As described so far, “Fuzzimetric Arcs” provides a
systematic selection mechanism where the selection
“fitness” factor may determine the final shape of the fuzzy
set. Moreover, Fuzzimetric Arcs allow a mutation of the
fuzzy sets by altering the range where the fuzzy set can be
defined. For example assuming 50% mutation would result
in an original initial selection of sin wave for the 1st half of
the fuzzy set and a “mutated” 2nd half of the fuzzy set which
might be half triangular, trapezoidal…etc. as it can be
shown in Figure 3 which shows samples of possible 50%
crossover and mutation combination between different
forms of fuzzy set shapes using the above equation. As a
result of the above description and in resemblance of a
biological or genetic structure which is represented in figure
4, the following definitions can be concluded.