A HEDGE ALGEBRAS BASED CLASSIFICATION REASONING METHOD WITH MULTI-GRANULARITY FUZZY PARTITIONING

Phạm Đình Phong; Nguyen Duc Du; Nguyen Thanh Thuy; Hoang Van Thong

doi:10.15625/1813-9663/35/4/14348

Author affiliations

Authors

Phạm Đình Phong Faculty of Information Technology, University of Transport and Communications, Hanoi, Vietnam
Nguyen Duc Du Faculty of Information Technology, University of Transport and Communications
Nguyen Thanh Thuy Faculty of Information Technology, University of Engineering and Technology, VNU, Hanoi, Vietnam
Hoang Van Thong Faculty of Information Technology, University of Transport and Communications, Hanoi, Vietnam

DOI:

https://doi.org/10.15625/1813-9663/35/4/14348

Keywords:

Classification reasoning, fuzzy rule based classifier, fuzziness interval, hedge algebras, multi-granularity, semantically quantifying mapping values

Abstract

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results.

Metrics

Metrics Loading ...

References

R. Alcalá, Y. Nojima, F. Herrera, H. Ishibuchi, “Multi-objective genetic fuzzy rule selection of single granularity-based fuzzy classiﬁcation rules and its interaction with the lateral tuning of membership functions”, Soft Computing, vol. 15, no. 12, pp. 2303-2318, 2011.

M. Antonelli, P. Ducange, F. Marcelloni, “A fast and efficient multi-objective evolutionary learning scheme for fuzzy rule-based classifiers”, Information Sciences 283, pp. 36–54, 2014.

C. Burges, “A tutorial on Support Vector Machines for pattern recognition”, Proceedings of Int Conference on Data Mining and Knowledge Discovery, vol. 2, no. 2, pp. 121-167, 1998.

J. Demˇsar, “Statistical Comparisons of Classifiers over Multiple Data Sets”, Journal of Machine Learning Research 7, pp. 1–30, 2006.

D. K. Dong, T. D. Khang, P. A. Phong, “Fuzzy clustering with hedge algebra”, Proceedings of the 2010 Symposium on Information and Communication Technology, SoICT 2010, Hanoi, Viet Nam, pp. 49–54, 2010.

M. Elkanoa, M. Galara, J. Sanza, H. Bustince, “CHI-BD: A fuzzy rule-based classification system for Big Data classification problems”, Fuzzy Sets and Systems, vol. 348, pp. 75–101, 2018.

M. Fazzolari, R. Alcalá, F. Herrera, “A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm”, Applied Soft Computing, vol. 24, pp. 470–481, 2014.

N. C. Ho, W. Wechler, “Hedge algebras: an algebraic approach to structures of sets of linguistic domains of linguistic truth values”, Fuzzy Sets and Systems, vol. 35, pp. 281-293, 1990.

N. C. Ho, W. Wechler, Extended algebra and their application to fuzzy logic, Fuzzy Sets and Systems, vol. 52, 1992, pp. 259–281.

N. C. Ho, H. V. Nam, T. D. Khang, L. H. Chau, “Hedge Algebras, Linguistic-valued logic and their application to fuzzy reasoning”, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, vol. 7, no. 4, pp. 347–361, 1999.

N. C. Ho, T. T. Son, T. D. Khang, L. X. Viet, “Fuzziness Measure, Quantified Semantic Mapping And Interpolative Method of Approximate Reasoning in Medical Expert Systems”, Journal of Computer Science and Cybernetics, vol. 18, no. 3, pp. 237-252, 2002.

N. C. Ho, N. V. Long, “Fuzziness measure on complete hedges algebras and quantifying semantics of terms in linear hedge algebras”, Fuzzy Sets and Systems, vol. 158, pp. 452-471, 2007.

N. C. Ho, “A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges”, Fuzzy Sets and Systems, vol. 158, 436–451, 2007.

N. C. Ho, V. N. Lan, L. X. Viet, “Optimal hedge-algebras-based controller: Design and application”, Fuzzy Sets and Systems, vol. 159, pp. 968 – 989, 2008.

N. C. Ho, W. Pedrycz, D. T. Long, T. T. Son, “A genetic design of linguistic terms for fuzzy rule based classifiers”, International Journal of Approximate Reasoning, vol. 54, no. 1, pp. 1-21, 2013.

N. C. Ho, T. T. Son, P. D. Phong, “Modeling of a semantics core of linguistic terms based on an extension of hedge algebra semantics and its application”, Knowledge-Based Systems, vol. 67, pp. 244–262, 2014.

N. C. Ho, H. V. Thong, N. V. Long, “A discussion on interpretability of linguistic rule based systems and its application to solve regression problems”, Knowledge-Based Systems, vol. 88, pp. 107–133, 2015.

A. K. Ghosh, “A probabilistic approach for semi-supervised nearest neighbor classification”, Pattern Recognition Letters, vol. 33, no. 9, pp. 1127–1133, 2012.

H. Ishibuchi, K. Nozaki, H. Tanaka, “Distributed representation of fuzzy rules and its application to pattern classification”, Fuzzy Sets and Systems, vol. 52, no. 1, pp. 21–32, 1992.

