Author

# Krishna Kundu

Bio: Krishna Kundu is an academic researcher from University of Calcutta. The author has contributed to research in topic(s): Inertial wave & Fuzzy classification. The author has an hindex of 4, co-authored 8 publication(s) receiving 86 citation(s).

##### Papers

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TL;DR: A new relationship is presented between fuzzy concept lattice built from the fuzzy relation and the set of minimal disconnections of the associated fuzzy graph, which is important from the point of view of application and computation.

Abstract: In this paper, we present a new relationship between fuzzy concept lattice and fuzzy graph. Given a fuzzy binary relation, we define an underlying fuzzy graph, and establish a new relation between the set of elements of the fuzzy concept lattice built from the fuzzy relation and the set of minimal disconnections of the associated fuzzy graph. This link is important from the point of view of application and computation.

55 citations

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Abstract: 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.

14 citations

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Abstract: The velocity potential due to the presence of a horizontal circular ring of wave sources of time-dependent strength in a fluid of finite constant depth with an inertial surface composed of uniformly distributed floating particles is obtained when the effect of surface tension at the inertial surface is included.

7 citations

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Abstract: This note is concerned with the problem of forced motion due to a vertical circular cylindrical wave-maker immersed in a liquid with an inertial surface composed of uniformly distributed floating particles. The techniques of Laplace transform in time and Weber transform in the radial co-ordinate are used to obtain the velocity potential and hence the inertial surface depression. For the special case of a time-harmonic wave-maker, the potential function is analysed for its steady-state development. It is shown that if the inertial surface is “too heavy”, the disturbance due to the wave-maker remains confined within a short distance only.

4 citations

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01 Jan 2015

TL;DR: This paper begins with defining a fuzzy graph corresponding to the L-context (fuzzy context), and goes on to demonstrate that t-concepts can be found to correspond with each maximal cliques of t-level graph of the defined fuzzy graph.

Abstract: 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.

2 citations

##### Cited by

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TL;DR: Fuzzy competition graph as a generalization of competition graph is introduced here and two generalizations of fuzzy competition graphs as fuzzy k-competition graphs and p-comp competition fuzzy graphs are also defined.

Abstract: Fuzzy competition graph as a generalization of competition graph is introduced here. Two generalizations of fuzzy competition graph as fuzzy k-competition graphs and p-competition fuzzy graphs are also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, related to fuzzy graphs, are also defined here. Besides, some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. And finally, several results to find strong edges of the above mentioned graphs have also been established.

142 citations

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TL;DR: 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 and some challenges about the proposed framework are discussed.

Abstract: 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

104 citations

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TL;DR: It is shown that an image can be represented by a fuzzy planar graph, and contraction of such animage can be made with the help of a fuzzyPlanar graph.

Abstract: 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.

103 citations

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TL;DR: This work proposes an algorithm for generating the bipolar fuzzy formal concepts, a method for ( α, β ) -cut ofipolar fuzzy formal context and its implications with illustrative examples.

Abstract: Formal Concept Analysis (FCA) is a mathematical framework for knowledge processing tasks. FCA has been successfully incorporated into fuzzy setting and its extension (interval-valued fuzzy set) for handling vagueness and impreciseness in data. However, the analysis in such settings is restricted to unipolar space. Recently, some applications of bipolar information are shown in bipolar fuzzy graph, lattice theory as well as in FCA. The adequate analysis of bipolar information using FCA requires incorporation of bipolar fuzzy set and an appropriate lattice structure. For this purpose, we propose an algorithm for generating the bipolar fuzzy formal concepts, a method for ( α , β ) -cut of bipolar fuzzy formal context and its implications with illustrative examples.

102 citations

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TL;DR: In this note, it is shown by examples that Definitions 3.1, 5.6, and 5.7 contain some flaws and then the correct versions are provided and a generalized bipolar fuzzy graph is introduced.

Abstract: In this note, we show by examples that Definitions 3.1, 5.6, and 5.7, Example 5.8, Propositions 5.9 and 5.10, and partial proof of Propositions 5.11 and 5.12 in a previous paper by Akram (Muhammad Akram, Bipolar fuzzy graphs, Inform. Sci. 181 (2011) 5548–5564) contain some flaws and then provide the correct versions. Finally, we introduce a generalized bipolar fuzzy graph.

82 citations