A very important generalization principle used in fuzzification of algebraic operations is a closure property.

The process of converting a crisp input value to a fuzzy value is called "fuzzification".

A similar generalization principle is used, for example, for fuzzification of the transitivity property.

The evolution of the fuzzification of mathematical concepts can be broken down into three stages:

Clarity of communication leaves no maneuvering room, whereas fuzzification provides the safety of flexible interpretations.

A mixed stochastic and non-stochastic fuzzification is often a basis for the LPI-procedure.

Representing fuzzification, fuzzy inference and defuzzification through multi-layers feed-forward connectionist networks.

Usually, a fuzzification of mathematical concepts is based on a generalization of these concepts from characteristic functions to membership functions.

A straightforward fuzzification is usually based on min and max operations because in this case more properties of traditional mathematics can be extended to the fuzzy case.

Noisy, but the noise is non-stationary, they are modeled as an interval type-2 fuzzy set (this latter kind of fuzzification cannot be done in a type-1 FLS).

Depending on the FIS type, there are several layers that simulate the processes involved in a fuzzy inference like fuzzification, inference, aggregation and defuzzification.

The fuzzification of the inputs and the defuzzification of the outputs are respectively performed by the input linguistic and output linguistic layers while the fuzzy inference is collectively performed by the rule, condition and consequence layers.

Fuzzification and Reduction of Information-Theoretic Rule Sets in Data Mining and Computational Intelligence, A. Kandel, M. Last, and H. Bunke (Eds), Physica-Verlag, Studies in Fuzziness and Soft Computing, Vol.