A type 2 adaptive fuzzy inferencing system

Type 2 fuzzy sets allow for linguistic grades of membership and, therefore, present a better representation of the 'fuzziness', when applied to a particular problem, than type 1 fuzzy sets. However, the associated cost is that the fuzzy membership grades and rules have somehow to be determined and no recognised approach yet exists. For type 1 systems a number of approaches have been adopted. One in particular is the adaptive network based fuzzy inferencing system (ANFIS) which has successfully been applied to a variety of applications. ANFIS takes domain data and learns the membership functions and rules for a type 1 fuzzy inferencing system. Our work aims to extend this approach for type 2 systems. Our Type 2 adaptive fuzzy inferencing system has inputs that are linguistic variables and the membership functions for these fuzzy grades are learnt from the relationship between these inputs and the given output. The paper describes the algorithm developed highlighting the theoretical and computational issues involved.

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

[2]  J. Corbin,et al.  Fuzzy interval approach to computations on the internet and information super highway , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

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

[4]  I. Turksen.  Measurement of membership functions and their acquisition , 1991 .

[5]  Lotfi A. Zadeh,et al.  Fuzzy Logic and Its Application to Approximate Reasoning , 1974, IFIP Congress.

[6]  A. Kandel.  Fuzzy Mathematical Techniques With Applications , 1986 .

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

[8]  N. N. Karnik,et al.  Introduction to type-2 fuzzy logic systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[9]  Phil Diamond.  Higher level fuzzy numbers arising from fuzzy regression , 1990 .

[10]  Chin-Teng Lin,et al.  A neural fuzzy system with linguistic teaching signals , 1995, IEEE Trans. Fuzzy Syst..

[11]  Robert John,et al.  The use of fuzzy sets for resource allocation in an advance request vehicle brokerage system—a case study , 1997 .

[12]  V. Kreinovich,et al.  How to avoid congestion in computer networks , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

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

[14]  Shouhong Wang.  Generating fuzzy membership functions: a monotonic neural network model , 1994 .

[15]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[16]  Isao Hayashi,et al.  NN-driven fuzzy reasoning , 1991, Int. J. Approx. Reason..

[17]  J. Mendel.  Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.

[18]  Tom J. Schwartz.  Fuzzy systems in the real world , 1990 .

[19]  E. Cox.  Adaptive fuzzy systems , 1993, IEEE Spectrum.

[20]  R. John.  Type 2 fuzzy sets for knowledge representation and inferencing , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

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