Most of the edge detection methods available in literature are gradient based, which further apply thresholding, to find the final edge map in an image. In this paper, we propose a novel method that is based on fuzzy logic for edge detection in gray images without using the gradient and thresholding. Fuzzy logic is a mathematical logic that attempts to solve problems by assigning values to an i...

In this paper a new unsupervised segmentation algorithm based on Fuzzy Gibbs Random Field (FGRF) is proposed. This algorithm, named as FGS, can deal with fuzziness and randomness simultaneously. A Classical Gibbs Random Field (CGRF) servers as bridge between prior FGRF and original image. The FGRF is equivalent to CGRF when no fuzziness is considered; therefore, the FGRF is obviously a generali...

the aim of this paper is to study the categorical relations betweenmatroids, goetschel-voxman’s fuzzy matroids and shi’s fuzzifying matroids.it is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. the category of matroids can be embedded in that offuzzifying matroids as a simul...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...