Probabilistic intuitionistic fuzzy rule based controller

This paper explores the connections between intuitionistic fuzzy logic and probability to discover the potential of the combination of these two forms of uncertainty in modeling of the real world events. We have defined intuitionistic fuzzy set on probabilistic spaces and discussed its links with evidence theory. The notion of probabilistic intuitionistic fuzzy rule is also introduced. An approach is devised to compute the net conditional possibility for such rules that can form the basis to extend the existing fuzzy models. The proposed approach is illustrated through a case-study.

[1]  Gert de Cooman,et al.  A behavioral model for linguistic uncertainty , 2001, Inf. Sci..

[2]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[3]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[4]  María Angeles Gil,et al.  The fuzzy approach to statistical analysis , 2006, Comput. Stat. Data Anal..

[5]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[6]  Hung T. Nguyen,et al.  Uncertainty Models for Knowledge-Based Systems; A Unified Approach to the Measurement of Uncertainty , 1985 .

[7]  Gert de Cooman,et al.  Supremum Preserving Upper Probabilities , 1999, Inf. Sci..

[8]  George J. Klir,et al.  Principles of uncertainty: What are they? Why do we need them? , 1995, Fuzzy Sets Syst..

[9]  Didier Dubois,et al.  Possibility theory and statistical reasoning , 2006, Comput. Stat. Data Anal..

[10]  Madasu Hanmandlu,et al.  Generalization of adaptive neuro-fuzzy inference systems , 2000, IEEE Trans. Neural Networks Learn. Syst..

[11]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[12]  Mauro Roisenberg,et al.  A hybrid fuzzy-probabilistic system for risk analysis in petroleum exploration prospects , 2009, Expert Syst. Appl..

[13]  D. Dubois,et al.  When upper probabilities are possibility measures , 1992 .

[14]  Mohammad Hossein Fazel Zarandi,et al.  A comprehensive fuzzy multi-objective model for supplier selection process , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[15]  B. Kosko.  Fuzzy Thinking: The New Science of Fuzzy Logic , 1993 .

[16]  Didier Dubois,et al.  A definition of subjective possibility , 2008, Int. J. Approx. Reason..

[17]  Uzay Kaymak,et al.  Probabilistic and statistical fuzzy set foundations of competitive exception learning , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[18]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

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

[20]  Ronald R. Yager.  A Foundation for a Theory of Possibility , 1980, Cybern. Syst..

[21]  Wang Pei-zhuang.  From the Fuzzy Statistics to the Falling Random Subsets , 1983 .

[23]  D. Dubois,et al.  On Possibility/Probability Transformations , 1993 .