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

This note is concerned with the derivation of velocity potentials describing the generation of infinitesimal gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles, due to fundamental line and point sources with time-dependent strengths submerged in a liquid of finite constant depth.

/pdf/a-note-on-the-singularities-in-the-theory-of-water-waves-3vuck75wdv.pdf

Krishna Kundu

Papers

Fuzzy graph representation of a fuzzy concept lattice

A note on the singularities in the theory of water waves with an inertial surface

Ring source potentials in a fluid with an inertial surface in the presence of surface tension

A note on the cylindrical wave-maker problem in a liquid with an inertial surface

A cylindrical wave-maker in liquid of finite depth with an inertial surface