Robustness of fuzzy connectives and fuzzy reasoning

Abstract In fuzzy control, practical fuzzy reasoning schemes are likely to be perturbed by various types of noise, and thus analysis of the stability and robustness of fuzzy reasoning are important issue. We used a concept similar to the modulus of continuity to characterize the robustness of fuzzy connectives and present robustness results for various fuzzy connectives. We investigated the robustness of fuzzy reasoning from the perspective of perturbation of membership functions. We propose a method for judging the most robust elements of different classes of fuzzy connectives. The results obtained are compared with previous findings in the literature.

[1]  Guosheng Cheng,et al.  Error Estimation of Perturbations Under CRI , 2006, IEEE Transactions on Fuzzy Systems.

[2]  Radko Mesiar,et al.  Triangular Norms , 2000, Trends in Logic.

[3]  Chunquan Li,et al.  Robustness of fuzzy reasoning via logically equivalence measure , 2007, Inf. Sci..

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

[5]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 2: logical approaches , 1991 .

[6]  Humberto Bustince,et al.  Automorphisms, negations and implication operators , 2003, Fuzzy Sets Syst..

[7]  Kai-Yuan Cai,et al.  δ-Equalities of fuzzy sets , 1995, Fuzzy Sets Syst..

[8]  G. Lorentz.  Approximation of Functions , 1966 .

[9]  Etienne E. Kerre,et al.  An overview of fuzzy quantifiers. (II). Reasoning and applications , 1998, Fuzzy Sets Syst..

[10]  Etienne E. Kerre,et al.  Mathematics of Fuzziness - Basic Issues , 2009, Studies in Fuzziness and Soft Computing.

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

[12]  C. Pappis.  Value approximation of fuzzy systems variables , 1991 .

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

[14]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[15]  Kai-Yuan Cai,et al.  Fuzzy Reasoning as a Control Problem , 2008, IEEE Transactions on Fuzzy Systems.

[16]  Hung T. Nguyen,et al.  On robustness of fuzzy logics , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[17]  Qing Zhu,et al.  Fuzzy and Evidence Reasoning , 1995 .

[18]  Etienne E. Kerre,et al.  An overview of fuzzy quantifiers. (I). Interpretations , 1998, Fuzzy Sets Syst..

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

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

[21]  LangJérôme,et al.  Fuzzy sets in approximate reasoning, part 2 , 1991 .

[22]  Yun Shi,et al.  On the characterizations of fuzzy implications satisfying I(x, y)=I(x, I(x, y)) , 2007, Inf. Sci..

[23]  Kai-Yuan Cai,et al.  Optimal fuzzy reasoning and its robustness analysis , 2004, Int. J. Intell. Syst..

[24]  J. W. GUAN,et al.  Approximate Reasoning and Evidence Theory , 1997, Inf. Sci..

[25]  Daowu Pei,et al.  Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances , 2012, Fuzzy Sets Syst..

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

[27]  Keyun Qin,et al.  Fuzzy XNOR connectives in fuzzy logic , 2011, Soft Comput..

[28]  Shyi-Ming Chen,et al.  A new interpolative reasoning method in sparse rule-based systems , 1998, Fuzzy Sets Syst..

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

[30]  D. Hong,et al.  A note on the value similarity of fuzzy systems variables , 1994 .

[31]  Michal Baczynski,et al.  Residual implications revisited. Notes on the Smets-Magrez Theorem , 2004, Fuzzy Sets Syst..