Existence and uniqueness of anti-fuzzy ideal

Min Li

Yanping Feng

Ying Han

pp. 101-106

in: Bing-yuan Cao, Cheng-yi Zhang, Tai-fu Li (eds), Fuzzy information and Engineering I, Berlin, Springer, 2009

Abstract

Let S ⊆ [0,1] satisfying (underline{s}=infSin S ) and C = {I ^t |t ∈ S} be an ascending chain of ideals in commutative ring R . This article presented and studied the following problem:(1) Whether is there an anti-fuzzy ideal μ of R such that μ(R) = {μ(x)| x ∈ R}= S and (C_{mu}={mu^{t}|tinmu(R)}=C) ?(2) If the anti-fuzzy ideal satisfying (1) exists, then whether is it unique ? We built theorems of existence and uniqueness of anti-fuzzy ideal.