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Proceedings ArticleDOI

Data Mining Through Fuzzy Social Network Analysis

24 Jun 2007-pp 251-255
TL;DR: A method to consolidate the information content of the fuzzy graph is proposed and a new fuzzy binary operation called consolidation operation is also introduced.
Abstract: In this paper, fuzzy theory has been applied to social network analysis (SNA). Social network analysis models meaningful relations that exist between entities as graph. These entities may be people, events, organizations, symbols in text, sounds in verbalizations, nations of the world and so on. However, the fuzzy graph can be very huge and thus the ability to arrive at meaningful conclusions in a timely fashion may be quite difficult. With this in mind, a method to consolidate the information content of the fuzzy graph is proposed. Since none of the existing fuzzy binary operations meet the requirements, a new fuzzy binary operation called consolidation operation is also introduced.
Citations
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Book
01 Aug 1996
TL;DR: Fuzzy sets as mentioned in this paper are a class of classes in which there may be grades of membership intermediate between full membership and non-membership, i.e., a fuzzy set is characterized by a membership function which assigns to each object its grade of membership.
Abstract: The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

885 citations

Journal ArticleDOI
TL;DR: This paper reviews over 100 applications of data mining in crime, covering a substantial quantity of research to date, presented in chronological order with an overview table of many important data mining applications in the crime domain as a reference directory.
Abstract: Crime continues to remain a severe threat to all communities and nations across the globe alongside the sophistication in technology and processes that are being exploited to enable highly complex criminal activities. Data mining, the process of uncovering hidden information from Big Data, is now an important tool for investigating, curbing and preventing crime and is exploited by both private and government institutions around the world. The primary aim of this paper is to provide a concise review of the data mining applications in crime. To this end, the paper reviews over 100 applications of data mining in crime, covering a substantial quantity of research to date, presented in chronological order with an overview table of many important data mining applications in the crime domain as a reference directory. The data mining techniques themselves are briefly introduced to the reader and these include entity extraction, clustering, association rule mining, decision trees, support vector machines, naive Bayes rule, neural networks and social network analysis amongst others. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016

94 citations


Cites methods from "Data Mining Through Fuzzy Social Ne..."

  • ...Nair and Sarasamma [85] performed SNA alongside fuzzy theory with the aim of modeling Statistical Analysis and Data Mining: The ASA Data Science Journal DOI:10.1002/sam multi-modal social networks....

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  • ...Nair and Sarasamma [85] performed SNA alongside fuzzy theory with the aim of modeling...

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Proceedings ArticleDOI
02 Nov 2007
TL;DR: This paper generalizes the notion of regular equivalence to fuzzy social networks based on two alternative definitions ofRegular equivalence is generalized based on the definition of role assignment or coloring, which can determine the role partition of the actors in a fuzzy social network.
Abstract: Social network analysis is a methodology used extensively in social and behavioral sciences, as well as in political science, economics, organization theory, and industrial engineering. Positional analysis of a social network aims to find similarities between actors in the network. One of the the most studied notions in the positional analysis of social networks is regular equivalence. According to Borgatti and Everett, two actors are regularly equivalent if they are equally related to equivalent others. In recent years, fuzzy social networks have also received considerable attention because they can represent both the qualitative relationship and the degrees of interaction between actors. In this paper, we generalize the notion of regular equivalence to fuzzy social networks based on two alternative definitions of regular equivalence. While these two definitions are equivalent for social networks, they induce different generalizations for fuzzy social networks. The first generalization, called regular similarity, is based on the characterization of regular equivalence as an equivalence relation that commutes with the underlying social relations. The regular similarity is then a fuzzy binary relation that specifies the degree of similarity between actors in the social network. The second generalization, called generalized regular equivalence, is based on the definition of role assignment or coloring. A role assignment (resp. coloring) is a mapping from the set of actors to a set of roles (resp. colors). The mapping is regular if actors assigned to the same role have the same roles in their neighborhoods. Consequently, generalized regular equivalence is an equivalence relation that can determine the role partition of the actors in a fuzzy social network.

43 citations


Cites background from "Data Mining Through Fuzzy Social Ne..."

  • ...In recent years, fuzzy social networks have also received considerable attention because they can represent both the qualitative relationship and the degrees of interaction between actors [ 19 ]....

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Journal ArticleDOI
TL;DR: This study proposes a data-summarization method that can reveal L-distributions of fuzzy groups of objects represented by a given dataset to the desired dataset L-attribute and requires the interpretability of the inherent semantic structures of the declared word-sets in their fs-representations structures.

