Interval‐valued equivalence measures respecting uncertainty in image processing

Abstract

A new concept of equivalence between intervals and the induced indistinguishability between interval‐valued (IV) fuzzy sets are proposed and considered. A new notion of the degree of IV equivalence is presented where partial or linear orders and the width of intervals are involved reflecting uncertainty. Furthermore, construction methods of the considered equivalences are provided and the relation between them and other notions of IV equivalences are studied. Finally, a methodology to apply the proposed equivalences in the field of image processing is shown, along with an illustrative example.

ℱ‐homogeneous functions and a generalization of directional monotonicity

“…We put this methodology to the test in two differente frameworks: Using two recent thresholding algorithms: one based on equivalence measures (EM) 20 and one based on a fuzzy entropy approach (FE) 21 ; Using two well‐known image thresholding algorithms in the literature: Otsu 22 and Tizhoosh 23 …”

“…Using two recent thresholding algorithms: one based on equivalence measures (EM) 20 and one based on a fuzzy entropy approach (FE) 21 ;…”

“…• Using two recent thresholding algorithms: one based on equivalence measures (EM) 20 and one based on a fuzzy entropy approach (FE) 21 ; • Using two well-known image thresholding algorithms in the literature: Otsu 22 and Tizhoosh. 23 To check whether our proposal improves the thresholded images, we consider 10 images that are commonly used to test image thresholding algorithms (see the first column of Figures 2 and 3).…”