In this paper, we introduce a fuzzy set theoretic approach for dealing with uncertainty in images in the context of spatial and topological relations existing among the objects in the image. We propose an object-oriented graph theoretic model for representing an image and this model allows us to assess the similarity between images using the concept of (fuzzy) graph matching. Sufficient flexibi...

In this paper, the effect of the removal of a node or an arc of a fuzzy graph on the minimum strong dominating set of the fuzzy graph is studied. The motivation behind this study is the identification of fault tolerance in the topological design of a network. That is, the ability of the network to provide service even when it contains a faulty component or components. MSC: 05C69.

The main aim of this paper is to study the maximum flow problem when the underlying associated structure is not well defined and must be modeled as a fuzzy graph. However, to deal with the problem it is necessary to develop several well known concepts from classical theory, in the fuzzy graph context, such as flow, network, and admissible flow. The above maximum flow problem is formulated and s...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

In this paper, we propose a new temporal data mining method considering a set of archæological objects which are temporally represented with fuzzy numbers. Our method uses an index which quantifies the anteriority between two fuzzy numbers for the construction of a weighted oriented graph. The vertices of the graph correspond to the temporal objects. Using this anteriority graph, we estimate th...

The concept of vague graph was introduced by Ramakrishna in [12]. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. The main purpose of this paper is to introduce the concept of dominating set, perfect dominating set, minimal perfect dominating set and i...

A vertex v in a connected fuzzy graph G is a fuzzy detour boundary vertex of a vertex u, if ) , ( ) , ( v u w u Δ ≤ Δ for every fuzzy detour neighbour w of v. This paper is devoted to see how the fuzzy detour boundary vertices are related to fuzzy detour interior vertices. Further, the relation between the fuzzy detour boundary vertices and fuzzy detour eccentric vertices are also studied. Some...

In a recent paper we studied how a fuzzy measure can be defined from a fuzzy graph. In this paper we explore its applicability to information retrieval, and, more specifically, to compute similarities between sets of words.