43 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
Transformation Based Interpolation with Generalized Representative Values
Fuzzy interpolation offers the potential to model
problems with sparse rule bases, as opposed to dense rule
bases deployed in traditional fuzzy systems. It thus supports the
simplification of complex fuzzy models and facilitates inferences
when only limited knowledge is available. This paper first
introduces the general concept of representative values (RVs),
and then uses it to present an interpolative reasoning method
which can be used to interpolate fuzzy rules involving arbitrary
polygonal fuzzy sets, by means of scale and move transformations.
Various interpolation results over different RV implementations
are illustrated to show the flexibility and diversity of this
method. A realistic application shows that the interpolation-based
inference can outperform the conventional inferences
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