Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes

The major point of proposed work is to study optimistic multi-granulation roughness of intuitionistic fuzzy ideals by using soft relations that is free from all the complications that challenged by many researchers. The combination of soft binary relations, optimistic multi-granulation rough sets, a...

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Main Authors: Shahida Bashir, Muhammad Shabir, Muhammad Zishan Anwar, Rabia Mazhar, Afraz Hussain Majeed, Ehab Ghith, Mehdi Tlija
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Heliyon
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Online Access:http://www.sciencedirect.com/science/article/pii/S2405844025008278
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author Shahida Bashir
Muhammad Shabir
Muhammad Zishan Anwar
Rabia Mazhar
Afraz Hussain Majeed
Ehab Ghith
Mehdi Tlija
author_facet Shahida Bashir
Muhammad Shabir
Muhammad Zishan Anwar
Rabia Mazhar
Afraz Hussain Majeed
Ehab Ghith
Mehdi Tlija
author_sort Shahida Bashir
collection DOAJ
description The major point of proposed work is to study optimistic multi-granulation roughness of intuitionistic fuzzy ideals by using soft relations that is free from all the complications that challenged by many researchers. The combination of soft binary relations, optimistic multi-granulation rough sets, and intuitionistic fuzzy sets is a useful technique to deal with uncertainty. In modern theories, this combination provides a powerful tool to manage daily life critical situations. Furthermore, the lower and upper approximations of intuitionistic fuzzy subsemigroups, intuitionistic fuzzy left (right) ideals, intuitionistic fuzzy interior ideals and intuitionistic fuzzy bi-ideals of semigroups are studied by using soft relations. Compatible relation is used for upper approximation and complete relation is used for lower approximation. This approach has potential impacts on fields like coding theory, automata theory, and cryptography, providing a flexible and robust method for handling imprecise data, where the use of optimization, and analysis in the industrial domain identify input data with uncertainty and vagueness and reachable multi-source information. At the end, a comparison study and conclusions of the presented work are given that proves how our technique is effective in contrast to fuzzy set.
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institution Kabale University
issn 2405-8440
language English
publishDate 2025-08-01
publisher Elsevier
record_format Article
series Heliyon
spelling doaj-art-9529cc9d01104ff59fa470a9f11d5e892025-08-20T03:58:36ZengElsevierHeliyon2405-84402025-08-011113e4244710.1016/j.heliyon.2025.e42447Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universesShahida Bashir0Muhammad Shabir1Muhammad Zishan Anwar2Rabia Mazhar3Afraz Hussain Majeed4Ehab Ghith5Mehdi Tlija6Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan; Corresponding author.Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, PakistanDepartment of Mathematics, University of Gujrat, Gujrat, 50700, PakistanDepartment of Mathematics, University of Gujrat, Gujrat, 50700, PakistanSchool of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, ChinaDepartment of Mechatronics, Faculty of Engineering, Ain Shams University, Cairo, 11566, EgyptDepartment of Industrial Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh, 11421, Saudi ArabiaThe major point of proposed work is to study optimistic multi-granulation roughness of intuitionistic fuzzy ideals by using soft relations that is free from all the complications that challenged by many researchers. The combination of soft binary relations, optimistic multi-granulation rough sets, and intuitionistic fuzzy sets is a useful technique to deal with uncertainty. In modern theories, this combination provides a powerful tool to manage daily life critical situations. Furthermore, the lower and upper approximations of intuitionistic fuzzy subsemigroups, intuitionistic fuzzy left (right) ideals, intuitionistic fuzzy interior ideals and intuitionistic fuzzy bi-ideals of semigroups are studied by using soft relations. Compatible relation is used for upper approximation and complete relation is used for lower approximation. This approach has potential impacts on fields like coding theory, automata theory, and cryptography, providing a flexible and robust method for handling imprecise data, where the use of optimization, and analysis in the industrial domain identify input data with uncertainty and vagueness and reachable multi-source information. At the end, a comparison study and conclusions of the presented work are given that proves how our technique is effective in contrast to fuzzy set.http://www.sciencedirect.com/science/article/pii/S240584402500827820M0720M1803B5203G1
spellingShingle Shahida Bashir
Muhammad Shabir
Muhammad Zishan Anwar
Rabia Mazhar
Afraz Hussain Majeed
Ehab Ghith
Mehdi Tlija
Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
Heliyon
20M07
20M18
03B52
03G1
title Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
title_full Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
title_fullStr Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
title_full_unstemmed Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
title_short Optimistic multi-granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
title_sort optimistic multi granulation roughness of intuitionistic fuzzy ideals based on soft relations over dual universes
topic 20M07
20M18
03B52
03G1
url http://www.sciencedirect.com/science/article/pii/S2405844025008278
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