Classification with Nominal Data Using Intuitionistic Fuzzy Sets

The classical classification problem with nominal data is considered. First, to make the problem practically tractable, some transformation into a numerical (real) domain is performed using a frequency based analysis. Then, the use of a fuzzy sets based, and --- in particular - an intuitionistic fuzzy sets based technique is proposed. To better explain the procedure proposed, the analysis is heavily based on an example. Importance of the results obtained for other areas exemplified by decision making and case based reasoning is mentioned.

[1]  Janusz Kacprzyk,et al.  Entropy for intuitionistic fuzzy sets , 2001, Fuzzy Sets Syst..

[2]  Janusz Kacprzyk,et al.  An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem , 2006, ICAISC.

[3]  J. Kacprzyk,et al.  Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work , 2006, 2006 3rd International IEEE Conference Intelligent Systems.

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

[5]  Pat Langley,et al.  Conceptual clustering and its relation to numerical taxonomy , 1986 .

[6]  Eulalia Szmidt,et al.  Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[7]  Hans-Hermann Bock,et al.  Advances in data science and classification , 1998 .

[8]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[9]  Francisco de A. T. de Carvalho.  Extension based proximities between constrained Boolean symbolic objects , 1998 .

[10]  Manabu Ichino,et al.  A Fuzzy Symbolic Pattern Classifier , 1996 .

[11]  Francisco de A. T. de Carvalho,et al.  Proximity Coefficients between Boolean symbolic objects , 1994 .

[12]  Hans-Hermann Bock,et al.  Analysis of Symbolic Data , 2000 .

[13]  Hans-Hermann Bock,et al.  Data Science, Classification and Related Methods , 1998 .

[14]  K. Yamada.  Probability-possibility transformation based on evidence theory , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[15]  Renata M. C. R. de Souza,et al.  Statistical proximity functions of Boolean symbolic objects based on histograms , 1998 .

[16]  M. Schader,et al.  New Approaches in Classification and Data Analysis , 1994 .

[17]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[18]  D. W. Goodall.  A New Similarity Index Based on Probability , 1966 .

[19]  Ryszard Tadeusiewicz,et al.  Artificial Intelligence and Soft Computing - ICAISC 2006, 8th International Conference, Zakopane, Poland, June 25-29, 2006, Proceedings , 2006, International Conference on Artificial Intelligence and Soft Computing.

[20]  Gautam Biswas,et al.  Unsupervised Learning with Mixed Numeric and Nominal Data , 2002, IEEE Trans. Knowl. Data Eng..

[21]  Victor Cheng,et al.  Dissimilarity learning for nominal data , 2004, Pattern Recognit..

[22]  Otto Opitz,et al.  Ordinal and Symbolic Data Analysis , 1996 .

[23]  M. P. Bekakos,et al.  Rule extraction from decision trees with complex nominal data , 2001, Neural Parallel Sci. Comput..

[24]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[25]  Manabu Ichino,et al.  Generalized Minkowski metrics for mixed feature-type data analysis , 1994, IEEE Trans. Syst. Man Cybern..

[26]  Anca L. Ralescu,et al.  Iterative Induction of a Category Membership Function , 1994, Int. J. Uncertain. Fuzziness Knowl. Based Syst..