RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process
Abstract A complex Polytopic fuzzy set (CPoFS) extends a Polytopic fuzzy set (PoFS) by handling vagueness with degrees that range from real numbers to complex numbers within the unit disc. This extension allows for a more nuanced representation of uncertainty. In this research, we develop Complex Po...
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Nature Portfolio
2024-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-65679-w |
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| author | Khaista Rahman Mohammad Khishe |
| author_facet | Khaista Rahman Mohammad Khishe |
| author_sort | Khaista Rahman |
| collection | DOAJ |
| description | Abstract A complex Polytopic fuzzy set (CPoFS) extends a Polytopic fuzzy set (PoFS) by handling vagueness with degrees that range from real numbers to complex numbers within the unit disc. This extension allows for a more nuanced representation of uncertainty. In this research, we develop Complex Polytopic Fuzzy Sets (CPoFS) and establish basic operational laws of CPoFS. Leveraging these laws, we introduce new operators under a confidence level, including the confidence complex Polytopic fuzzy Einstein weighted geometric aggregation (CCPoFEWGA) operator, the confidence complex Polytopic fuzzy Einstein ordered weighted geometric aggregation (CCPoFEOWGA) operator, the confidence complex Polytopic fuzzy Einstein hybrid geometric aggregation (CCPoFEHGA) operator, the induced confidence complex Polytopic fuzzy Einstein ordered weighted geometric aggregation (I-CCPoFEOWGA) operator and the induced confidence complex Polytopic fuzzy Einstein hybrid geometric aggregation (I-CCPoFEHGA) operator, enhancing decision-making precision in uncertain environments. We also investigate key properties of these operators, including monotonicity, boundedness, and idempotency. With these operators, we create an algorithm designed to solve multiattribute decision-making problems in a Polytopic fuzzy environment. To demonstrate the effectiveness of our proposed method, we apply it to a numerical example and compare its flexibility with existing methods. This comparison will underscore the advantages and enhancements of our approach, showing its efficiency in managing complex decision-making scenarios. Through this, we aim to demonstrate how our method provides superior performance and adaptability across different situations. |
| format | Article |
| id | doaj-art-c76b64c5f641402f95adbc6119ca4c1a |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-c76b64c5f641402f95adbc6119ca4c1a2025-01-26T12:34:59ZengNature PortfolioScientific Reports2045-23222024-07-0114112310.1038/s41598-024-65679-wRETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making processKhaista Rahman0Mohammad Khishe1Department of Mathematics, Shaheed Benazir Bhutto University SheringalDepartment of Electrical Engineering, Imam Khomeini Naval Science University of NowshahrAbstract A complex Polytopic fuzzy set (CPoFS) extends a Polytopic fuzzy set (PoFS) by handling vagueness with degrees that range from real numbers to complex numbers within the unit disc. This extension allows for a more nuanced representation of uncertainty. In this research, we develop Complex Polytopic Fuzzy Sets (CPoFS) and establish basic operational laws of CPoFS. Leveraging these laws, we introduce new operators under a confidence level, including the confidence complex Polytopic fuzzy Einstein weighted geometric aggregation (CCPoFEWGA) operator, the confidence complex Polytopic fuzzy Einstein ordered weighted geometric aggregation (CCPoFEOWGA) operator, the confidence complex Polytopic fuzzy Einstein hybrid geometric aggregation (CCPoFEHGA) operator, the induced confidence complex Polytopic fuzzy Einstein ordered weighted geometric aggregation (I-CCPoFEOWGA) operator and the induced confidence complex Polytopic fuzzy Einstein hybrid geometric aggregation (I-CCPoFEHGA) operator, enhancing decision-making precision in uncertain environments. We also investigate key properties of these operators, including monotonicity, boundedness, and idempotency. With these operators, we create an algorithm designed to solve multiattribute decision-making problems in a Polytopic fuzzy environment. To demonstrate the effectiveness of our proposed method, we apply it to a numerical example and compare its flexibility with existing methods. This comparison will underscore the advantages and enhancements of our approach, showing its efficiency in managing complex decision-making scenarios. Through this, we aim to demonstrate how our method provides superior performance and adaptability across different situations.https://doi.org/10.1038/s41598-024-65679-wCPoFSsConfidence levelAggregation operatorsDecision-making process |
| spellingShingle | Khaista Rahman Mohammad Khishe RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process Scientific Reports CPoFSs Confidence level Aggregation operators Decision-making process |
| title | RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process |
| title_full | RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process |
| title_fullStr | RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process |
| title_full_unstemmed | RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process |
| title_short | RETRACTED ARTICLE: Confidence level based complex polytopic fuzzy Einstein aggregation operators and their application to decision-making process |
| title_sort | retracted article confidence level based complex polytopic fuzzy einstein aggregation operators and their application to decision making process |
| topic | CPoFSs Confidence level Aggregation operators Decision-making process |
| url | https://doi.org/10.1038/s41598-024-65679-w |
| work_keys_str_mv | AT khaistarahman retractedarticleconfidencelevelbasedcomplexpolytopicfuzzyeinsteinaggregationoperatorsandtheirapplicationtodecisionmakingprocess AT mohammadkhishe retractedarticleconfidencelevelbasedcomplexpolytopicfuzzyeinsteinaggregationoperatorsandtheirapplicationtodecisionmakingprocess |