{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:39Z","timestamp":1760243439682,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T00:00:00Z","timestamp":1666915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Science and Technology, India","award":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"],"award-info":[{"award-number":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"]}]},{"name":"SRIC, Indian Institute of Technology, Kharagpur","award":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"],"award-info":[{"award-number":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"]}]},{"DOI":"10.13039\/501100005357","name":"Slovak Research and Development Agency","doi-asserted-by":"publisher","award":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"],"award-info":[{"award-number":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Palacky University Olomouc","award":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"],"award-info":[{"award-number":["IIT\/SRIC\/ISIRD\/2020-2021\/22","APVV-18-0052","IGAPrF2021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) 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\u2019s home environment quality evaluation with detailed analysis.<\/jats:p>","DOI":"10.3390\/axioms11110600","type":"journal-article","created":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T23:45:00Z","timestamp":1667087100000},"page":"600","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM"],"prefix":"10.3390","volume":"11","author":[{"given":"Debasmita","family":"Banerjee","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Patna 800013, India"}]},{"given":"Debashree","family":"Guha","sequence":"additional","affiliation":[{"name":"School of Medical Science and Technology, Indian Institute of Technology, Kharagpur 721302, India"}]},{"given":"Radko","family":"Mesiar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, 811 05 Bratislava, Slovakia"},{"name":"Department of Algebra and Geometry, Faculty of Science, Palack\u00fd University Olomouc, 17. Listopadu 12, 771 46 Olomouc, Czech Republic"}]},{"given":"Juliet","family":"Karmakar Mondol","sequence":"additional","affiliation":[{"name":"Counselling Centre, Indian Institute of Technology, Kharagpur 721302, India"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1142\/S021962201830001X","article-title":"Decision making methods based on fuzzy aggregation operators: Three decades review from 1986 to 2017","volume":"17","author":"Mardani","year":"2018","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_2","unstructured":"Mesiar, R., Koles\u00e1rov\u00e1, A., Calvo, T., and Komorn\u00edkov\u00e1, M. (2008). A review of aggregation functions. 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