Title: The intuitionistic fuzzy subrings and fuzzy ideals
Abstract: In this paper,we present the concept of (α, β)-intuitionistic fuzzy subring(ideal). And we show that, in 16 kinds of (α, β)- intuitionistic fuzzy subrings(ideals), the significant ones are the (∈, ∈q)-intuitionistic fuzzy subring(ideal), the (∈, ∈ ⋁q)-intuitionistic fuzzy subring(ideal) and the (∈ ∧q; ∈)- intuitionistic fuzzy subring(ideal). We also show that A is a (∈, ∈)- intuitionistic fuzzy subring(ideal) of R if and only if, for any a ∈ (0, 1], the cut set A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> of A is a 3-valued fuzzy subring(ideal) of R, and A is a (∈,∈ ⋁q)-intuitionistic fuzzy subring(ideal)( or (∈ ∧q, ∈)-intuitionistic fuzzy subring(ideal)) of R if and only if, for any a ∈ (0, 0.5] (or for any a ∈ (0.5,1]), the cut set A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> of A is a 3-valued fuzzy subring(ideal) of R. At last, we generalize the (∈,∈)- intuitionistic fuzzy subring(ideal), the (∈,∈ ⋁q)-intuitionistic fuzzy subring(ideal) and the (∈ ∧q, ∈)- intuitionistic fuzzy subring(ideal) to intuitionistic fuzzy subring(ideal) with thresholds, i.e.,(s, t]- intuitionistic fuzzy subring(ideal). We show that A is a (s, t]- intuitionistic fuzzy subring(ideal) of R if and only if, for any a ∈ (s, t], the cut set A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> of A is a 3-valued fuzzy subring(ideal) of R. We also characterize the (s, t]- intuitionistic fuzzy subring(ideal) by the neighborhood relations between a fuzzy point x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> and an intuitionistic fuzzy set A.
Publication Year: 2011
Publication Date: 2011-07-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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