Rough bipolar fuzzy ideals in semigroups

被引：13

作者：

Malik, Nosheen ^{[1
]}

Shabir, Muhammad ^{[1
]}

Al-shami, Tareq M. ^{[2
]}

Gul, Rizwan ^{[1
]}

Arar, Murad ^{[3
]}

Hosny, M. ^{[4
]}

机构：

[1] Quaid i Azam Univ, Dept Math, Islamabad 45320, Pakistan

[2] Sanaa Univ, Dept Math, Sanaa, Yemen

[3] Prince Sattam bin Abdulaziz Univ, Coll Sci & Humanities Aflaj, Dept Math, Riyadh, Saudi Arabia

[4] King Khalid Univ, Fac Sci Girls, Dept Math, Abha, Saudi Arabia

来源：

COMPLEX & INTELLIGENT SYSTEMS | 2023年 / 9卷 / 06期

关键词：

Rough set; Bipolar fuzzy sets; Semigroup; Congruence relation; BI-IDEALS; SETS; (ALPHA; MODEL;

D O I：

10.1007/s40747-023-01132-1

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, the bipolar FS (BFS) theory can tackle the uncertainty and the bipolarity of the data in different circumstances. This article aims to introduce the idea of rough bipolar fuzzy ideals in semigroup (SG), which is a generalization of the concept of rough BFSs (RBFSs) in an SG. We also investigate the roughness in the bipolar fuzzy subsemigroup (BF-SSG) with the help of congruence relation (cng-R) defined on the SG and studied some relevant structural properties. Moreover, the idea is extended to the rough bipolar fuzzy left ideal, rough bipolar fuzzy right ideal, rough bipolar fuzzy two-sided ideal, rough bipolar fuzzy interior ideal, and rough bipolar fuzzy bi-ideal in SGs. Further, it is seen that cng-Rs and complete cng-Rs play vital roles in the construction of rough approximations of bipolar fuzzy ideals. Consequently, their associated properties are explored by using cng-Rs and complete cng-Rs.

引用

页码：7197 / 7212

页数：16

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