{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T21:58:06Z","timestamp":1773784686669,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["R.G.P.1\/383\/43"],"award-info":[{"award-number":["R.G.P.1\/383\/43"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this investigation. It is suggested that these processes be simulated using a method utilizing a hesitant fuzzy set, a rough set, and a probabilistic single-valued neutrosophics set. The proposed approach is employed in the decision-making process, while taking into consideration the decision-makers\u2019 (DMs\u2019) level of confidence in the data they have obtained in order to deal with ambiguity, incomplete data, and uncertainty in lower and upper approximations. The major goal was to outline the issue\u2019s complexities in order to pique interest among experts in the health care sector and encourage them to evaluate SMDs using various evaluation standards. The analysis of the technique\u2019s outcomes demonstrated that the rankings and the results themselves were adequate and trustworthy. The effectiveness of our suggested improvements is also demonstrated through a symmetrical analysis. The symmetry behavior shows that the current techniques address more complex and advanced data.<\/jats:p>","DOI":"10.3390\/sym15030578","type":"journal-article","created":{"date-parts":[[2023,2,23]],"date-time":"2023-02-23T03:25:56Z","timestamp":1677122756000},"page":"578","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["An Optimization Strategy for MADM Framework with Confidence Level Aggregation Operators under Probabilistic Neutrosophic Hesitant Fuzzy Rough Environment"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2358-178X","authenticated-orcid":false,"given":"Muhammad","family":"Kamran","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Punjab, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7080-3824","authenticated-orcid":false,"given":"Rashad","family":"Ismail","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, King Khalid University, Muhayl Assir 61913, Saudi Arabia"},{"name":"Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb 70270, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0418-193X","authenticated-orcid":false,"given":"Esmail Hassan Abdullatif","family":"Al-Sabri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, King Khalid University, Muhayl Assir 61913, Saudi Arabia"},{"name":"Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb 70270, Yemen"}]},{"given":"Nadeem","family":"Salamat","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Punjab, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7616-0500","authenticated-orcid":false,"given":"Muhammad","family":"Farman","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Punjab, Pakistan"},{"name":"Department of Mathematics, Faculty of Arts and Sciences, Near East University, Near East Boulevard, Nicosia, 99138 Mersin, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8616-8829","authenticated-orcid":false,"given":"Shahzaib","family":"Ashraf","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Punjab, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"656","DOI":"10.2307\/2272014","article-title":"Fuzzy sets. 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