Representations with fuzzy darts
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TL;DR
From this perspective, fuzzy numbers with “continuous boundaries” are approximated by Pn-fuzzy numbers, and within the framework of fuzzy level sets, the problem of comparing PN-fBuzzy numbers is addressed.
Abstract
Fuzzy information is organized by partitioning the fuzzy interval [0, 1] into layers of "fuzzy strata". At each level fuzzy information is approximated by a fuzzy dart; information at all levels is combined and recorded as an n-tuple of fuzzy darts. From this perspective, fuzzy numbers with "continuous boundaries" are approximated by Pn-fuzzy numbers. Then, within the framework of fuzzy level sets, the problem of comparing Pn-fuzzy numbers is addressed. For applications, differentiably smooth fuzzy maps which are either "expansive" or "contractive" are characterized by their derivatives. Finally, anti-fuzzy numbers are introduced and discussed.