The development of fuzzy decision trees in the framework of Axiomatic Fuzzy Set logic

Decision trees are one among interesting and commonly encountered architectures used for learning, reasoning and organization of datasets. This study being positioned in the realm of decision trees is aimed at two main objectives. First, we propose a new algorithmic framework for building fuzzy sets (membership functions) and their logic operators based upon theoretical findings of the Axiomatic Fuzzy Set (logic) theory (AFS). Second, we cast the design processes of fuzzy decision trees in this framework. A number of illustrative examples are included. We demonstrate how the AFS setting results in the improvement of the performance of the resulting trees. The findings are contrasted with the outcomes produced by the decision trees studied by Janikow; in particular, we show the performance of different trees in the case of large number of fuzzy attributes.

[1]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[2]  Xiaodong Liu,et al.  A new fuzzy model of pattern recognition and hitch diagnoses of complex systems , 1999, Fuzzy Sets Syst..

[3]  Witold Pedrycz,et al.  Logic-oriented fuzzy clustering , 2002, Pattern Recognit. Lett..

[4]  Liu Xiaodong,et al.  The Fuzzy Theory Based on AFS Algebras and AFS Structure , 1998 .

[5]  David A. Landgrebe,et al.  A survey of decision tree classifier methodology , 1991, IEEE Trans. Syst. Man Cybern..

[6]  Bart Kosko,et al.  Fuzzy Engineering , 1996 .

[7]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[8]  Xizhao Wang,et al.  A comparative study on heuristic algorithms for generating fuzzy decision trees , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Witold Pedrycz,et al.  Axiomatics fuzzy sets logic , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[10]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[11]  Cezary Z. Janikow,et al.  Fuzzy decision trees: issues and methods , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[12]  D. S. Yeung,et al.  Learning weighted fuzzy rules from examples with mixed attributes by fuzzy decision trees , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[13]  M. Shaw,et al.  Induction of fuzzy decision trees , 1995 .

[14]  L. Jain,et al.  Generation of fuzzy decision trees by fuzzy ID3 with adjusting mechanism of AND/OR operators , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[15]  Liu Xiaodong,et al.  The Topology of AFS Structure and AFS Algebras , 1998 .

[16]  Witold Pedrycz,et al.  Designing decision trees with the use of fuzzy granulation , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[17]  Sankar K. Pal,et al.  Fuzzy decision tree, linguistic rules and fuzzy knowledge-based network: generation and evaluation , 2002, IEEE Trans. Syst. Man Cybern. Part C.

[18]  Hidetomo Ichihashi,et al.  Neuro-fuzzy ID3: a method of inducing fuzzy decision trees with linear programming for maximizing entropy and an algebraic method for incremental learning , 1996, Fuzzy Sets Syst..

[19]  Aiko M. Hormann,et al.  Programs for Machine Learning. Part I , 1962, Inf. Control..

[20]  Xiaodong Liu,et al.  The fuzzy sets and systems based on AFS.structure, EI algebra and EII algebra , 1998, Fuzzy Sets Syst..

[21]  L. Zadeh.  The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[22]  Jack E. Graver,et al.  Combinatorics with emphasis on the theory of graphs , 1977 .

[23]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[24]  Masaharu Mizumoto,et al.  Fuzzy controls under various fuzzy reasoning methods , 1988, Inf. Sci..

[25]  Xizhao Wang,et al.  On the optimization of fuzzy decision trees , 2000, Fuzzy Sets Syst..

[26]  Teuvo Kohonen,et al.  Self-organization and associative memory: 3rd edition , 1989 .

[27]  Witold Pedrycz,et al.  The design of decision trees in the framework of granular data and their application to software quality models , 2001, Fuzzy Sets Syst..

[28]  Ki Hang Kim.  Boolean matrix theory and applications , 1982 .

[29]  L. A. Zadeh,et al.  Fuzzy logic and approximate reasoning , 1975, Synthese.

[30]  Liu Xiao.  AFS Fuzzy Logic System and Its Applications to Fuzzy Information Processing , 2002 .

[31]  J. R. Quinlan.  DECISION TREES AS PROBABILISTIC CLASSIFIERS , 1987 .

[32]  Wang Guo-jun,et al.  Theory of topological molecular lattices , 1992 .

[33]  Cullen Schaffer.  Overfitting avoidance as bias , 2004, Machine Learning.

[34]  Xizhao Wang,et al.  On the handling of fuzziness for continuous-valued attributes in decision tree generation , 1998, Fuzzy Sets Syst..

[35]  J. Ross Quinlan,et al.  Unknown Attribute Values in Induction , 1989, ML.

[36]  Jane Yung-jen Hsu,et al.  Integration of fuzzy classifiers with decision trees , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.

[37]  Tharam S. Dillon,et al.  Using single-layered neural networks for the extraction of conjunctive rules and hierarchical classifications , 1991, Applied Intelligence.