{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T04:35:37Z","timestamp":1769315737431,"version":"3.49.0"},"reference-count":48,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The m-polar fuzzy sets (mF sets) have a representative and fundamental role in several fields of science and decision-making. The fusion of mF sets with several other theories of mathematics has become a favorable practice for depicting numerous types of uncertainties under multi-polar information. In this article, we introduce an innovative hybrid model, called m-polar hesitant fuzzy sets (mHF-sets), a hybridization of hesitancy and mF sets, which enables us to tackle multi-polar information with hesitancy. Hesitancy incorporates symmetry into the treatment of the data, whereas the m-polar fuzzy format allows for differentiated or asymmetric sources of information. We highlight and explore basic key properties of mHF-sets and formulate intrinsic operations. Moreover, we develop an m-polar hesitant fuzzy TOPSIS (mHF-TOPSIS) approach for multi-criteria group decision-making (MCGDM), which is a natural extension of the TOPSIS method to this framework. We describe applications of mHF-sets in group decision-making. Further, we show the efficiency of our proposed approach by applying it to the industrial field. Finally, we generate a computer programming code that implements our decision-making procedure for ease of lengthy calculations.<\/jats:p>","DOI":"10.3390\/sym11060795","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T11:19:58Z","timestamp":1560511198000},"page":"795","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7217-7962","authenticated-orcid":false,"given":"Muhammad","family":"Akram","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arooj","family":"Adeel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-9281","authenticated-orcid":false,"given":"Jos\u00e9 Carlos R.","family":"Alcantud","sequence":"additional","affiliation":[{"name":"BORDA Research Unit and IME, Universidad de Salamanca, Salamanca 37008, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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