{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T16:21:33Z","timestamp":1777134093551,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,19]],"date-time":"2019-10-19T00:00:00Z","timestamp":1571443200000},"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 VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for \u201cVIekriterijumsko KOmpromisno Rangiranje\u201d, a Serbian term for \u201cmulti-criteria optimization and compromise solution\u201d. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon\u2019s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented.<\/jats:p>","DOI":"10.3390\/sym11101313","type":"journal-article","created":{"date-parts":[[2019,10,21]],"date-time":"2019-10-21T03:40:29Z","timestamp":1571629229000},"page":"1313","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":87,"title":["Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information"],"prefix":"10.3390","volume":"11","author":[{"family":"Shumaiza","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7217-7962","authenticated-orcid":false,"given":"Muhammad","family":"Akram","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\/0000-0001-5559-5951","authenticated-orcid":false,"given":"Ahmad N.","family":"Al-Kenani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia"}],"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, University of Salamanca, 37007 Salamanca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,19]]},"reference":[{"key":"ref_1","first-page":"172","article-title":"An approximate measure of value","volume":"2","author":"Churchman","year":"1954","journal-title":"J. Oper. Res. Soc. Am."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1287\/mnsc.32.7.841","article-title":"Axiomatic foundation of the analytic hierarchy process","volume":"32","author":"Saaty","year":"1986","journal-title":"Manag. 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