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Encyclopedia of Complexity and Systems Science pp 4324–4339Cite as

Granular Computing, Philosophical Foundation for

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Definition of the Subject

In a little more than a decade, granular computing (GrC) has emerged as a major research field for further abstraction,generalization and unification of granule‐based key concepts traditionally scattered throughout a wide range of scientific disciplines,offering new opportunities for systematic studies of challenging computational issues cross multiple disciplines. An examination of foundations ofgranular computing, particularly on its philosophical dimension, is extremely important because it should reveal the hidden nature of granular computing,shed useful light for future directions and provide guidelines for researchers working in this area. In order to make this article useful to the researchcommunity in granular computing, instead of using philosophical/epistemological jargon, we will stay with basic terminology used in granularcomputing.

An important advantage of studying the philosophical foundation of granular computing is to identify what is still...

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Abbreviations

Fuzzy set and fuzzy logic:

Unlike a conventional set, in a fuzzy set, a fuzzy membership function is used to define the degree of an element belonging to the set. Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth as defined by membership functions. Fuzzy logic contributes to the machinery of granular computing.

Granular computing (GrC):

In a broad sense, granular computing is the general term referring to any computing theory/technology that involves elements and granules, with granule, granulated view, granularity, and hierarchy as its key concepts.

Granular structure :

Granular structure is a collection of granules in which the internal structure of each granule is visible.

Granularity:

The granularity of a level refers to the collective properties of granules in a level with respect to their sizes.

Granulation:

Granulation refers to the process of forming granules.

Granule:

As the fundamental concept in granular computing, a granule is a clump of elements drawn together by various criteria such as indistinguishability, equivalence, similarity, proximity or functionality.

Hierarchy:

In granular computing, hierarchy captures the ordering of levels.

Neighborhood system:

A neighborhood system of a point (an element) in the universe is the nonempty family of subsets (referred to as the neighborhood of that point) associated to it.

Rough set:

Rough set is a formal approximation of a conventional set, using a pair of sets as the lower and the upper approximations of the original set. Rough sets provide a single‐layered granulation structure of the universe.

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Acknowledgments

The author thanks Dr. T. Y. Lin's useful comments for the improvement of the paper.

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Authors and Affiliations

  1. Department of Computer Science, University of Nebraska at Omaha, Omaha, USA

    Zhengxin Chen

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  1. Zhengxin Chen
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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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Chen, Z. (2009). Granular Computing, Philosophical Foundation for. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_255

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