in this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group g and give four equivalent conditions each ofwhich characterizes this relation. we demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. moreover, we study the behavior of these equivalence classes under theaction of a...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

We design an approximation algorithm for maximizing \(\alpha\)-bisubmodular function with matroid constraint, where the is a generalization of bisubmodular function. The concept \(\alpha\)- bisubmodularity provided by Huber, Krokhin, and Powell [[1], 2014], rank delta-matroids cut capacity directed networks have \(\alpha\)-bisubmodularity. consider two cases problem, monotone non-monotone objec...

In this paper, we present a new background estimation algorithm which effectively represents both background and foreground. The problem is formulated with a labeling problem over a patch-based Markov random field (MRF) and solved with a graph-cuts algorithm. Our method is applied to the problem of mosaic blending considering the moving objects and exposure variations of rotating and zooming ca...

Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

Quantitative measurements of tumor in general and tumor volume in particular, become more realistic with the use of Magnetic Resonance imaging, especially when the tumor morphological changes become irregular and difficult to assess by clinical examination. However, tumor volume estimation strongly depends on the image segmentation, which is fuzzy by nature. In this paper a fuzzy approach is pr...