Fuzzy Hypergraphs Research Articles

Evolution of Concentric Fuzzy Hypergraph for Inclusive Decision Making

Fuzzy hypergraphs plays a pivotal role in reaching concrete resolutions at times when the circumstances of making decisions is characterized by uncertainty. Decision making is an integrated process involving the dominance of cognition in the nature of decision making environment and the associated factors. The process of making managerial decisions centres on state of affairs, which can be tackled with the formulation of Concentric Fuzzy Hypergraph, an extended concept of fuzzy hypergraph to arrive at compatible and feasible pronouncements. The notion of Concentric Fuzzy Hypergraph is introduced and a comprehensive decision making model with the integration of Fuzzy Cognitive Maps is proposed. This research work outlines the conceptual framework of Concentric Fuzzy hypergraph and presents a comparative analysis of concentric fuzzy hypergraphic approach with Fuzzy Cognitive maps over fuzzy hypergraphic approach to justify the efficiency of the former. The idea of concentric fuzzy hypergraph will certainly open new vistas in the field of decision making.

A Study on Hypergraph Representations of Complex Fuzzy Information

The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.

Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment

In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

A FUZZY HYPERGRAPH APPROACH TO RESEARCH OF THE VALUE OF SOCIAL NETWORKS

Goal. In modern conditions, applied research is required in the field of analysis such properties of social networks as «social correlation», group interaction, the existence of «leaders of influence», the value of a social network taking into account reputation, conformism, activity of its agents. Materials and methods. The article proposes an original approach based on using the operation of differentiating a fuzzy hypergraph, building its derivative, which is a fuzzy graph of social correlation and mutual influence of network agents, and the interpretation of the results obtained in relation to social networks is presented as well. Results. Using a fuzzy hypergraphic formal representation of a social network in which the edges connect individual or group network agents that make up a particular group, coalition or configuration, and its differentiation operation, a fuzzy relation of network value is constructed, and indicators of the value of agents and the network as a whole are introduced. Conclusion. This approach allows us to analyze the influence of the leaders of agents on the social community, to assess how critical their influence is, to determine the most influential agents of the social network with the greatest value in terms of informational influences.

Learning with fuzzy hypergraphs: A topical approach to query-oriented text summarization

Existing graph-based methods for extractive document summarization represent sentences of a corpus as the nodes of a graph in which edges depict relationships of lexical similarity between sentences. This approach fails to capture semantic similarities between sentences when they express a similar information but have few words in common and are thus lexically dissimilar. To overcome this issue, we propose to extract semantic similarities based on topical representations of sentences. Inspired by the Hierarchical Dirichlet Process, we propose a topic model to infer topic distributions of sentences. As each topic defines a semantic connection among sentences with a certain degree of membership for each sentence, we propose a fuzzy hypergraph model in which nodes are sentences and fuzzy hyperedges are topics. To produce an informative summary, we extract a set of sentences from the corpus by simultaneously maximizing their relevance to a user-defined query, their centrality in the fuzzy hypergraph and their coverage of topics present in the corpus. We formulate an algorithm building on the theory of submodular functions to solve the associated optimization problem. A thorough comparative analysis with other graph-based summarizers demonstrates the superiority of our method in terms of content coverage of the summaries.

On shadowed hypergraphs

Fuzzy hypergraphs are useful tools for representing granular structures when describing the relations between objects and set of hyperedges, at minute detail, in a specific granularity. Their merit over classical hypergraphs lies in their ability to model uncertainty that may arise with objects and/or granules incident to each other. Many previous studies on fuzzy hypergraphs seek to exploit their strong descriptive potential to analyze n-ary relations in several contexts. However, due to the very detailed numeric membership grades of their objects, fuzzy hypergraphs are sensitive to noise, which may be overwhelming in their general interpretation. To address this issue, a principle of least commitment to certain membership grades is sort by embracing a framework of shadowed sets. The specific concern of this paper is to study a noise-tolerable framework, viz. shadowed hypergraph. Our goal is to capture and quantify noisy objects in clearly marked out zones. We discuss some characteristic properties of shadowed hypergraph and describe an algorithm for transforming a given fuzzy hypergraph into its resulting shadowed hypergraph. Finally, some illustrative examples are provided to demonstrate the essence of shadowed hypergraphs.

