Membership Functions for Fuzzy Focal Elements

• Autorzy: Porębski S. , Straszecka E.

Identyfikatory

DOI

10.1515/acsc-2016-0022

• Języki publikacji: EN

Abstrakty

EN

The paper presents a study on data-driven diagnostic rules, which are easy to interpret by human experts. To this end, the Dempster-Shafer theory extended for fuzzy focal elements is used. Premises of the rules (fuzzy focal elements) are provided by membership functions which shapes are changing according to input symptoms. The main aim of the present study is to evaluate common membership function shapes and to introduce a rule elimination algorithm. Proposed methods are first illustrated with the popular Iris data set. Next experiments with five medical benchmark databases are performed. Results of the experiments show that various membership function shapes provide different inference efficiency but the extracted rule sets are close to each other. Thus indications for determining rules with possible heuristic interpretation can be formulated.

Słowa kluczowe

EN

diagnostic rule extraction; medical diagnosis support; fuzzy focal elements; membership functions; Dempster-Shafer theory

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2016
• Tom: Vol. 26, no. 3
• Strony: 395--427
• Opis fizyczny: Bibliogr. 36 poz., rys., tab., wykr., wzory

Twórcy

autor

Porębski S.

• Institute of Electronics, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland

autor

Straszecka E.

• Institute of Electronics, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland

