An eternal $m$-secure set of a graph $G = (V,E)$ is aset $S_0subseteq V$ that can defend against any sequence ofsingle-vertex attacks by means of multiple-guard shifts along theedges of $G$. A suitable placement of the guards is called aneternal $m$-secure set. The eternal $m$-security number$sigma_m(G)$ is the minimum cardinality among all eternal$m$-secure sets in $G$. An edge $uvin E(G)$ is ...

Spatial information requires models which allow us to answer ‘maybe’ to questions asking whether a location lies within a region. At the same time, models must account for data at varying levels of detail. Existing theories of fuzzy relations and fuzzy graphs do not support notions of granularity that generalize the successes of rough set theory to rough and fuzzy graphs. This paper presents a ...

Fuzzy models are present everywhere from natural to artificial structures, embodying the dynamic processes in physical, biological, and social systems. As real-life problems often uncertain on account of inconsistent indeterminate information, it seems very demanding for an expert solve those using a fuzzy model. In this regard, we develop hybrid new model m-polar Diophantine neutrosophic N-sof...

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...

A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − ‫〉ܦ‬ is connected. The Non-split domination number ߛ ௡௦ ሺ‫ܩ‬ሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௡௦ ሺ‫ܩ‬ሻwith other known parameters of IFG G. 1. In...

A path P connecting a pair of vertices in connected fuzzy graph is called detour, if its μ - length maximum among all the feasible paths between them. In this paper we establish notion detour convex sets, covering, basis, number, blocks and investigate some their properties. It has been proved that, for complete G, set any G covering. necessary sufficient condition to become block also establis...

The Fuzzy logic concept is implemented in several image processing operations such as edge detection, segmentation, object recognition, etc. In this paper, a novel Image encryption algorithm based on multiple fuzzy graph (FG) mapping technique is proposed. The Fuzzy graphs are obtained from a matrix of size n and then they are used to encrypt an image. Here fuzzy graphs with triangular and sigm...

Systems applying fuzzy logic are rule based ones. The collection of the rules the so called rule base can be characterized as dense or sparse depending on whether there exist rules for all the possible observations. In the sparse case for some observations there are no rules whose antecedent part would overlap the observation at least partially. Therefore the classical compositional reasoning m...