42 citations

References
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Book
25 Nov 1994
TL;DR: This paper presents mathematical representation of social networks in the social and behavioral sciences through the lens of Dyadic and Triadic Interaction Models, which describes the relationships between actor and group measures and the structure of networks.
Abstract: Part I. Introduction: Networks, Relations, and Structure: 1. Relations and networks in the social and behavioral sciences 2. Social network data: collection and application Part II. Mathematical Representations of Social Networks: 3. Notation 4. Graphs and matrixes Part III. Structural and Locational Properties: 5. Centrality, prestige, and related actor and group measures 6. Structural balance, clusterability, and transitivity 7. Cohesive subgroups 8. Affiliations, co-memberships, and overlapping subgroups Part IV. Roles and Positions: 9. Structural equivalence 10. Blockmodels 11. Relational algebras 12. Network positions and roles Part V. Dyadic and Triadic Methods: 13. Dyads 14. Triads Part VI. Statistical Dyadic Interaction Models: 15. Statistical analysis of single relational networks 16. Stochastic blockmodels and goodness-of-fit indices Part VII. Epilogue: 17. Future directions.

17,104 citations

Journal ArticleDOI
TL;DR: This work characterizes networked structures in terms of nodes (individual actors, people, or things within the network) and the ties, edges, or links that connect them.
Abstract: Social Network Analysis Methods And Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes (individual actors, people, or things within the network) and the ties, edges, or links (relationships or interactions) that connect them. Examples of social structures commonly visualized through social network ...

12,634 citations

Book
01 Jan 2011
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
Abstract: (1982). Fuzzy Sets and Systems — Theory and Applications. Journal of the Operational Research Society: Vol. 33, No. 2, pp. 198-198.

5,861 citations

Book
01 Aug 1996
TL;DR: Fuzzy sets as mentioned in this paper are a class of classes in which there may be grades of membership intermediate between full membership and non-membership, i.e., a fuzzy set is characterized by a membership function which assigns to each object its grade of membership.
Abstract: The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

885 citations

Book
26 Apr 2000
TL;DR: Fuzzy Subsets: Fuzzy Relations.- FuzzY Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- fuzzy Graphs: Paths and Connectedness.
Abstract: Fuzzy Subsets: Fuzzy Relations.- Fuzzy Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- Fuzzy Graphs: Paths and Connectedness. Bridges and Cut Vertices. Forests and Trees. Trees and Cycles. A Characterization of Fuzzy Trees. (Fuzzy) Cut Sets. (Fuzzy Chords, (Fuzzy) Cotrees, and (Fuzzy) Twigs. (Fuzzy) 1-Chain with Boundary 0, (Fuzzy) Coboundary, and (Fuzzy) Cocycles. (Fuzzy) Cycle Set and (Fuzzy) Cocycle Set.- Fuzzy Line Graphs.- Fuzzy Interval Graphs. Fuzzy Intersection Graphs. Fuzzy Interval Graphs. The Fulkerson and Gross Characterization. The Gilmore and Hoffman Characterization.- Operations on Fuzzy Graphs: Cartesian Product and Composition. Union and Join.- On Fuzzy Tree Definition.- References.- Applications of Fuzzy Graphs: Clusters.- Cluster Analysis. Cohesiveness. Slicing in Fuzzy Graphs.- Application to Cluster Analysis.- Fuzzy Intersection Equations. Existence of Solutions.- Fuzzy Graphs in Database Theory. Representation of Dependency Structure r(X,Y) by Fuzzy Graphs.- A Description of Strengthening and Weakening Members of a Group. Connectedness Criteria. Inclusive Connectedness Categories. Exclusive Connectedness Categories.- An Application of Fuzzy Graphs to the Problem Concerning Group Structure. Connectedness of a Fuzzy Graph. Weakening and Strenghtening Points of a Fuzzy Directed Graph.- References.- Fuzzy Hypergraphs: Fuzzy Hypergraphs.- Fuzzy Transversals of Fuzzy Hypergraphs. Properties of Tr(H). Construction of H3.- Coloring of Fuzzy Hypergraphs. beta-degree Coloring Procedures. Chromatic Values of Fuzzy Colorings.- Intersecting Fuzzy Hypergraphs. Characterization of Strongly Intersecting Hypergraphs. Simply Ordered Intersecting Hypergraphs. H-dominant Transversals.- Hebbian Structures.- Additional Applications.- References.

468 citations


Additional excerpts

  • ...More information on fuzzy graphs can be found in [1-8]....

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