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.

A note on fuzzy-transform approximation of fuzzy numbers

STEFANINI, LUCIANO
2015

Abstract

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.
2015
978-1-4673-7248-0
978-1-4673-7248-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2630530
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