A Similarity Measure between Type-2 Fuzzy Sets with Its Application to Clustering

In this paper we propose a new similarity measure between type-2 fuzzy sets with its property. We also combine the proposed similarity measures with Yang and Shih's algorithm as a clustering method for type-2 fuzzy data. According to different sigma-level, these clustering results consist of a usefully hierarchical tree.

[1]  J. Buckley,et al.  Fuzzy input-output controllers are universal approximators , 1993 .

[2]  RONALD R. YAGER,et al.  Fuzzy Subsets of Type Ii in Decisions , 1980, Cybern. Syst..

[3]  Liu Xuecheng,et al.  Entropy, distance measure and similarity measure of fuzzy sets and their relations , 1992 .

[4]  Jerry M. Mendel,et al.  Operations on type-2 fuzzy sets , 2001, Fuzzy Sets Syst..

[5]  I. Burhan Türksen,et al.  An approximate analogical reasoning approach based on similarity measures , 1988, IEEE Trans. Syst. Man Cybern..

[6]  G. C. Mouzouris,et al.  Designing fuzzy logic systems , 1997 .

[7]  Miin-Shen Yang,et al.  Cluster analysis based on fuzzy relations , 2001, Fuzzy Sets Syst..

[8]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[9]  M. Wagenknecht,et al.  Application of fuzzy sets of type 2 to the solution of fuzzy equation systems , 1988 .

[10]  Miin-Shen Yang,et al.  On a similarity measure between LR‐type fuzzy numbers and its application to database acquisition , 2005, Int. J. Intell. Syst..

[11]  Juhani Nieminen,et al.  On the algebraic structure of fuzzy sets of type 2 , 1977, Kybernetika.

[12]  H. B. Mitchell.  Pattern recognition using type-II fuzzy sets , 2005, Inf. Sci..

[13]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[14]  Miin-Shen Yang,et al.  Similarity Measures Between Type-2 Fuzzy Sets , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[15]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[16]  Weixin Xie,et al.  Some notes on similarity measure and proximity measure , 1999, Fuzzy Sets Syst..

[17]  M. Mizumoto,et al.  Fuzzy sets and type 2 under algebraic product and algebraic sum , 1981 .

[18]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[19]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[20]  K. Selçuk Candan,et al.  Similarity-based ranking and query processing in multimedia databases , 2000, Data Knowl. Eng..

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

[22]  Masaharu Mizumoto,et al.  Some Properties of Fuzzy Sets of Type 2 , 1976, Inf. Control..

[23]  Jia Zeng,et al.  Type-2 fuzzy hidden Markov models and their application to speech recognition , 2006, IEEE Transactions on Fuzzy Systems.

[24]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[25]  Jerry M. Mendel,et al.  Applications of Type-2 Fuzzy Logic Systems to Forecasting of Time-series , 1999, Inf. Sci..