Skip to main content
Log in

Clustering and hierarchization of fuzzy systems

  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

    Google Scholar 

  • 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

    Google Scholar 

  • Dickerson JA, Kosko B (1996) Fuzzy function approximation with ellipsoidal rules. IEEE Trans Syst Man Cybern 26: 542–560

    Google Scholar 

  • 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

    Google Scholar 

  • Wang LX (1998) Universal approximation by hierarchical fuzzy systems. Fuzzy Sets Syst 93: 223–230

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paulo Salgado.

Additional information

This work was supported by FCT – POSI/SRI/41975/2001

Rights and permissions

Reprints 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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-004-0405-4

Keywords

Navigation