Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM
In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">EPBM</mi></semantics&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/600 |
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| author | Debasmita Banerjee Debashree Guha Radko Mesiar Juliet Karmakar Mondol |
| author_facet | Debasmita Banerjee Debashree Guha Radko Mesiar Juliet Karmakar Mondol |
| author_sort | Debasmita Banerjee |
| collection | DOAJ |
| description | In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">EPBM</mi></semantics></math></inline-formula>) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis. |
| first_indexed | 2024-03-09T19:15:57Z |
| format | Article |
| id | doaj.art-3d321bd885fb4395b40f0253d5fcdffa |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:15:57Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3d321bd885fb4395b40f0253d5fcdffa2023-11-24T03:44:05ZengMDPI AGAxioms2075-16802022-10-01111160010.3390/axioms11110600Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDMDebasmita Banerjee0Debashree Guha1Radko Mesiar2Juliet Karmakar Mondol3Department of Mathematics, Indian Institute of Technology, Patna 800013, IndiaSchool of Medical Science and Technology, Indian Institute of Technology, Kharagpur 721302, IndiaDepartment of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, 811 05 Bratislava, SlovakiaCounselling Centre, Indian Institute of Technology, Kharagpur 721302, IndiaIn this article, we propose the generalized version of the extended, partitioned Bonferroni mean (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">EPBM</mi></semantics></math></inline-formula>) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis.https://www.mdpi.com/2075-1680/11/11/600extended aggregation operatorpartitioned Bonferroni meanweighting trianglehierarchy |
| spellingShingle | Debasmita Banerjee Debashree Guha Radko Mesiar Juliet Karmakar Mondol Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM Axioms extended aggregation operator partitioned Bonferroni mean weighting triangle hierarchy |
| title | Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM |
| title_full | Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM |
| title_fullStr | Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM |
| title_full_unstemmed | Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM |
| title_short | Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM |
| title_sort | development of the generalized multi dimensional extended partitioned bonferroni mean operator and its application in hierarchical mcdm |
| topic | extended aggregation operator partitioned Bonferroni mean weighting triangle hierarchy |
| url | https://www.mdpi.com/2075-1680/11/11/600 |
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