An Efficient Configuration for Probabilistic Fuzzy Logic System

A novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process. The probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set. Besides the faster inference operation, it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound. The computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method. Its effectiveness can be further demonstrated on the application to modeling of an industrial curing process. The robust modeling performance discloses its potential in process modeling under complex environment.

[1]  Zhi Liu,et al.  Probabilistic fuzzy logic system: A tool to process stochastic and imprecise information , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[2]  Jonathan M. Garibaldi,et al.  New Concepts Related to Non-Stationary Fuzzy Sets , 2007, 2007 IEEE International Fuzzy Systems Conference.

[3]  W. Graf,et al.  Fuzzy probabilistic method for the safety assessment , 2001 .

[4]  A. Krogh,et al.  Predicting transmembrane protein topology with a hidden Markov model: application to complete genomes. , 2001, Journal of molecular biology.

[5]  Yue Zhang,et al.  The theory of fuzzy stochastic processes , 1992 .

[6]  Henri Prade,et al.  Fuzzy sets and probability: misunderstandings, bridges and gaps , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

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

[8]  Fengming Song,et al.  What does a probabilistic interpretation of fuzzy sets mean? , 1996, IEEE Trans. Fuzzy Syst..

[9]  Hiroaki Ishii,et al.  On flexible product-mix decision problems under randomness and fuzziness☆ , 2009 .

[10]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[11]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[12]  Gert de Cooman,et al.  A random set description of a possibility measure and its natural extension , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Mohammad Bagher Menhaj,et al.  Fuzzy Probabilistic Neural Networks: A Practical Approach to the Implementation of Baysian Classifier , 2001, Fuzzy Days.

[14]  Shaoyuan Li,et al.  A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems , 2007, IEEE Transactions on Fuzzy Systems.

[15]  H. Hagras,et al.  Type-2 FLCs: A New Generation of Fuzzy Controllers , 2007, IEEE Computational Intelligence Magazine.

[16]  Jonathan M. Garibaldi,et al.  Nonstationary Fuzzy Sets , 2008, IEEE Transactions on Fuzzy Systems.

[17]  Zhi Liu,et al.  A probabilistic fuzzy logic system for modeling and control , 2005, IEEE Transactions on Fuzzy Systems.

[18]  Amir H. Meghdadi,et al.  Uncertainty modeling through probabilistic fuzzy systems , 2003, Fourth International Symposium on Uncertainty Modeling and Analysis, 2003. ISUMA 2003..

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

[20]  Uzay Kaymak,et al.  Fuzzy classification using probability-based rule weighting , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[21]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

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

[23]  Marc Roubens,et al.  Comparison of Methodologies for Multicriteria Feasibility — Constrained Fuzzy and Multiple-Objective Stochastic Linear Programming , 1988 .

[24]  G. Klir,et al.  Bayesian inference based on fuzzy probabilities , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[25]  W. Woodall,et al.  A probabilistic and statistical view of fuzzy methods , 1995 .

[26]  Mohammad R. Akbarzadeh-Totonchi,et al.  Probabilistic fuzzy logic and probabilistic fuzzy systems , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[27]  Uzay Kaymak,et al.  A fuzzy additive reasoning scheme for probabilistic Mamdani fuzzy systems , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[28]  L. Zadeh,et al.  Probability theory and fuzzy logic are complementary rather than competitive , 1995 .

[29]  Yuan Yan Chen,et al.  Fuzzy analysis of statistical evidence , 2000, IEEE Trans. Fuzzy Syst..

[30]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[31]  S. Mitter Filtering and stochastic control: a historical perspective , 1996 .

[32]  L. Zadeh Discussion: probability theory and fuzzy logic are complementary rather than competitive , 1995 .

[33]  M. Aral,et al.  Probabilistic-fuzzy health risk modeling , 2004 .

[34]  Jonathan M. Garibaldi,et al.  Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making , 2007, IEEE Transactions on Fuzzy Systems.

[35]  Ana Colubi,et al.  Simulation of random fuzzy variables: an empirical approach to statistical/probabilistic studies with fuzzy experimental data , 2002, IEEE Trans. Fuzzy Syst..

[36]  M. K. Luhandjula Fuzziness and randomness in an optimization framework , 1996, Fuzzy Sets Syst..

[37]  Zhi Liu,et al.  A Probabilistic Neural-Fuzzy Learning System for Stochastic Modeling , 2008, IEEE Transactions on Fuzzy Systems.

[38]  Shaoyuan Li,et al.  Analytical Study and Stability Design of a 3-D Fuzzy Logic Controller for Spatially Distributed Dynamic Systems , 2008, IEEE Transactions on Fuzzy Systems.

[39]  Ronald R. Yager,et al.  Including probabilistic uncertainty in fuzzy logic controller modeling using Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[40]  A. Dale Probability, Vague Statements and Fuzzy Sets , 1980, Philosophy of Science.

[41]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[42]  Joseph A. Wolkan Introduction to Probability and Statistics (2nd ed.) , 1992 .

[43]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[44]  Abraham Kandel,et al.  Constraints on belief functions imposed by fuzzy random variables , 1995, IEEE Trans. Syst. Man Cybern..

[45]  Z. Zenn Bien,et al.  Iterative Fuzzy Clustering Algorithm With Supervision to Construct Probabilistic Fuzzy Rule Base From Numerical Data , 2008, IEEE Transactions on Fuzzy Systems.

[46]  Norberto Corral,et al.  The minimun inaccuracy fuzzy estimation: An extension of the maximum likelihood principle. , 1984 .

[47]  Richard M. Leahy,et al.  Statistical Modeling and Reconstruction of Randoms Precorrected PET Data , 2006, IEEE Transactions on Medical Imaging.

[48]  Yuan Yan Chen,et al.  Statistical inference based on the possibility and belief measures , 1995 .