Robustness of fuzzy reasoning via logically equivalence measure

Abstract In this paper, we discuss robustness of fuzzy reasoning. After proposing the definition of perturbation of fuzzy sets based on some logic-oriented equivalence measure, we present robustness results for various fuzzy logic connectives, fuzzy implication operators, inference rules and fuzzy reasoning machines, and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators. The robustness results are presented in terms of δ -equalities of fuzzy sets based on some logic-oriented equivalence measure, and the maximum of δ (which ensures the corresponding δ -equality holds) is derived.

[1]  Francisco Herrera,et al.  Searching for basic properties obtaining robust implication operators in fuzzy control , 2000, Fuzzy Sets Syst..

[2]  A. Kandel,et al.  Applicability of some fuzzy implication operators , 1989 .

[3]  Kai-Yuan Cai,et al.  Robustness of fuzzy reasoning and δ-equalities of fuzzy sets , 2001, IEEE Trans. Fuzzy Syst..

[4]  D. Dubois,et al.  Fuzzy sets in approximate reasoning. I, Inference with possibility distributions , 1991 .

[5]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[6]  Ronald R. Yager,et al.  On some new classes of implication operators and their role in approximate reasoning , 2004, Inf. Sci..

[7]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

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

[9]  Mingsheng Ying,et al.  Perturbation of fuzzy reasoning , 1999, IEEE Trans. Fuzzy Syst..

[10]  Martina Danková,et al.  On approximate reasoning with graded rules , 2007, Fuzzy Sets Syst..

[11]  Guojun Wang,et al.  On the Logic Foundation of Fuzzy Reasoning , 1999, Inf. Sci..

[12]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions , 1999 .

[13]  Witold Pedrycz,et al.  An approach to measure the robustness of fuzzy reasoning , 2005, Int. J. Intell. Syst..

[14]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[15]  Zhou Zhi-ying.  The Application of Fuzzy Technic in the Malfunction Diagnosis of Diesel Motor , 2005 .