The Monotonicity And Sub-Additivity Properties Of Fuzzy Inference Systems And Their Applications
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Date
2011-01
Authors
Tay, Kai Meng
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The Fuzzy Inference System (FIS) is a popular computing paradigm for undertaking
modelling, control, and decision-making problems. In this thesis, the focus of
investigation is on two theoretical properties of an FIS model, i.e., the monotonicity
and sub-additivity properties. These properties are defined, and their applicability to
tackling real-world problems is discussed. This research contributes to formulating a
systematic procedure that is based on a mathematical foundation (i.e., the sufficient
conditions) to develop monotonicity-preserving FIS models. A method to improve
the sub-additivity property is also proposed. The applicability of these proposed
approaches are demonstrated using real-world problems, i.e., Failure Mode and
Effect Analysis (FMEA) methodology, education assessment problem, and control
problem. The use of Fuzzy Rule Interpolation (FRI) for handling the incomplete rule
base issue in FIS modelling is studied. This research indicates that whenever the
monotonicity property is needed, FRI that predicts each rule consequent separately is
not a viable solution to handling the incomplete rule base problem in multi-input
FIS-based models. As such, FRI is formulated as a constrained optimization
problem for the case of multi-input FIS-based models. A new FRI technique
incorporating a Non-linear Programming (NLP) method with the sufficient
conditions is proposed, and its application to the FMEA methodology is
demonstrated. The results confirm the effectiveness of the new FRI scheme in
satisfying the monotonicity property in undertaking FMEA problems.
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Keywords
The monotonicity and sub-additivity Properties , of fuzzy inference systems And their applications