Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets
The Neutrosophic Set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi>...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/18/3817 |
| _version_ | 1797579004655435776 |
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| author | Said Broumi Raman Sundareswaran Marayanagaraj Shanmugapriya Prem Kumar Singh Michael Voskoglou Mohamed Talea |
| author_facet | Said Broumi Raman Sundareswaran Marayanagaraj Shanmugapriya Prem Kumar Singh Michael Voskoglou Mohamed Talea |
| author_sort | Said Broumi |
| collection | DOAJ |
| description | The Neutrosophic Set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, false <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and indeterminacy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi></mrow></mfenced></mrow></semantics></math></inline-formula> values crosses the membership value of one, that is, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>+</mo><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi><mo>+</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. It becomes more crucial during decision-making processes like medical diagnoses or any data sets where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>+</mo><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi><mo>+</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. To achieve this goal, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables even when dealing with incomplete or vague information. In the present work, we introduce the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>, which deals with partial ignorance in true, false, or uncertain regions independently for multi-decision processes. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> contains the interval-valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> value, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> value, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> for knowledge representation. The algebraic properties and set theory between the interval-valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> have also been presented with an illustrative example. |
| first_indexed | 2024-03-10T22:29:41Z |
| format | Article |
| id | doaj.art-224c96c57470498bb69ba5f03051ac32 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:29:41Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-224c96c57470498bb69ba5f03051ac322023-11-19T11:48:01ZengMDPI AGMathematics2227-73902023-09-011118381710.3390/math11183817Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic SetsSaid Broumi0Raman Sundareswaran1Marayanagaraj Shanmugapriya2Prem Kumar Singh3Michael Voskoglou4Mohamed Talea5Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca 20000, MoroccoDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603110, IndiaDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603110, IndiaDepartment of Computer Science and Engineering, Gandhi Institute of Technology and Management, Visakhapatnam 530045, IndiaSchool of Engineering, University of Peloponnese, 26334 Patras, GreeceLaboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca 20000, MoroccoThe Neutrosophic Set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, false <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and indeterminacy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="|"><mrow><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi></mrow></mfenced></mrow></semantics></math></inline-formula> values crosses the membership value of one, that is, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>+</mo><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi><mo>+</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. It becomes more crucial during decision-making processes like medical diagnoses or any data sets where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi><mo>+</mo><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi><mo>+</mo><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. To achieve this goal, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables even when dealing with incomplete or vague information. In the present work, we introduce the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>, which deals with partial ignorance in true, false, or uncertain regions independently for multi-decision processes. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>V</mi><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> contains the interval-valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">T</mi><mi mathvariant="bold-italic">r</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> value, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">I</mi><mi mathvariant="bold-italic">n</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> value, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">F</mi><mi mathvariant="bold-italic">a</mi></mrow><mrow><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">h</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">p</mi></mrow></msub></mrow></semantics></math></inline-formula> for knowledge representation. The algebraic properties and set theory between the interval-valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> have also been presented with an illustrative example.https://www.mdpi.com/2227-7390/11/18/3817Fermatean neutrosophic setsinterval-valued Fermatean neutrosophic setsfaculty performance evaluationmulticriteria decision analysis |
| spellingShingle | Said Broumi Raman Sundareswaran Marayanagaraj Shanmugapriya Prem Kumar Singh Michael Voskoglou Mohamed Talea Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets Mathematics Fermatean neutrosophic sets interval-valued Fermatean neutrosophic sets faculty performance evaluation multicriteria decision analysis |
| title | Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets |
| title_full | Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets |
| title_fullStr | Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets |
| title_full_unstemmed | Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets |
| title_short | Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets |
| title_sort | faculty performance evaluation through multi criteria decision analysis using interval valued fermatean neutrosophic sets |
| topic | Fermatean neutrosophic sets interval-valued Fermatean neutrosophic sets faculty performance evaluation multicriteria decision analysis |
| url | https://www.mdpi.com/2227-7390/11/18/3817 |
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