Fuzzy theory provides a rigorous, flexible approach to the problem of defining and computing. Therefore, to facilitate decision-making in geographic information system (GIS), the graph layer indicator and the Takagi Sugeno (TS) fuzzy model have to be integrated. This study explains several versions of the TS fuzzy model based on fuzzy theory and fuzzy operation. An inference model is constructe...

We present a direct and fairly simple proof of the following incidence bound: Let P be a set of m points and L a set of n lines in R, for d ≥ 3, which lie in a common algebraic two-dimensional surface of degree D that does not contain any 2-flat, so that no 2-flat contains more than s ≤ D lines of L. Then the number of incidences between P and L is

We investigate some new properties of intuitionistic fuzzy competition graphs. We present the construction of intuitionistic fuzzy competition graph. We study new type of intuitionistic fuzzy graphs by considering intuitionistic fuzzy open neighbourhood and intuitionistic fuzzy closed neighbourhood of the vertices. We also present an application of intuitionistic fuzzy competition graphs. c ©20...

An incidence of a graph G is a pair (v, e) where v is a vertex of G and e an edge incident to v. Two incidences (v, e) and (w, f) are adjacent whenever v = w, or e = f , or vw = e or f . The incidence coloring game [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980–1987] is a variation of the ordinary coloring game where the two players, Alice and Bob, alte...

The incidence coloring game has been introduced in [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980– 1987] as a variation of the ordinary coloring game. The incidence game chromatic number ιg(G) of a graph G is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on G. In [C. Charpentier and É. Sopen...

In a graph G, a vertex dominates itself and its neighbors. A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. The minimum cardinality taken over all, the minimal double dominating set which is called Fuzzy Double Domination Number and which is denoted as ) (G fdd  . A set V S  is called a Triple dominating set of a graph G if every ...

The chromatic sum of a graph G, ∑ (G), is introduced in the dissertation of Kubicka [3]. It is defined as the smallest possible total over all vertices that can occur among all colorings of G using natural numbers for the colors. It is known that computing the chromatic sum of an arbitrary graph is an NP-complete problem. The vertex-strength of the graph G, denoted by s(G), is the smallest inte...

A generic de.nition of fuzzy morphism between graphs (GFM) is introduced that includes classical graph related problem de.nitions as sub-cases (such as graph and subgraph isomorphism). The GFM uses a pair of fuzzy relations, one on the vertices and one on the edges. Each relation is a mapping between the elements of two graphs. These two fuzzy relations are linked with constraints derived from ...