On monotonic sufficient conditions of fuzzy inference systems and their applications

Tay, Kai Meng and Lim, Chee Peng 2011, On monotonic sufficient conditions of fuzzy inference systems and their applications, International journal of uncertainty, fuzziness and knowlege-based systems, vol. 19, no. 5, pp. 731-757.

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Title On monotonic sufficient conditions of fuzzy inference systems and their applications
Author(s) Tay, Kai Meng
Lim, Chee Peng
Journal name International journal of uncertainty, fuzziness and knowlege-based systems
Volume number 19
Issue number 5
Start page 731
End page 757
Total pages 27
Publisher World Scientific Publishing
Place of publication Singapore
Publication date 2011-10
ISSN 0218-4885
1793-6411
Keyword(s) Failure Mode and Effect Analysis (FMEA)
Fuzzy controller
Monotonicity property
Risk assessment
Sub-additivity property
Sufficient conditions
Failure Mode
Effect Analysis
Summary An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets and fuzzy rules. In this paper, two useful qualitative properties of the FIS model, i.e., the monotonicity and sub-additivity properties, are studied. The monotonic sufficient conditions of the FIS model with Gaussian membership functions are further analyzed. The aim is to incorporate the sufficient conditions into the FIS modeling process, which serves as a simple (which can be easily understood by domain users), easy-to-use (which can be easily applied to or can be a part of the FIS model), and yet reliable (which has a sound mathematical foundation) method to preserve the monotonicity property of the FIS model. Another aim of this paper is to demonstrate how these additional qualitative information can be exploited and extended to be part of the FIS designing procedure (i.e., for fuzzy sets and fuzzy rules design) via the sufficient conditions (which act as a set of useful governing equations for designing the FIS model). The proposed approach is able to avoid the "trial and error" procedure in obtaining a monotonic FIS model. To assess the applicability of the proposed approach, two practical problems are examined. The first is an FIS-based model for water level control, while the second is an FIS-based Risk Priority Number (RPN) model in Failure Mode and Effect Analysis (FMEA). To further illustrate the importance of the sufficient conditions as the governing equations, an analysis on the consequences of violating the sufficient conditions of the FIS-based RPN model is presented.
Language eng
Field of Research 109999 Technology not elsewhere classified
Socio Economic Objective 970110 Expanding Knowledge in Technology
HERDC Research category C1.1 Refereed article in a scholarly journal
Copyright notice ©2011, World Scientific Publishing Company
Persistent URL http://hdl.handle.net/10536/DRO/DU:30048785

Document type: Journal Article
Collection: Institute for Frontier Materials
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