Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making
Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the un...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2058 |
| _version_ | 1827742871580573696 |
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| author | Zeeshan Ali Tahir Mahmood Miin-Shen Yang |
| author_facet | Zeeshan Ali Tahir Mahmood Miin-Shen Yang |
| author_sort | Zeeshan Ali |
| collection | DOAJ |
| description | Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches. |
| first_indexed | 2024-03-11T04:13:30Z |
| format | Article |
| id | doaj.art-bd58991fd2ed4dbb9672900d0c801ae0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:13:30Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bd58991fd2ed4dbb9672900d0c801ae02023-11-17T23:19:26ZengMDPI AGMathematics2227-73902023-04-01119205810.3390/math11092058Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-MakingZeeshan Ali0Tahir Mahmood1Miin-Shen Yang2Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanDepartment of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan 32023, TaiwanComplex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches.https://www.mdpi.com/2227-7390/11/9/2058fuzzy setsintuitionistic fuzzy setscomplex intuitionistic fuzzy setsfrank prioritized aggregation operatorsWASPAS techniquesmulti-attribute decision-making |
| spellingShingle | Zeeshan Ali Tahir Mahmood Miin-Shen Yang Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making Mathematics fuzzy sets intuitionistic fuzzy sets complex intuitionistic fuzzy sets frank prioritized aggregation operators WASPAS techniques multi-attribute decision-making |
| title | Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making |
| title_full | Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making |
| title_fullStr | Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making |
| title_full_unstemmed | Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making |
| title_short | Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making |
| title_sort | frank prioritized aggregation operators and waspas method based on complex intuitionistic fuzzy sets and their application in multi attribute decision making |
| topic | fuzzy sets intuitionistic fuzzy sets complex intuitionistic fuzzy sets frank prioritized aggregation operators WASPAS techniques multi-attribute decision-making |
| url | https://www.mdpi.com/2227-7390/11/9/2058 |
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