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

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Title:	Ranking Fuzzy Sets with Signed Distance and Its Algebraic Structure connected to Algebraic Structure on R 以有號距離對模糊集的排序及和實數集的代數結構的關聯性
Authors:	江哲賢(Jershan Chiang) 李明嘉(Ming-Gar Lee) 程友文(Yuwen Cheng)
Contributors:	理學院
Keywords:	Ordering Signed Distance Algebraic Structure
Date:	2002
Issue Date:	2012-05-14 11:27:26 (UTC+8)
Abstract:	我們利用在R上的有號距離d，推廣到Fs上得有號距離d。Fs為在R上的模糊集其α-cut存在，且為α的連續函數，0≦α≦1，所形成的集合F和模糊點所形成的集合R之聯集。在(R,d,<,=,+,.)上的性質利用(R,d ,< ,? ,⊕,(‧))或(TE ,<* ,=,⊕* ) 都可以轉移到(Fs ,d* ,< ,= , ⊕* ,(‧))。 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, <* ,= , ⊕*).
Relation:	華岡理科學報； 19 期 (2002 / 05 / 01) ， P1 - 12
Appears in Collections:	[College of Science] Hwa Kang Journal of Sciences

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