A note on fuzzy-transform approximation of fuzzy numbers

A possibilistic representation of fuzzy numbers/intervals can be obtained in terms of a fuzzy distribution function (the average of the possibility and necessity functions). The fuzzy distribution function is monotonic non decreasing upper-semicontinuous and there exists a simple one-to-one correspondence between the space of such functions and the space of fuzzy numbers, i.e., with normal, upper semicontinuous quasi concave membership function. As a consequence, the monotonic F-transform approximation of the fuzzy distribution function produces an approximation of any fuzzy number. Properties and examples are given.