Satellite cloud image classification for cyclone prediction using Dichotomous Logistic Regression Based Fuzzy Hypergraph model

Abstract Satellite cloud image classification is a significant step in weather forecasting and climate analysis. Image classification has drawn lots of attention for several decades by remote sensing communities to mitigate the damage caused by cyclones. Classical deep convolutional neural network is being used for detecting the intensity of tropical cyclones. However, it is difficult to improve cyclone prediction accuracy with less time complexity. Dichotomous Logistic Regression Based fuzzy Hypergraph (DLR-FH) model has been developed for improving the classification accuracy of the satellite cyclone image with minimum time. Satellite cyclone images are taken from the cyclone dataset. DLR-FH model consists of three processing steps namely preprocessing, feature extraction and image classification. Preprocessing is carried out using lee filter to remove the noise artifacts from cyclone images. Cyclone feature extraction is then carried out using independent component analysis for extracting the necessary features from the image by estimating the separation matrix. After extracting the cyclone features, dichotomous logistic regression based hypergraph model is used for measuring the relationship between independent variables (extracted feature values) and dependent variables (outcomes) to classify the images. Fuzzy membership function is then applied to estimate the intensity of the cyclone. Cyclone prediction is thus carried out with minimum time and high accuracy. Experimental evaluation of proposed DLR-FH model is carried out using cyclone images with different factors such as peak signal to noise ratio, classification accuracy, classification time and false positive rate. We have considered sufficient number of cyclone images taken from the image dataset.

An m-Polar Fuzzy Hypergraph Model of Granular Computing

An m-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The m-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An m-polar fuzzy set assigns the membership degree to an object belonging to [ 0 , 1 ] m describing the m distinct attributes of that element. Granular computing deals with representing and processing information in the form of information granules. These information granules are collections of elements combined together due to their similarity and functional/physical adjacency. In this paper, we illustrate the formation of granular structures using m-polar fuzzy hypergraphs and level hypergraphs. Further, we define m-polar fuzzy hierarchical quotient space structures. The mappings between the m-polar fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of a universal set is more efficient through m-polar fuzzy hypergraphs as compared to crisp hypergraphs. We also present some examples and a real-world problem to signify the validity of our proposed model.

Q-Rung Orthopair Fuzzy Hypergraphs with Applications

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q-rung orthopair fuzzy sets and hypergraphs. We define q-rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q-rung orthopair fuzzy hypergraphs, ( α , β ) -level hypergraphs, transversals, and minimal transversals of q-rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q-rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

Intuitionistic Fuzzy Soft Hypergraph

In this paper the notions of intuitionistic fuzzy soft hypergraph and strong intuitionistic fuzzy soft hypergraph are introduced. Also studied about union of two intuitionistic fuzzy soft hypergraphs with suitable examples..

Metric Induced Morphological Operators on Intuitionistic Fuzzy Hypergraphs

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.

On constructing morphological erosion of intuitionistic fuzzy hypergraphs

Intuitionistic fuzzy hypergraphs (IFHG) are hypergraphs in which a second degree (non membership) is also included with membership degree for every node in it. Likewise every hyperedge is also having a membership and non membership degree. If a system is modeled using IFHG, the membership degree actually shows the wantedness of the hyperedge/node with respect to the application and the non membership degree shows the unwantedness of the node/hyperedge. The focus of this paper is to show the results of morphological erosion on the sub IFHGs which are created by $$(\alpha ,\beta )$$ cut considering their union, intersection, complement etc and to show their applications in the field of document processing and networking. This is a premier work which defines morphological erosion on IFHG.

