Similarity-based method for reduction of fuzzy rules

Fuzzy Similarity Measures (FSMs) are widely used for comparison of fuzzy sets, as well as fuzzy rules. A multitude of different FSMs have been proposed so far. It is not straightforward to identify a single FSM that is the most suitable for a given task. In this paper, we investigate suitability of a few FSMs for the problem of reduction of number of rules for an image segmentation process. We use Dirichlet-based approach to generate fuzzy sets that are further used for construction of fuzzy if-then rules. We analyze similarity of these rules and select a specified number of rules for image segmentation purposes. We applied this approach to two different images.

[1]  I. Turksen,et al.  An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets , 1990 .

[2]  Chia-Feng Juang,et al.  A self-generating fuzzy system with ant and particle swarm cooperative optimization , 2009, Expert Syst. Appl..

[3]  T. Liao,et al.  A review of similarity measures for fuzzy systems , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[4]  Bernhard Sendhoff,et al.  On generating FC3 fuzzy rule systems from data using evolution strategies , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[5]  C. Pappis,et al.  A comparative assessment of measures of similarity of fuzzy values , 1993 .

[6]  Andres Mendez-Vazquez,et al.  Learning fuzzy rules through ant optimization, LASSO and Dirichlet Mixtures , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[7]  Simone Santini,et al.  Similarity Measures , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Wen-June Wang,et al.  New similarity measures on fuzzy sets and on elements , 1997, Fuzzy Sets Syst..

[9]  Swapan Raha,et al.  Similarity in fuzzy systems , 2014 .

[10]  Hoel Le Capitaine,et al.  Towards a Unified Logical Framework of Fuzzy Implications to Compare Fuzzy Sets , 2009, IFSA/EUSFLAT Conf..

[11]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..

[12]  Mohamed Chtourou,et al.  A new method for fuzzy rule base reduction , 2013, J. Intell. Fuzzy Syst..

[13]  B. Baets,et al.  A comparative study of similarity measures , 1995 .

[14]  Atul Negi,et al.  A survey of distance/similarity measures for categorical data , 2014, 2014 International Joint Conference on Neural Networks (IJCNN).

[15]  Wenyi Zeng,et al.  Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations , 2006, Int. J. Intell. Syst..

[16]  Jorge Casillas,et al.  Learning Fuzzy Rules Using Ant Colony Optimization Algorithms , 2000 .

[17]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  Nikhil R. Pal,et al.  Similarity-based approximate reasoning: methodology and application , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[19]  Derek A. Linkens,et al.  Rule-base self-generation and simplification for data-driven fuzzy models , 2004, Fuzzy Sets Syst..

[20]  H. Lee-Kwang,et al.  Similarity measure between fuzzy sets and between elements , 1994 .