Combination of Fuzzy Sets

Fuzzy sets may have to be combined with other fuzzy sets. Common operations are 'and', 'or', and 'not'. These operations can be defined as:

Definition 1 (Fuzzy AND Min)

Definition 2 (Fuzzy OR Max)

Definition 3 (Fuzzy NOT)

These definitions will be used as parts offuzzy models. Alternative definitions for fuzzy 'and' and 'or' are

Definition 4 (Fuzzy AND Prod)

Definition 5 (Fuzzy OR Add)

These definitions are based on fuzzy t-norm and t-conorm. In fuzzy models the definitions 4 and 5 often show a better behavior than definitions 1 and 2. This will be explained in greater detail below (minimum/ maximum and/or was used because simple fixed-point micro-controllers are faster that way; floating-point-PCs are not (multiplication is faster than floating-point comparison)).

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