124 research outputs found
Fuzzy interpolative reasoning via scale and move transformation
Interpolative reasoning does not only help reduce the
complexity of fuzzy models but also makes inference in sparse
rule-based systems possible. This paper presents an interpolative
reasoning method by means of scale and move transformations. It
can be used to interpolate fuzzy rules involving complex polygon,
Gaussian or other bell-shaped fuzzy membership functions. The
method works by first constructing a new inference rule via
manipulating two given adjacent rules, and then by using scale
and move transformations to convert the intermediate inference
results into the final derived conclusions. This method has three
advantages thanks to the proposed transformations: 1) it can
handle interpolation of multiple antecedent variables with simple
computation; 2) it guarantees the uniqueness as well as normality
and convexity of the resulting interpolated fuzzy sets; and 3) it suggests
a variety of definitions for representative values, providing
a degree of freedom to meet different requirements. Comparative
experimental studies are provided to demonstrate the potential of
this method
Scale and move transformation-based fuzzy interpolative reasoning:A revisit
This paper generalises the previously proposed
interpolative reasoning method 151 to cover interpolations involving
complex polygon, Gaussian or other bell-shaped fuzzy
membership functions. This can be achieved by the generality
of the proposed scale and move transformations. The method
works by first constructing a new inference rule via manipulating
two given adjacent rules, and then by using scale and move
transformations to convert the intermediate inference results into
the final derived conclusions. This generalised method has two
advantages thanks to the elegantly proposed transformations: I)
It can easily handle interpolation of multiple antecedent variables
with simple computation; and 2) It guarantees the uniqueness as
well as normality and convexity of the resulting interpolated fuzzy
sets. Numerical examples are provided to demonstrate the use of
this method
Adaptive Fuzzy Interpolation and Extrapolation with Multiple-antecedent Rules
Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning owning to its efficient identification and correction of defective interpolated rules during the interpolation process. This approach assumes that: i) two closest adjacent rules which flank the observation or a previously inferred result are always available; ii) only single-antecedent rules are involved. In practice, however, variable values of these rules may lie just on one side of the observation or inferred result. Also, there may be certain rules with multiple antecedents in the rule base. This paper extends the adaptive approach, in order to cover fuzzy extrapolation and to support rule base with multiple-antecedent rules. Adaptive fuzzy interpolation and extrapolation complement each other, which jointly improve the applicability of fuzzy interpolative reasoning, as it significantly reduces the restriction over the given rule base
Improving fuzzy rule interpolation performance with information gain-guided antecedent weighting
Fuzzy rule interpolation (FRI) makes inference possible when dealing with a sparse and imprecise rule base. However, the rule antecedents are commonly assumed to be of equal signicance in most FRI approaches in the implementation of interpolation. This may lead to a poor performance of interpolative reasoning due to inaccurate or incorrect interpolated results. In order to improve the accuracy by minimising the disadvantage of the equal significance assumption, this paper presents a novel inference system where an information gain (IG)-guided fuzzy rule interpolation method is embedded. In particular, the rule antecedents in FRI are weighted using IG to evaluate the relative importance given the consequent for decision making. The computation of antecedent weights is enabled by introducing an innovative reverse engineering process that artifically converts fuzzy rules into training samples. The antecedent weighting scheme is integrated with scale and move transformation-based interpolation (though other FRI techniques may be improved in the same manner). An illustrative example is used to demonstrate the execution of the proposed approach, while systematic comparative experimental studies are reported to demonstrate the potential of the proposed work.publishersversionPeer reviewe
Transformation-Based Fuzzy Rule Interpolation With Mahalanobis Distance Measures Supported by Choquet Integral
Fuzzy rule interpolation (FRI) strongly supports approximate inference when a new observation matches no rules, through selecting and subsequently interpolating appropriate rules close to the observation from the given (sparse) rule base. Traditional ways of implementing the critical rule selection process are typically based on the exploitation of Euclidean distances between the observation and rules. It is conceptually straightforward for implementation but applying this distance metric may systematically lead to inferior results because it fails to reflect the variations of the relevance or significance levels amongst different domain features. To address this important issue, a novel transformation-based FRI approach is presented, on the basis of utilising the Mahalanobis distance metric. The new FRI method works by transforming a given sparse rule base into a coordinates system where the distance between instances of the same category becomes closer while that between different categories becomes further apart. In so doing, when an observation is present that matches no rules, the most relevant neighbouring rules to implement the required interpolation are more likely to be selected. Following this, the scale and move factors within the classical transformation-based FRI procedure are also modified by Choquet integral. Systematic experimental investigation over a range of classification problems demonstrates that the proposed approach remarkably outperforms the existing state-of-the-art FRI methods in both accuracy and efficiency
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