preferences or uncertain knowledge. Many existing de nitions of possibilistic similarity indexes aggregate pairwise distances between each situation in possibility distributions. This paper goes one step further, and discusses de nitions of possibilistic similarity meas...

Let P be a distribution with support S. The salient features of S can be quantified with persistent homology, which summarizes topolog-ical features of the sublevel sets of the distance function (the distance of any point x to S). Given a sample from P we can infer the persistent homology using an empirical version of the distance function. However, the empirical distance function is highly non...

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing distance inequalities. also a sharp upper estimate outer volume ratio from an arbitrary convex body unit balls subspaces $L_p$.