Abstract
The readability of fuzzy models is related to their organizational structure and the corresponding rule base. On this basis, a new methodology for organizing the information, the Separation of Linguistic Information Methodology (SLIM), is developed. Based on its results, different algorithms are presented for different structures: the Parallel Collaborative Structure (PCS) - SLIM-PCS algorithm and the Hierarchical Prioritized Structure (HPS), SLIM-HPS algorithm. Finally, it is proposed a Fuzzy Clustering of Fuzzy Rules Algorithm (FCFRA) that allows the automatic organisation of the sets of fuzzy IF ... THEN rules of one fuzzy system in a Parallel Collaborative Structure, the probabilistic Fuzzy Clustering, and in a Hierarchical Prioritized Structure, the Possibilistic Fuzzy Clustering.
References
Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90: 111–127
Ying H (1998) Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent, IEEE Trans Syst Man Cybern 28: 515–520
Dickerson JA, Kosko B (1996) Fuzzy function approximation with ellipsoidal rules. IEEE Trans Syst Man Cybern 26: 542–560
Wang LX (1992) Fuzzy systems are universal approximators. In: Proc. IEEE Int Conf Fuzzy Syst San Diego, CA, Mar. 1992, 1163–1170
Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation, and orthogonal least-square learning. IEEE Trans Neural Networks 3: 807–814
Wang LX (1998) Universal approximation by hierarchical fuzzy systems. Fuzzy Sets Syst 93: 223–230
Klir Y (1995) Fuzzy Sets and Fuzzy Logic. Prentice Hall PTR, N. J
Wang LX (1994) Adaptive Fuzzy Systems and Control, Design and Stability Analysis. Prentice-Hall.
Wang LX (1997) A course in fuzzy systems and control. Prentice-Hall
Jamshidi M (1997) Titli A, Zadeh L, Bovorie S (Ed), Applications of Fuzzy Logic, Towards Quotient Systems. Prentice Hall
Höppner, Frank, Klawonn F, Kruse R, Runkler T (1999) Fuzzy Cluster Analysis, methods for classification, data analysis and image recognition. John Wiley & Sons
Pal SK, Mitra S (1999) Neuro-Fuzzy Pattern Recognition, methods in soft computing. John Wiley & Sons.
Salgado P (1999), News methods for fuzzy identification ( only on Portuguese language - Novos métodos de Identificação Difusa), Ph.D. Thesis, UTAD, July 1999, Portugal
Salgado P, Couto C, Melo-Pinto P, Bulas-Cruz J (2000) Relevance as a new measure of relative importance of sets of rules. Proceendings of the IEEE Conf on Syst Man and Cybernetics 2000, Nashville, USA, 3770-3777
Yager R (1993) On a Hierarchical Structure for Fuzzy Modeling and Control. IEEE Trans On Syst Man and Cybernetics 23: 1189–1197
Yager R (1993) Hierarchical representation of fuzzy if-then rules. In: Bouchon-Meunier B, Valverde L, Yager RR, (Eds) Advanced Methods in Artificial Intelligence. Springer-Verlag Berlin, Germany 239–247
Yager R (1998) On the Construction of Hierarchical Fuzzy Systems Models. IEEE Trans On Syst Man, and Cyber.Part C: Applications and reviews 28: 55–66
Roubens M, Vincke P (1989) Preference Modeling. Springer-Verlag Berlin, Germany
Kosko B (1996) Additive Fuzzy Systems: from functions approximation to learning. In: Chen CH (Ed) Fuzzy Logic and Neural Network Handbook, 9.1–9.22, McGraw-Hill, Inc
Kosko B (1998) Global Stability of Generalized Additive Fuzzy Systems. IEEE Trans on Syst Man, and Cyber 28: 441–452
Jamshidi, Mohammad (1997) Large-scale systems: modeling, control and fuzzy logic. Prentice Hall PTR, Upper Saddle River, N. J. 07458
Salgado P, Boaventura Cunha J (20039, Greenhouse climate hierarchical fuzzy modelling. Submitted to Control Engineering Practices
Luenberger DG (1973) Introduction to linear and non-linear programming. Addison Wesley
Krishnapuram R, Keller (1993) A possibilistic approach to clustering. IEEE Trans Fuzzy Syst 1: 85–110
Bezdek JC, Pal SK (eds) (1992) Fuzzy Models for Pattern Recognition: Methods that Search for Patterns in Data. IEEE Press, N.Y
Bezdek JC (1980) A Convergence Theorem for Fuzzy ISODATA Clustering Algorithms. IEEE Trans Pattern Analysis and Machine Intelligence 2: 1–8
Salgado P et al. (2004) Clustering of fuzzy systems. (Submitted for publication)
Bot GPA (1983) Greehouse climate: from physical process to a dynamic model, Ph. D. Thesis, Wageningen Agricultural University, Wageningen
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by FCT – POSI/SRI/41975/2001
Rights and permissions
About this article
Cite this article
Salgado, P. Clustering and hierarchization of fuzzy systems. Soft Comput 9, 715–731 (2005). https://doi.org/10.1007/s00500-004-0405-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-004-0405-4