Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems
The <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOF) set, an extension of the <inline-fo...
| Հիմնական հեղինակներ: | , , , , , |
|---|---|
| Ձևաչափ: | Հոդված |
| Լեզու: | English |
| Հրապարակվել է: |
IEEE
2023-01-01
|
| Շարք: | IEEE Access |
| Խորագրեր: | |
| Առցանց հասանելիություն: | https://ieeexplore.ieee.org/document/10271277/ |
| _version_ | 1827794614839410688 |
|---|---|
| author | Muhammad Rahim Kamal Shah Thabet Abdeljawad Maggie Aphane Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa |
| author_facet | Muhammad Rahim Kamal Shah Thabet Abdeljawad Maggie Aphane Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa |
| author_sort | Muhammad Rahim |
| collection | DOAJ |
| description | The <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOF) set, an extension of the <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair fuzzy set (<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ROF) set, offers a more comprehensive approach to information representation, adept at managing data uncertainties. Unlike the restrictive conditions of <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ROF set, which require that the sum of <inline-formula> <tex-math notation="LaTeX">$q^{th}$ </tex-math></inline-formula> power of membership (<inline-formula> <tex-math notation="LaTeX">$\eta$ </tex-math></inline-formula>) and non-membership function (<inline-formula> <tex-math notation="LaTeX">$\vartheta$ </tex-math></inline-formula>) must not exceed one (<inline-formula> <tex-math notation="LaTeX">$\eta ^{q}+\vartheta ^{q}\preccurlyeq 1$ </tex-math></inline-formula>), <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOFS relaxes these limitations. Here, the combined value of the <inline-formula> <tex-math notation="LaTeX">$p^{th}$ </tex-math></inline-formula> power of membership and <inline-formula> <tex-math notation="LaTeX">$q^{th}$ </tex-math></inline-formula> power of non-membership is confined within one i.e., <inline-formula> <tex-math notation="LaTeX">$\eta ^{p}+\vartheta ^{q} \preccurlyeq 1$ </tex-math></inline-formula>, under the conditions <inline-formula> <tex-math notation="LaTeX">$p,q \succcurlyeq 1$ </tex-math></inline-formula> and various relationships between <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$p=q$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$p\succ q$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">$p\prec q$ </tex-math></inline-formula>). This study explores leveraging confidence levels tied to each <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy number (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>–QOFN) to devise a set of averaging and geometric aggregation operators (AOs). These operators effectively combine rating values from distinct criteria, as presented by decision-makers. By harnessing these operators, a novel approach for multi-criteria group decision-making (MCGDM) is formulated, well-suited to resolving real-life decision-making (DM) challenges. An illustrative example underscores the method’s efficacy and validity. Finally, a comparative assessment against existing methods highlights the superior performance of the proposed approach. |
| first_indexed | 2024-03-11T18:36:26Z |
| format | Article |
| id | doaj.art-f7f531c57cbe4421aed2b612a07fe867 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-11T18:36:26Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-f7f531c57cbe4421aed2b612a07fe8672023-10-12T23:01:33ZengIEEEIEEE Access2169-35362023-01-011110998310999610.1109/ACCESS.2023.332187610271277Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making ProblemsMuhammad Rahim0https://orcid.org/0000-0003-0064-0414Kamal Shah1https://orcid.org/0000-0002-8851-4844Thabet Abdeljawad2https://orcid.org/0000-0002-8889-3768Maggie Aphane3Alhanouf Alburaikan4Hamiden Abd El-Wahed Khalifa5Department of Mathematics, Hazara University, Mansehra, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South AfricaDepartment of Mathematics, College of Science and Arts, Qassim University, Al Badayea, Saudi ArabiaDepartment of Mathematics, College of Science and Arts, Qassim University, Al Badayea, Saudi ArabiaThe <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOF) set, an extension of the <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-rung orthopair fuzzy set (<inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ROF) set, offers a more comprehensive approach to information representation, adept at managing data uncertainties. Unlike the restrictive conditions of <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ROF set, which require that the sum of <inline-formula> <tex-math notation="LaTeX">$q^{th}$ </tex-math></inline-formula> power of membership (<inline-formula> <tex-math notation="LaTeX">$\eta$ </tex-math></inline-formula>) and non-membership function (<inline-formula> <tex-math notation="LaTeX">$\vartheta$ </tex-math></inline-formula>) must not exceed one (<inline-formula> <tex-math notation="LaTeX">$\eta ^{q}+\vartheta ^{q}\preccurlyeq 1$ </tex-math></inline-formula>), <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-QOFS relaxes these limitations. Here, the combined value of the <inline-formula> <tex-math notation="LaTeX">$p^{th}$ </tex-math></inline-formula> power of membership and <inline-formula> <tex-math notation="LaTeX">$q^{th}$ </tex-math></inline-formula> power of non-membership is confined within one i.e., <inline-formula> <tex-math notation="LaTeX">$\eta ^{p}+\vartheta ^{q} \preccurlyeq 1$ </tex-math></inline-formula>, under the conditions <inline-formula> <tex-math notation="LaTeX">$p,q \succcurlyeq 1$ </tex-math></inline-formula> and various relationships between <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$p=q$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$p\succ q$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">$p\prec q$ </tex-math></inline-formula>). This study explores leveraging confidence levels tied to each <inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>-quasirung orthopair fuzzy number (<inline-formula> <tex-math notation="LaTeX">$p,q$ </tex-math></inline-formula>–QOFN) to devise a set of averaging and geometric aggregation operators (AOs). These operators effectively combine rating values from distinct criteria, as presented by decision-makers. By harnessing these operators, a novel approach for multi-criteria group decision-making (MCGDM) is formulated, well-suited to resolving real-life decision-making (DM) challenges. An illustrative example underscores the method’s efficacy and validity. Finally, a comparative assessment against existing methods highlights the superior performance of the proposed approach.https://ieeexplore.ieee.org/document/10271277/p, q-quasirung orthopair fuzzy setconfidence levelsmulti-criteria group decision-makingoptimization methodaggregation operatorsoptimization |
| spellingShingle | Muhammad Rahim Kamal Shah Thabet Abdeljawad Maggie Aphane Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems IEEE Access p, q-quasirung orthopair fuzzy set confidence levels multi-criteria group decision-making optimization method aggregation operators optimization |
| title | Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems |
| title_full | Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems |
| title_fullStr | Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems |
| title_full_unstemmed | Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems |
| title_short | Confidence Levels-Based <italic>p</italic>, <italic>q</italic>-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems |
| title_sort | confidence levels based italic p italic italic q italic quasirung orthopair fuzzy operators and its applications to criteria group decision making problems |
| topic | p, q-quasirung orthopair fuzzy set confidence levels multi-criteria group decision-making optimization method aggregation operators optimization |
| url | https://ieeexplore.ieee.org/document/10271277/ |
| work_keys_str_mv | AT muhammadrahim confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems AT kamalshah confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems AT thabetabdeljawad confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems AT maggieaphane confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems AT alhanoufalburaikan confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems AT hamidenabdelwahedkhalifa confidencelevelsbaseditalicpitalicitalicqitalicquasirungorthopairfuzzyoperatorsanditsapplicationstocriteriagroupdecisionmakingproblems |