On constructing morphological erosion of intuitionistic fuzzy hypergraphs

Dhanya, P. M.; Sreekumar, A.; Jathavedan, M.; Ramkumar, P. B.

doi:10.1007/s41478-018-0096-3

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…An ( , ) cut can be applied on the medical report IFHGs to find sub IFHG (1) = number of nodes (2) = number of hyperedges; Read (3) for each = 1 to do (4) Read of all nodes (5) = 1 -(6) end for (7) for each = 1 to do (8) for each = 1 to number of elements in an edge do…”

Section: Applicationsmentioning

confidence: 99%

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Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

Dhanya

Sreekumar

Jathavedan

et al. 2018

International Journal of Mathematics and Mathematical Sciences

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A hypergraph consisting of hyperedges and nodes can be made intuitionistic fuzzy hypergraph (IFHG) by assigning membership and nonmembership degrees for both nodes and edges. Just as a hypergraph, an IFHG is also having hyperedges consisting of many nodes. Many flavours of a given IFHG can be created by applying morphological operators like dilation, erosion, adjunction, etc. The focus of this paper is to define morphological adjunction, opening, closing, and Alternative Sequential Filter (ASF) on IFHG. The system modeled in this way finds application in text processing, image processing, network analysis, and many other areas.

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Section: Applicationsmentioning

confidence: 99%

“…Morphological operations like dilation, erosion, adjunction are already defined on hypergraphs [2]. Dilation operation [3] and erosion [4] is already defined on IFHG. The purpose of this paper is to define adjunction, opening, closing, and ASF on IFHG.…”

Section: Introductionmentioning

confidence: 99%

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

Dhanya

Sreekumar

Jathavedan

et al. 2018

International Journal of Mathematics and Mathematical Sciences

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“…3. Now let us apply morphological operations (Bino et al, 2017;Dhanya et al, 2018a;2018b) on this X IF . Let X n be the node set in X IF and X e be the edge set in X IF .…”

Section: Assigning Membership Degreesmentioning

confidence: 99%

Text Summarization Using Morphological Filtering of Intuitionistic Fuzzy Hypergraph

Mohanan¹,

Rao²,

Jathavedan³

et al. 2018

Journal of Computer Science

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Text Summarization has been an area of interest for many years. It refers to creating a concise text of a document without any lose of information. Researchers in the area of natural language processing have developed many abstractive and extractive methods for creating summary. Abstractive summaries modifies the sentences and creates a modified concise form, while extractive summaries pick relevant sentences. The extractive method used in this study is a novel one which models the document as an Intuitionistic Fuzzy Hypergraph (IFHG). This IFHG is subjected to morphological filtering in order to create a concise summary. This is the premier work which applies morphological operations on IFHG that is modeled on a text. The method has generated summary which is almost similar to a human generated summary and showed more accuracy when compared with other machine generated summaries.

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“…Abraham Jacob and P. B. Ramkumar introduced the concept of Morphological Topology on Intuitionistic Fuzzy graph [1]. Various works based on mathematical morphology operators of intuitionistic fuzzy hypergraphs has been done by Dhanya P.M, Sreekumar A, Jathavedan M, Ramkumar P.B [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Graph Mathematical Morphology and Some of its Properties

Jacob

Ramkumar

2022

Preprint

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This paper studies the mathematical morphology operators acting on a lattice of all intuitionistic fuzzy sub graphs of an intuitionistic fuzzy graph (IFG). pn-adjacency of vertices and edges are defined as neighbourhoods of vertices and edges. We define vertex dilation, vertex erosion, edge dilation, edge erosion and some of their properties on intuionistic fuzzy graph using pn-adjacency of vertices and edges. We propose elementary mathematical morphology operators, dilation and erosion, on intuionistic fuzzy graph using pn-adjacency of vertices and edges based on lattice theory and also prove following basic properties of the proposed intuitionistic fuzzy graph mathematical morphology operators, dilation and erosion. (1) Dilation and erosion on IFG are increasing (2) Dilation is extensive. (3) Erosion is anti-extensive. (4) Dilation is distributive with respect to union and Erosion on IFG is distributive with respect to intersection. These properties are analogous to the properties of dilation and erosion in the classical Mathematical Morphology. So this paper is a theoretical extension of mathematical morphology on graphs to mathematical morphology on intuitionistic fuzzy graph. MSC Classification: 68U10 , 05C72

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On constructing morphological erosion of intuitionistic fuzzy hypergraphs

Cited by 3 publications

References 9 publications

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

Text Summarization Using Morphological Filtering of Intuitionistic Fuzzy Hypergraph

Intuitionistic Fuzzy Graph Mathematical Morphology and Some of its Properties

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