Text Summarization Using Morphological Filtering of Intuitionistic Fuzzy Hypergraph

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.

An Application of Stability of Fuzzy Hypergraphs in Medical Field

An Application of Stability of Fuzzy Hypergraphs in Medical Field

Fuzzy shortest path in an interval-valued fuzzy hypergraph using similarity measures

In this paper, a new approach is introduced to find the shortest path between two given vertices on interval-valued fuzzy hypergraphs. When only crisp numbers are not sufficient to measure a real world parameter, fuzzy numbers are considered. But, there are many types of fuzzy numbers available in literature. Most useful fuzzy number is trapezoidal fuzzy numbers. Throughout this paper the interval-valued trapezoidal fuzzy number is used as the arc length of the interval-valued fuzzy hypergraph. We have measured similarity between two interval-valued fuzzy numbers to find the shortest path. An algorithm is also designed to find all possible hyperpaths in a hypergraph and calculated its time complexity

An application of fuzzy hypergraphs and hypergraphs in granular computing

Granular computing emphasizes the exploitation of useful structures known as granular structures characterized by multi-level and multi-view. This paper studies the construction of granular structures models using fuzzy hypergraph and hypergraph, so that granules could be represented more intuitively and visually. In fuzzy hypergraph model and hypergraph model of granular computing, a vertex refers to an object, a fuzzy hyperedge or hyperedge corresponds to a granule. In particular, in the hypergraph model, the hyperedge is a partition of the universe, which is got from fuzzy equivalence relation. A fuzzy hypergraph or hypergraph relates to a set of granules and their relations in a specific granularity, and a series of hypergraphs correspond to a hierarchical structure. Based on granular structures, the mapping between fuzzy hypergraphs or hypergraphs presents the relations of the granules in different levels. The results show that it is efficient to represent the partition by means of fuzzy hypergraph and hypergraph, and it is a useful way to represent granular structures through fuzzy hypergraph model or hypergraph model.

Information granulation for rough fuzzy hypergraphs

Rough-granular computing is a basic model for applying the concept of both rough set theory and granular computing methodology into different knowledge discovery processes; to classify data sets. In the literature, authors have used techniques of rough-granular computing which involve the construction of certain generalizations of Pawlak’s rough set model by deploying sets with structures such as graphs or, more generally, hypergraphs. Indeed, a hypergraph model, with its fairly strong descriptive potential to analyze structures of complex information systems, has occupied a central position in granular computing. A specific concern for this paper is to provide a generalization of the formulation of approximations in rough set model of information granulation. Generalized approximation operators are constructed to account for various combinations of information resident in input granules, instead of mere local descriptions of specific parts of an information system at multiple levels of attributes. An algorithm which describes information granulation for hypergraphs and accounts for information provided by overlapping granules is constructed and illustrated. Finally, an extension of this generalized technique to fuzzy hypergraph models is indicated.

On the connection of fuzzy hypergraph with fuzzy information system

On the connection of fuzzy hypergraph with fuzzy information system

Transversals of m-polar fuzzy hypergraphs with applications

Transversals of m-polar fuzzy hypergraphs with applications

Novel applications of m-polar fuzzy hypergraphs

A hypergraph is one of the most developing tool for modeling various practical problems in different fields, including computer science, biological sciences, social networks and psychology. Sometimes information in a network model is based on multi-object, multi-polar information or uncertainty rat her than a single bit. Our aim in this research paper is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of hypergraphs. We introduce the notion of m-polar fuzzy hypergraphs, dual m-polar fuzzy hypergraphs, m-polar fuzzy line graphs and 2-section of m-polar fuzzy hypergraphs. We develop certain algorithms to construct dual m-polar fuzzy hypergraphs and m-polar fuzzy line graphs. We also present some applications of m-polar fuzzy hypergraphs in planet surface networks, social networks and grouping of incompatible chemical substances.