The family of k-additive measures has been introduced as a midterm between probabilities and general fuzzy measures and finds a wide number of applications in practice. However, its structure is different from other families of fuzzy measures and is certainly more complex (for instance, its vertices are not always {0, 1}valued), so it has not been yet fully studied. In this paper we present som...

Fuzzy-Attribute Graph (FAG) was proposed to handle fuzziness in the pattern primitives in structural pattern recogni~~on [l]. FAG has the advantage that we can combine several possible definition into a single template, and hence only one matching is required instead of one for each definition. Also, each vertex or edge of the graph can contain fuzzy attributes to model real-life situation. How...

Fuzzy-Attribute Graph (FAG) was proposed to handle fuzziness in the pattern primitives in structural pattern recognition. FAG has the advantage that we can combine several possible definitions into a single template, and hence only one matching is required instead of one for each definition. Also, each vertex or edge of the graph can contain fuzzy attributes to model real-life situations. Howev...

We prove that for any finite point set P in the plane, a triangle T , and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at least 144k8 points of P contains at least one of each color. This is the first polynomial bound for range spaces induced by homothetic polygons. The only previously known bound for this problem applies to the ...

There are several topological results ensuring in any properly colored graph the existence of a colorful complete bipartite subgraph, whose order is bounded from below by some topological invariants of some topological spaces associated to the graph. Meunier [Electron. J. Combin., 2014] presented the first colorful type result for uniform hypergraphs. In this paper, we give some new generalizat...

By combining the notions of interval-valued m-polar fuzzy graphs and graphs, notion cubic is first introduced. Then, degree a vertex in complete defined. After that, concepts direct product strong are given. Moreover, weak isomorphism co-weak defined, examples given to prove that not an isomorphism. Finally, complement presented.

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...