Fuzzy k -competition graphs and p -competition fuzzy graphs

Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowski's graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.

Fuzzy Planar Graphs

Due to the rapid advances of information technologies, Big Data, recognized with 4Vs characteristics (volume, variety, veracity, and velocity), bring significant benefits as well as many challenges A major benefit of Big Data is to provide timely information and proactive services for humans The primary purpose of this paper is to review the current state-of-the-art of Big Data from the aspects of organization and representation, cleaning and reduction, integration and processing, security and privacy, analytics and applications, then present a novel framework to provide high-quality so called Big Data-as-a-Service The framework consists of three planes, namely sensing plane, cloud plane and application plane, to systemically address all challenges of the above aspects Also, to clearly demonstrate the working process of the proposed framework, a tensor-based multiple clustering on bicycle renting and returning data is illustrated, which can provide several suggestions for rebalancing of the bicycle-sharing system Finally, some challenges about the proposed framework are discussed

A Big Data-as-a-Service Framework: State-of-the-Art and Perspectives

Bipolar fuzzy graph representation of concept lattice

Notes on “Bipolar fuzzy graphs”

Fuzzy graph representation of a fuzzy concept lattice

Since one major disadvantage of application of fuzzy formal concept analysis is that large numbers of fuzzy concepts are generated from fuzzy context, it is practically impossible to analyze such a large amount of concepts. Often it may be required to consider some particular concepts. For example, one might be interested to find out the fuzzy concepts containing all those objects which share some specific property with a specific/required degree from a given fuzzy context. Given such a situation, proto-fuzzy concepts may play a very useful role. This paper proposes a proto-fuzzy concept generation technique using fuzzy graph on uncertainty data. In this paper, we begin with defining a fuzzy graph corresponding to the L-context (fuzzy context). We then go on to demonstrate that t-concepts can be found to correspond with each maximal cliques of t-level graph of the defined fuzzy graph. After that, we determine all those cliques which corresponds to the proto-fuzzy concepts of degree \(t\). Finally, a demonstration has been made using an example with the proposed technique.

Partha Ghosh

Papers

Fuzzy graph representation of a fuzzy concept lattice

Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph