Robustness of fuzzy operators in environments with random perturbations

In many applications, such as intelligent decision systems, there are usually random perturbations caused by the constant changing of real situations, thus the analysis of the robustness with respect to random perturbations is practically important. In the side of fuzzy methods, a corresponding problem arises: will a small random perturbation of fuzzy input cause a big variance of fuzzy output? This paper study the robustness of fuzzy schemes in environments with random perturbations. It focuses on fuzzy algebraic operators, and proposes two methods to analyze their robustness in environments with random perturbations. The effectiveness and features of the methods are shown by simulations.

[1]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[2]  J. Kacprzyk.  Decision-making in a fuzzy environment with fuzzy termination time , 1978 .

[3]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

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

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

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

[7]  Da Ruan,et al.  Intelligent multi-criteria fuzzy group decision-making for situation assessments , 2007, Soft Comput..

[8]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[9]  Christer Carlsson,et al.  Fuzzy reasoning in decision making and optimization , 2001, Studies in Fuzziness and Soft Computing.

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

[11]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

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

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

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

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

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

[17]  H. Zimmermann,et al.  Comparison of fuzzy reasoning methods , 1982 .

[18]  Witold Pedrycz,et al.  An approach to measure the robustness of fuzzy reasoning: Research Articles , 2005 .

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

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

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

[22]  Michal Holcapek,et al.  A structure of fuzzy systems for support of decision making , 2003, Soft Comput..

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