From the data-mining viewpoint fizzy logic refers to numerical computations
based on fizzy rules, for the purpose of modeling functional relationships in a
data set. It also encompasses t%zzyset-based methods for approximate reasoning.
With this property fizzy logic by contrast to neural networks, is a transparent
box with its predictions. Also it allows linguistic and qualitative interpretations
of the outputs.
For data-mining especially Sugeno-type fuzzy systems [1] is concern where
the system approximates any fictional relationship with a combination of
several linear systems, by decomposing the whole input space into several partial
fuzzy spaces known as fuzzy sets and representing each output space with a
linear equation as local models. The fazzy sets are described by functions called
tizzy membership fictions as local models, which allow convenient application
of powerful learning techniques for their identification Ilom data.
To obtain fuzzy models from the data set, different approaches can be used,
like fuzzy relational modeling [2], and product space clustering [3,4]. In a
multidimensional variable space, fuzzy modeling is accomplished by means of
one-dimensional fizzy sets obta~ed from the multidimensional fuzzy sets by
projections onto space of each input variable [5]. The complexity of fuzzy
modeling exponentially increases with the dimension of the fuzzy product space,
which is known as curse of dimensionality. This may be considered as the price
paid in return to its desirable properties as being transparent, i.e., tracing
possibility for reasoning on fuzzy model predictions.