Ranking Fuzzy Sets with Signed Distance and Its Algebraic Structure connected to Algebraic Structure on R

We use the signed distance d on R = (-∞,∞) and extend to the signed distane d* on Fs. Fs is the union of F and R*, where R* is the set of fuzzy point and F is the family of the fuzzy set on R with its existence of α-cut, 0≦α≦1 and being a continuous function of α for the two endpoints of α-cut on [0,1]. The properties on the system (R,d,＜,=,+,.) can be transferred to the system (Fs,d* ,＜ ,? ,⊕,(‧))through the systems (R*, d* , ＜ ,=,⊕,(‧)) or (TE, ＜* ,= , ⊕*).