Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision Making Article Swipe
Muhammad Shoaib Anwar
,
Shahida Bashir
,
Muhammad Shabir
,
Majed Alharbi
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.3390/math9202587
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.3390/math9202587
Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math9202587
- https://www.mdpi.com/2227-7390/9/20/2587/pdf?version=1638865081
- OA Status
- gold
- Cited By
- 12
- References
- 74
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3206301893
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3206301893Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/math9202587Digital Object Identifier
- Title
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Multigranulation Roughness of Intuitionistic Fuzzy Sets by Soft Relations and Their Applications in Decision MakingWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-10-15Full publication date if available
- Authors
-
Muhammad Shoaib Anwar, Shahida Bashir, Muhammad Shabir, Majed AlharbiList of authors in order
- Landing page
-
https://doi.org/10.3390/math9202587Publisher landing page
- PDF URL
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https://www.mdpi.com/2227-7390/9/20/2587/pdf?version=1638865081Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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-
goldOpen access status per OpenAlex
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https://www.mdpi.com/2227-7390/9/20/2587/pdf?version=1638865081Direct OA link when available
- Concepts
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Rough set, Mathematics, Set (abstract data type), Fuzzy set, Space (punctuation), Fuzzy logic, Pure mathematics, Mathematical optimization, Computer science, Artificial intelligence, Programming language, Operating systemTop concepts (fields/topics) attached by OpenAlex
- Cited by
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12Total citation count in OpenAlex
- Citations by year (recent)
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2025: 1, 2024: 3, 2023: 3, 2022: 5Per-year citation counts (last 5 years)
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74Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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