Optimization of knowledge bases on the basis of fuzzy relations by the criteria “accuracy – complexity”
DOI:
https://doi.org/10.15587/1729-4061.2017.95870Keywords:
optimization of fuzzy knowledge bases, min-max clustering, fuzzy relational modelsAbstract
The method of optimization of fuzzy classification knowledge bases by the criteria “inference accuracy – complexity” was proposed. A relational fuzzy model, which corresponds to the fuzzy classification knowledge base, was developed. The matrix of fuzzy relations in the form of one-dimensional projection “input terms – output classes” is a simplified representation of the system of classification rules. A problem on the optimization of a knowledge base is reduced to the problem on the min-max clustering and comes down to selecting such partition matrices “inputs – output” that provide for the required or extreme levels of inference accuracy and the number of rules.
In the relational models, a question about optimal choice of the number of output terms remains open. A selection of output classes, input terms and rules is reduced to the problem on discrete optimization of the algorithm reliability indicators, in order to solve which, we employed the gradient method. The number and location of hyperboxes are determined by the relations matrix, and the sizes of hyperboxes are defined as a result of tuning of the triangular membership functions. A selection of the number of input and output terms in the partition matrices may be performed both under the offline mode and by adaptive adding/removing of terms.
Known methods of the min-max clustering apply heuristic procedures for the selection of the number of rules (classes). The proposed method generates variants of fuzzy knowledge bases in accordance with the formalized procedures of reliability analysis and synthesis of algorithmic processes. This resolves a general problem on the methods of min-max clustering related to the minimization of the number of input terms without losing inference accuracy.
A transition to the relational fuzzy model provides simplification of the process of the knowledge bases tuning both for the assigned and unknown output classes.
References
- Yager, R., Filev, D. (1994). Essentials of fuzzy modeling and control. New York: John Willey & Sons, 408.
- Rotshtein, A. P., Rakytyanska, H. B. (2012). Fuzzy Evidence in Identification, Forecasting and Diagnosis. Heidelberg: Springer, 314. doi: 10.1007/978-3-642-25786-5
- Mandal, S., Jayaram, B. (2015). SISO fuzzy relational inference systems based on fuzzy implications are universal approximators. Fuzzy Sets and Systems, 277, 1–21. doi: 10.1016/j.fss.2014.10.003
- Scherer, R. (2012). Relational Modular Fuzzy Systems. Studies in Fuzziness and Soft Computing. Springer Berlin Heidelberg, 39–50. doi: 10.1007/978-3-642-30604-4_4
- Gonzalez, A., Perez, R., Caises, Y., Leyva, E. (2012). An Efficient Inductive Genetic Learning Algorithm for Fuzzy Relational Rules. International Journal of Computational Intelligence Systems, 5 (2), 212–230. doi: 10.1080/18756891.2012.685265
- Graves, D., Noppen, J., Pedrycz, W. (2012). Clustering with proximity knowledge and relational knowledge. Pattern Recognition, 45 (7), 2633–2644. doi: 10.1016/j.patcog.2011.12.019
- De Carvalho, F. de A. T., Lechevallier, Y., de Melo, F. M. (2013). Relational partitioning fuzzy clustering algorithms based on multiple dissimilarity matrices. Fuzzy Sets and Systems, 215, 1–28. doi: 10.1016/j.fss.2012.09.011
- Bargiela, A., Pedrycz, W. (2013). Optimised Information Abstraction in Granular Min/Max Clustering. Smart Innovation, Systems and Technologies, 31–48. doi: 10.1007/978-3-642-28699-5_3
- Gaspar, P., Carbonell, J., Oliveira, J. L. (2012). Parameter Influence in Genetic Algorithm Optimization of Support Vector Machines. Advances in Intelligent and Soft Computing, 43–51. doi: 10.1007/978-3-642-28839-5_5
- Wu, Z., Zhang, H., Liu, J. (2014). A fuzzy support vector machine algorithm for classification based on a novel PIM fuzzy clustering method. Neurocomputing, 125, 119–124. doi: 10.1016/j.neucom.2012.07.049
- Mohammed, M. F. Lim, C. P. (2017). Improving the Fuzzy Min-Max neural network with a K-nearest hyperbox expansion rule for pattern classification. Applied Soft Computing, 52, 135–145. doi: 10.1016/j.asoc.2016.12.001
- Seera, M., Lim, C. P., Loo, C. K., Singh, H. (2015). A modified fuzzy min-max neural network for data clustering and its application to power quality monitoring. Applied Soft Computing, 28, 19–29. doi: 10.1016/j.asoc.2014.09.050
- Reyes-Galaviz, O. F., Pedrycz, W. (2015). Granular fuzzy modeling with evolving hyperboxes in multi-dimensional space of numerical data. Neurocomputing, 168, 240–253. doi: 10.1016/j.neucom.2015.05.102
- Rotshtein, A. P., Rakytyanska, H. B. (2014). Optimal Design of Rule-Based Systems by Solving Fuzzy Relational Equations. Studies in Computational Intelligence, 167–178. doi: 10.1007/978-3-319-06883-1_14
- Rakytyanska, H. (2015). Optimization of composite fuzzy knowledge bases on rules and relations. Inf. Technol. Comput. Eng., 1, 17–26.
- Rakytyanska, H. (2015). Fuzzy classification knowledge base construction based on trend rules and inverse inference. Eastern-European Journal of Enterprise Technologies, 1 (3 (73)), 25–32. doi: 10.15587/1729-4061.2015.36934
- Rotshtein, A. P., Rakytyanska, H. B. (2012). Fuzzy Genetic Object Identification: Multiple Inputs/Multiple Outputs Case. Advances in Intelligent and Soft Computing, 375–394. doi: 10.1007/978-3-642-23172-8_25
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Hanna Rakytyanska
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.