H. Ishibuchi, T. Yamamoto, “Fuzzy Rule Selection by Multi-Objective Genetic Local Search Algorithms and Rule Evaluation Measures in Data Mining”, Fuzzy Sets and Systems, vol. 141, no .1, pp. 59-88, 2004.

H. Ishibuchi, T. Yamamoto, “Rule weight specification in fuzzy rule-based classification systems”, IEEE Transactions on Fuzzy Systems, vol. 13, no. 4, pp. 428–435, 2005.

H. Ishibuchi, Y. Nojima, “Analysis of interpretability-accuracy tradeoff of fuzzy systems by multi-objective fuzzy genetics-based machine learning”, International Journal of Approximate Reasoning, vol. 44, pp. 4–31, 2007.

L. N. Hung, V. M. Loc, “Primacy of Fuzzy Relational Databases Based on Hedge Algebras”, Volume 144 of the series Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, pp. 292-305, 2015.

N. H. Huy, N. C. Ho, N. V. Quyen, “Multichannel image contrast enhancement based on linguistic rule-based intensificators”, Applied Soft Computing Journal, vol. 76, pp. 744–762, 2019.

H. Langseth, T. D. Nielsen, “Classification using Hierarchical Naïve Bayes models”, Machine Learning, vol. 63, no. 2, pp. 135–159, 2006.

L. V. T. Lan, N. M. Han, N. C. Hao, “An algorithm to build a fuzzy decision tree for data classification problem based on the fuzziness intervals matching”, Journal of Computer Science and Cybernetics, vol. 32, no. 4, pp. 367-380, 2016.

V. N. Lan, T. T. Ha, L. K. Lai, N. T. Duy, “The application of the hedge algebras in forecast control based on the models”, In Proceedings of The 11st National Conference on Fundamental and Applied IT Research, Hanoi, Vietnam, pp. 521-528, 2018.

B. H. Le, N. C. Ho, V. N. Lan, N. C. Hung, “General design method of hedge-algebras-based fuzzy controllers and an application for structural active control”, Applied Intelligence, vol. 43, no. 2, pp. 251–275, 2015.

B. H. Le, L. T. Anh, B. V. Binh, “Explicit formula of hedge-algebras-based fuzzy controller and applications in structural vibration control”, Applied Soft Computing, vol. 60, pp. 150–166, 2017.

D. T. Long, “A genetic algorithm based method for timetabling problems using linguistics of hedge algebra in constraints”, Journal of Computer Science and Cybernetics, vol. 32, no. 4, pp. 285—301, 2016.

M. S. Lechuga, Multi-Objective Optimization using Sharing in Swarm Optimization Algorithms, Doctor thesis, School of Computer Science, The University of Birmingham, 2006.

M. M. Mazid, A. B. M. S. Ali, K. S. Tickle, “Improved C4.5 Algorithm for Rule Based Classification”, Proceedings of the 9th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Databases, University of Cambridge, UK, pp. 296-301, 2010.

D. Nauck, R. Kruse, “NEFCLASS: A neuro-fuzzy approach for the classification of data”, In Proc. of the 1995 ACM Symposium on Applied Computing, Nashville, TN, pp. 461–465, 1995.

M. I. Rey, M. Galende, M. J. Fuente, G. I. Sainz-Palmero, “Multi-objective based Fuzzy Rule Based Systems (FRBSs) for trade-off improvement in accuracy and interpretability: A rule relevance point of view”, Knowledge-Based Systems, vol. 127, pp. 67–84, 2017.

S. B. Roh, W. Pedrycz, T. C. Ahn, “A design of granular fuzzy classifier”, Expert Systems with Applications, vol. 41, pp. 6786–6795, 2014.

F. Rudzinski, “A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers”, Applied Soft Computing, vol. 38, pp. 118–133, 2016.

P. D. Phong, N. C. Ho, N. T. Thuy, “Multi-objective Particle Swarm Optimization Algorithm and its Application to the Fuzzy Rule Based Classifier Design Problem with the Order Based Semantics of Linguistic Terms”, In Proceedings of The 10th IEEE RIVF International Conference on Computing and Communication Technologies (RIVF-2013), Hanoi, Vietnam, pp. 12–17, 2013.

M. Pota, M. Esposito, G. D. Pietro, “Designing rule-based fuzzy systems for classification in medicine”, Knowledge-Based Systems, vol. 124, pp. 105–132, 2017.

J. Sanz, A. Fernández, H. Bustince, F. Herrera, “A genetic tuning to improve the performance of Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets: Degree of ignorance and lateral position”, International Journal of Approximate Reasoning, vol. 52, pp. 751–766, 2011.

M. Soui, I. Gasmi, S. Smiti, K. Ghédira, “Rule-based credit risk assessment model using multi-objective evolutionary algorithms”, Expert Systems With Applications, vol. 126, pp. 144–157, 2019.

T. T. Son, N. T. Anh, “Partition fuzzy domain with multi-granularity representation of data based on hedge algebra approach”, Journal of Computer Science and Cybernetics, vol. 34, no. 1, pp. 63–75, 2018.

D. V. Thang, D. V. Ban, “Query data with fuzzy information in object-oriented databases an approach the semantic neighborhood of hedge algebras”, International Journal of Computer Science and Information Security, vol. 9, no. 5, pp. 37-42, 2011.