let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

The purpose of this paper is to investigate and propose a fuzzy extended economic production quantity model based on an elaboratively modeled unit cost structure. This unit cost structure consists of the various lot-size correlative components such as on-line setups, off-line setups, initial production defectives, direct material, labor, and depreciation in addition to lot-size noncorrelative i...

A simplex spanned by a colored point set in Euclidean d-space is colorful if all vertices have distinct colors. The union of all full-dimensional colorful simplices spanned by a colored point set is called the colorful union. We show that for every d ∈ N, the maximum combinatorial complexity of the colorful union of n colored points in R is between Ω(n(d−1) 2 ) and O(n(d−1) 2 log n). For d = 2,...

The colorful Carathéodory theorem, proved by Bárány in 1982, states that given d+1 sets of points S1, . . . ,Sd+1 in R , such that each Si contains 0 in its convex hull, there exists a set T ⊆ ⋃ d+1 i=1 Si containing 0 in its convex hull and such that |T ∩Si| ≤ 1 for all i ∈ {1, . . . , d + 1}. An intriguing question – still open – is whether such a set T , whose existence is ensured, can be fo...

This paper proposes a novel approach for smoothing surfaces represented by triangular meshes. The proposed method is a two-step procedure: surface normal smoothing through fuzzy vector median (FVM) filtering followed by vertex position update based on the least square error criteria. This paper applies the fuzzy ordering theory to the vector based data and introduces the fuzzy vector median. Th...

Since metabolites cannot be predicted from the genome sequence, high-throughput de novo identification of small molecules is highly sought. Mass spectrometry (MS) in combination with a fragmentation technique is commonly used for this task. Unfortunately, automated analysis of such data is in its infancy. Recently, fragmentation trees have been proposed as an analysis tool for such data. Additi...

In this paper, we define fuzzy graph chains, which comprise vertex identification. These graphs are isomorphic graphs, provide that after applying various features to the chain of as special .