{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T18:24:27Z","timestamp":1784139867574,"version":"3.55.0"},"reference-count":72,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["No. XDJK2019C085250"],"award-info":[{"award-number":["No. XDJK2019C085250"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013160","name":"Venture and Innovation Support Program for Chongqing Overseas Returnees","doi-asserted-by":"publisher","award":["No. cx2018077"],"award-info":[{"award-number":["No. cx2018077"]}],"id":[{"id":"10.13039\/501100013160","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.<\/jats:p>","DOI":"10.3390\/e22020195","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T11:50:28Z","timestamp":1581076228000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1924-8060","authenticated-orcid":false,"given":"Haiyi","family":"Mao","sequence":"first","affiliation":[{"name":"School of Computer and Information Science, Southwest University, No. 2 Tiansheng Road, BeiBei District, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9955-9036","authenticated-orcid":false,"given":"Rui","family":"Cai","sequence":"additional","affiliation":[{"name":"Business College, Southwest University, No.160 Xueyuan Road, Rongchang District, Chongqing 402460, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.inffus.2018.09.004","article-title":"FusionGAN: A generative adversarial network for infrared and visible image fusion","volume":"48","author":"Ma","year":"2019","journal-title":"Inf. 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