Bibliografia

• [1] V. Antoine, N. Labroche and V. Viet-Vu: Evidential seed-based semi-supervised clustering. In 15th Int. Symp. on Soft Computing and Intelligent Systems (SCIS), Joint 7th Int. Conf. on and Advanced Intelligent Systems (ISIS), 2014, (2014), 706-711.
• [2] J. C. Bezdek: Fuzzy models – what are they, and why? [editorial]. IEEE Trans. on Fuzzy Systems, 1(1), (1993), 1-6.
• [3] K. Boegl, K.-P. Adlassnig, Y. Hayashi, T. E. Rothenfluh and H. Leitich: Knowledge acquisition in the fuzzy knowledge representation framework of a medical consultation system. Artificial Intelligence in Medicine, 30(1), (2004), 1-26.
• [4] A. H. Chen, S. Y. Huang, P.S. Hong, C. H. Cheng and E. J. Lin: Hdps: Heart disease prediction system. In Computing in Cardiology, 2011, (2011), 557-560.
• [5] D. Coomans: Thyroid Gland Data. https://archive.ics.uci.edu/ml/machine-learning-databases/thyroid-disease/new.thyroid.data, 1992. [Online; accessed 18-February-2016].
• [6] K. Cpałka, O. Rebrova, R. Nowicki and L. Rutkowski: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. of General Systems, 42(6), (2013), 706-720.
• [7] A. P. Dempster: A generalization of bayesian inference. J. of the Royal Statistical Society. Series B (Methodological), 30(2), (1968), 205-247.
• [8] R. Detrano: Heart Disease Database (Cleveland). https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.cleveland.data, 1990. [Online; accessed 18-February-2016].
• [9] D. Dubois and H. Prade: Mathematical aspects of fuzzy sets random sets and fuzzy interval analysis. Fuzzy Sets and Systems, 42(1), (1991), 87-101.
• [10] W. Duch, R. Adamczak and K. Grabczewski: A new methodology of extraction, optimization and application of crisp and fuzzy logical rules. IEEE Trans. on Neural Networks, 12(2), (2001), 277-306.
• [11] M. Fathurachman, U. Kalsum, N. Safitri and C.P. Utomo: Heart disease diagnosis using extreme learning based neural networks. In Int. Conf. of Advanced Informatics: Concept, Theory and Application (ICAICTA), 2014, (2014), 23-27.
• [12] R. A. Fisher: Iris Plants Database. https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data, 1988. [Online; accessed 10-February-2016].
• [13] Qinghua Hu, D. Zhang, Shuang An, D. Zhang and Daren Yu: On robust fuzzy rough set models. IEEE Trans. on Fuzzy Systems, 20(4), (2012), 636-651.
• [14] S. Kantarci, A. Vahaplar, A. O. Kinay and E. Nasibov: Influence of tnorm and t-conorm operators in fuzzy id3 algorithm. In IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE), 2015, (2015), 1-6.
• [15] L. Fang and Z. Zhiguang: A new data classification method based on chaotic particle swarm optimization and least square-support vector machine. Chemometrics and Intelligent Laboratory Systems, 147 (2015), 147-156.
• [16] A. L. Medaglia, S.-C. Fang, H. L.W. Nuttle and J. R. Wilson: An efficient and flexible mechanism for constructing membership functions. European J. of Operational Research, 139(1), (2002), 84-95.
• [17] C. Mencar, C. Castiello, R. Cannone and A.M. Fanelli: Design of fuzzy rule-based classifiers with semantic cointension. Information Sciences, 181(20), (2011), 4361-4377. Special Issue on Interpretable Fuzzy Systems.
• [18] K. Neshatian, Mengjie Zhang and P. Andreae: A filter approach to multiple feature construction for symbolic learning classifiers using genetic programming. IEEE Trans. on Evolutionary Computation, 16(5), (2012), 645-661.
• [19] Kemal Polat and Salih Günes: A new feature selection method on classification of medical datasets: Kernel f-score feature selection. Expert Systems with Applications, 36(7), (2009), 10367-10373.
• [20] I. Rojas, H. Pomares, E. Ros and A. Pietro: Automatic construction of fuzzy rules and membership functions from training examples. In Proc. EUFIT’98, (1998), 618-622.
• [21] J. A. Sanz, A. Fernandez, H. Bustince and F. Herrera: Ivturs: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection. IEEE Trans. on Fuzzy Systems, 21(3), (2013), 399-411.
• [22] G. Shafer: A mathematical theory of evidence. Princeton University Press, New Jersey, 1976.
• [23] J. Shen, W. Shen, H. J. Sun and J. Y. Yang: Fuzzy neural nets with nonsymmetric π membership functions and applications in signal processing and image analysis. Signal Processing, 80(6), (2000), 965-983.
• [24] V. Sigillito: Pima Indians Diabetes Database. https://archive.ics.uci.edu/ml/machine-learning-databases/pima-indians-diabetes/pima-indians-diabetes.data, 1990. [Online; accessed 18-February-2016].
• [25] M Sikora: Transactions on Rough Sets XI, volume 5946, chapter Decision rule-based data models using TRS and NetTRS – methods and algorithms, pages 130-160. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.
• [26] J. Łęski: Systemy neuronowo-rozmyte. WNT, Warsaw, 2008. (in Polish).
• [27] E. Straszecka: Combining uncertainty and imprecision in models of medical diagnosis. Information Sciences, 176(20), (2006), 3026-3059.
• [28] E. Straszecka: Combining knowledge from different sources. Expert Systems, 27(1), (2010), 40-52.
• [29] E. Straszecka and J. Straszecka: Medical diagnosis support using uncertainty and imprecision measures. In IEEE Int. Conf. on Systems, Man and Cybernetics, 2004, 6 (2004), 5835-5840.
• [30] E. Straszecka and J. Straszecka: Computer Recognition Systems: Proceedings of the 4th Int. Conf. on Computer Recognition Systems CORES ’05, chapter Interpretation of Medical Symptoms Using Fuzzy Focal Elements, pages 287–293. Springer Berlin Heidelberg, Berlin, Heidelberg, 2005.
• [31] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on Systems, Man, and Cybernetics, SMC-15(1), (1985), 116-132.
• [32] S. M. Weiss and I. Kapouleas: An empirical comparison of pattern recognition, neural nets, and machine learning classification methods. In Proc. of the Eleventh Int. Joint Conf. on Artificial Intelligence, (1989), 781-787.
• [33] W. H. Wolberg: Wisconsin Breast Cancer Database (Original). https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data, 1992. [Online; accessed 18-February-2016].
• [34] R. R. Yager: Uncertainty representation using fuzzy measures. IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), 32(1), (2002), 13-20.
• [35] J. Yen: Generalizing the dempster-schafer theory to fuzzy sets. IEEE Trans. on Systems, Man, and Cybernetics, 20(3), (1990), 559-570.
• [36] Yunong Zhang, Yonghua Yin, Dongsheng Guo, Xiaotian Yu and Lin Xiao: Cross-validation based weights and structure determination of chebyshev-polynomial neural networks for pattern classification. Pattern Recognition, 47(10), (2014), 3414-3428.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę