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Encyclopedia of Complexity and Systems Science pp 8333–8345Cite as

Social Networks and Granular Computing

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Definition of theSubject

Granular computing (GrC) is a problem‐solvingconcept deeply rooted in human thinking. Hence, it has playeda major role in solving many important problems throughoutthe history of mathematics. GrC is concerned with the processingof information granules, which are groups of objects drawntogether by indiscernibility, similarity, proximity, orfunctionality [37]. The process of forminginformation granules is called granulation. If the process isbased totally on the attributes of the objects, it is calledfunctional granulation, sinceattributes are mathematical functions from the set of objects tothe set of values; if, in addition, the granulation process isalso based on the relationship between objects, it is calledrelationalgranulation [11,20].

Interestingly, social scientists have applied thetechniques of relational granulation (albeit by different names)to positional analysis in social networks [7,8,10,19,35]. Social networkanalysis (SNA) is a methodology used...

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Abbreviations

Granulation:

The process of drawing a set of objects (or points) together by indiscernibility, similarity, proximity, or functionality.

Functional granulation:

The granulation process is functional if it is based on the attributes of the objects. It is called functional granulation because each attribute is a function from the set of objects to the set of values.

Relational granulation:

The granulation process is relational if it is based on the relationships between objects.

Functional granulation:

The granulation process is functional if it is based on the attributes of the objects. It is called functional granulation because each attribute is a function from the set of objects to the set of values.

Relational granulation:

The granulation process is relational if it is based on the relationships between objects.

Rough set:

A rough set is defined by the lower and upper approximations of a concept. The lower approximation contains all elements that necessarily belong to the concept, while the upper approximation contains those that possibly belong to the concept. In rough set theory, a concept is considered a classical set.

Social network:

A social network is comprised of a set of actors, called the domain, and a family of relations on the domain. It is usually represented as a graph, where each node represents an actor and an edge between two nodes represents a relational tie between these two actors. An edge can be labeled with the relation it represents.

Positional equivalence:

Two actors are in equivalent positions if their “pattern” of relationships with other actors is the same.

Structural equivalence:

Two actors are structurally equivalent if they are related to the same actors.

Regular equivalence:

Two actors are regularly equivalent if they are equally related to equivalent actors.

Exact equivalence:

Two actors are exactly equivalent if they are related to the same number of equivalent actors.

Structural equivalence:

Two actors are structurally equivalent if they are related to the same actors.

Regular equivalence:

Two actors are regularly equivalent if they are equally related to equivalent actors.

Exact equivalence:

Two actors are exactly equivalent if they are related to the same number of equivalent actors.

Modal logic:

Modal logic was originally developed as a type of philosophical logic for reasoning about necessity and possibility. However, it has been extended to broadly cover a family of logics for reasoning about modalities including tense, obligation, belief, and knowledge. Semantically, it is also a powerful mathematical discipline that deals with (restricted) description languages for discussing various kinds of relational structures, where a relational structure comprises a set of elements and a collection of relations on that set.

Hybrid logic:

Hybrid logic is a branch of modal logic that allows direct reference to the elements in a relational structure. Traditionally, only the properties of the elements could be represented by modal logic formulas.

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Authors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Churn-Jung Liau

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  1. Churn-Jung Liau
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Liau, CJ. (2009). Social Networks and Granular Computing. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_495

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