{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T15:02:33Z","timestamp":1781794953660,"version":"3.54.5"},"reference-count":11,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T00:00:00Z","timestamp":1556323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper we introduced a new class of strong negations, which were generated via conical sections. This paper focuses on the fact that simple mathematical and computational processes generate new strong fuzzy negations, through purely geometrical concepts such as the ellipse and the hyperbola. Well-known negations like the classical negation, Sugeno negation, etc., were produced via the suggested conical sections. The strong negations were a structural element in the production of fuzzy implications. Thus, we have a machine for producing fuzzy implications, which can be useful in many areas, as in artificial intelligence, neural networks, etc. Strong Fuzzy Negations refers to the discrepancy between the degree of difficulty of the effort and the significance of its results. Innovative results may, therefore, derive for use in literature in the specific field of mathematics. These data are, moreover, generated in an effortless, concise, as well as self-evident manner.<\/jats:p>","DOI":"10.3390\/a12050089","type":"journal-article","created":{"date-parts":[[2019,4,29]],"date-time":"2019-04-29T02:57:32Z","timestamp":1556506652000},"page":"89","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Algorithm for Producing Fuzzy Negations via Conical Sections"],"prefix":"10.3390","volume":"12","author":[{"given":"Georgios","family":"Souliotis","sequence":"first","affiliation":[{"name":"Department of Civil Engineering Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6519-895X","authenticated-orcid":false,"given":"Basil","family":"Papadopoulos","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,27]]},"reference":[{"key":"ref_1","unstructured":"Baczy\u0144ski, M., and Balasubramaniam, J. (2008). Fuzzy Implications, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Baczy\u0144ski, M., Beliakov, G., Bustince, S.H., and Pradera, A. (2013). Advances in Fuzzy Implication Functions, Springer.","DOI":"10.1007\/978-3-642-35677-3"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Souliotis, G., and Papadopoulos, B. (2018, January 4\u20137). Fuzzy Implications Generating from Fuzzy Negations. ICANN 2018. Proceedings of the 27th International Conference on Artificial Neural Networks, Rhodes, Greece.","DOI":"10.1007\/978-3-030-01418-6_72"},{"key":"ref_4","unstructured":"Gottwald, S. (2001). A Treatise on Many-Valued Logics, Research Studies Press."},{"key":"ref_5","unstructured":"Klir, G.J., and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice Hall."},{"key":"ref_6","unstructured":"Nguyen, H.T., and Walker, E.A. (2000). A First Course in Fuzzy Logic, CRC Press. 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Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures. Symmetry, 11.","DOI":"10.3390\/sym11020286"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/5\/89\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:47:37Z","timestamp":1760186857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/5\/89"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,27]]},"references-count":11,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["a12050089"],"URL":"https:\/\/doi.org\/10.3390\/a12050089","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,27]]}}}