In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left ...
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https://www.riss.kr/link?id=O106874144
2021년
-
0884-8173
1098-111X
SCIE;SCOPUS
학술저널
4415-4438 [※수록면이 p5 이하이면, Review, Columns, Editor's Note, Abstract 등일 경우가 있습니다.]
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left ...
In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left [right, two‐sided] ideals) over semigroups, which is a generalization of the concept of an bipolar valued fuzzy set (BVFS) in a semigroup. The purpose of this paper is to deal with the algebraic structure of semigroups by applying IVBFS theory. We give characterizations of different classes of (intra‐regular, left [right] regular, regular, semisimple) semigroups by the properties of their IVBF‐ideals. We also characterize these classes in terms of IVBF‐left ideals, IVBF‐right ideals, and IVBF‐two‐sided ideals. In this respect, we prove that a semigroup is regular if and only if for every IVBF‐right ideal
A
˜
=
μ
A
P
˜
,
μ
A
N
˜
and every IVBF‐left ideal
B
˜
=
μ
B
P
˜
,
μ
B
N
˜
over
S
, we have
A
˜
∩
B
˜
=
A
˜
⊙
B
˜
. Further, we characterize intra‐regular and regular semigroups and prove that a semigroup is intra‐regular and regular if and only if for every IVBF‐left ideal
A
˜
=
μ
A
P
˜
,
μ
A
N
˜
and every IVBF‐right ideal
B
˜
=
μ
B
P
˜
,
μ
B
N
˜
over
S
we have
A
˜
∩
B
˜
≼
A
˜
⊙
B
˜
.
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