Paper Info
Title
The Design of Free Structure Granular Mappings: The Use of the Principle of Justifiable Granularity
Abstract
The study introduces a concept of mappings realized in presence of information granules and offers a design framework supporting the formation of such mappings. Information granules are conceptually meaningful entities formed on a basis of a large number of experimental input–output numeric data available for the construction of the model. We develop a conceptually and algorithmically sound way of forming information granules. Considering the directional nature of the mapping to be formed, this directionality aspect needs to be taken into account when developing information granules. The property of directionality implies that while the information granules in the input space could be constructed with a great deal of flexibility, the information granules formed in the output space have to inherently relate to those built in the input space. The input space is granulated by running a clustering algorithm; for illustrative purposes, the focus here is on fuzzy clustering realized with the aid of the fuzzy C-means algorithm. The information granules in the output space are constructed with the aid of the principle of justifiable granularity (being one of the underlying fundamental conceptual pursuits of Granular Computing). The construct exhibits two important features. First, the constructed information granules are formed in the presence of information granules already constructed in the input space (and this realization is reflective of the direction of the mapping from the input to the output space). Second, the principle of justifiable granularity does not confine the realization of information granules to a single formalism such as fuzzy sets but helps form the granules expressed any required formalism of information granulation. The quality of the granular mapping (viz. the mapping realized for the information granules formed in the input and output spaces) is expressed in terms of the coverage criterion (articulating how well the experimental data are “covered” by information granules produced by the granular mapping for any input experimental data). Some parametric studies are reported by quantifying the performance of the granular mapping (expressed in terms of the coverage and specificity criteria) versus the values of a certain parameters utilized in the construction of output information granules through the principle of justifiable granularity. The plots of coverage–specificity dependency help determine a knee point and reach a sound compromise between these two conflicting requirements imposed on the quality of the granular mapping. Furthermore, quantified is the quality of the mapping with regard to the number of information granules (implying a certain granularity of the mapping). A series of experiments is reported as well.
Year
DOI
Venue
2013
10.1109/TCYB.2013.2240384
Cybernetics, IEEE Transactions
Keywords
Field
DocType
fuzzy set theory,granular computing,pattern clustering,coverage criteria,coverage criterion,design framework,directionality aspect,free structure granular mappings design,fuzzy C-means algorithm,fuzzy clustering,fuzzy sets,granular computing,information granulation formalism,information granules,justifiable granularity principle,mappings concept,model construction,output space,specificity criteria,Clustering,free structure modeling,granular mappings,information granules,principle of justifiable granularity
Fuzzy clustering,Data mining,Mathematical optimization,Fuzzy logic,Algorithm,Input/output,Fuzzy set,Parametric statistics,Granular computing,Granularity,Cluster analysis,Mathematics
Journal
Volume
Issue
ISSN
43
6
2168-2267
Citations 
PageRank 
References 
18
0.65
14
Authors
4
Name
Order
Citations
PageRank
W. Pedrycz1139661005.85
Rami Al-hmouz232319.34
Ali Morfeq327517.38
Abdullah Balamash41679.16