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Granular Computing, Principles and Perspectives of

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Computational Complexity

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Article Outline

Glossary

Definition of the Subject

Introduction

Neighborhood System: A Mathematical Structure of Granular Computing

Rough Set System: An Equivalence Neighborhood System

Fuzzy Set System: A Fuzzy Neighborhood System

Granular Computing in Data Mining

Granular Computing in Software Engineering

Future Directions

Bibliography

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Abbreviations

Granular computing :

Granular computing is a strategy of problem solving. The basic idea of granular computing comes from the strategy of divide‐and‐conquer. It is a twofold process: First it granulates a complex program into granules and then it computes these granules and integrates results to form a solution to the complex problem. Granulation of problems into granules is of different forms such as chucking, clustering, partitioning, division, or decomposition, while granules are clumps of objects or points. Computations with granules are either within granules or granule with environment.

Neighborhood system :

Neighborhood system is a mathematical structure of granular computing to model granules, and can be used to compute structure of granules and/or between granules and ambient spaces. A neighborhood system at a point is a framework to capture the concept of “near” objects, and any subset of objects can be approximated by a set of neighborhoods. A neighborhood system defines a set of binary relations, and a set of binary relationships can be used to define a neighborhood system.

Fuzzy set theory :

Unlike the classic set theory where a set is represented as an indicator function to specify if an object belongs or not to it, a fuzzy set is an extension of a classic set where a subset is represented as a membership function to characterize the degree that an object belongs to it. The indicator function of a classic set takes value of 1 or 0, whereas the membership function of a fuzzy set takes value between 1 and 0.

Rough set theory :

The rough set theory deals with inexact information systems. In an information system, a decision table consists of a set of objects which are characterized by a set of condition attributes and decision attributes. Objects in the decision table can be classified into equivalence classes using an indiscernibility relation, and equivalence classes are explored to approximate crisp sets of objects.

Data mining:

Data mining is a very important step of knowledge discovery in databases to extract nontrivial, previously unknown, and potentially useful patterns that are hidden from large data sets. Data mining tasks include classification and clustering analysis of objects into categories, discovery of associations and correlations among data items, characterization and summarization of subsets of objects, finding sequential patterns and similarities in ordered data, etc.

Software engineering:

Software engineering is an engineering discipline that applies a systematic approach to produce reliable and efficient software. Software development process consists of different phases, including requirements, analysis, design, specification, implementation, testing, deployment, and maintenance. Object‐oriented methodology to software engineering is based on several techniques and principles such as inheritance, modularity, polymorphism and encapsulation.

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Author information

Authors and Affiliations

  1. Department of Computer Science, California State University, Dominguez Hills, Carson, USA

    Jianchao Han

  2. Faculty of Science and Engineering, York University, Toronto, Canada

    Nick Cercone

Authors
  1. Jianchao Han
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  2. Nick Cercone
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Editor information

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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© 2012 Springer-Verlag

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Han, J., Cercone, N. (2012). Granular Computing, Principles and Perspectives of. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_90

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