a. Draw a graph of a characterizing function and construct five δ-cuts for this characterizing function, with δ = 0.2, 0.4, 0.5, 0.7 and 0.9.
b. Let the color intensity for a one-dimensional quantity be given by the following function:
Find the characterizing function of the fuzzy boundary between low color intensity and maximal color intensity using the method described in Section 2.1.
c. Calculate the δ-cuts of a fuzzy vector with vector-characterizing function
d. Explain that the combination of fuzzy numbers, based on the minimum t-norm, yields a fuzzy vector.
e. Prove the following: The combination of k fuzzy intervals, based on the minimum t-norm, yields a fuzzy k-dimensional interval.