{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T08:14:04Z","timestamp":1770279244831,"version":"3.49.0"},"reference-count":50,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T00:00:00Z","timestamp":1557619200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,6,11]]},"abstract":"<jats:p>\n                    Nullnorms are aggregation functions on the unit interval [0, 1] related to ordinal sums of t-conorms defined on [0,\n                    <jats:italic>a<\/jats:italic>\n                    ] and t-norms defined on [\n                    <jats:italic>a<\/jats:italic>\n                    , 1], where\n                    <jats:italic>a<\/jats:italic>\n                    is the annihilator of the considered aggregation function. In this paper some basic algebraic properties like idempotent and nilpotent elements of nullnorms on the unit interval are introduced and discussed. Then, the direct product of nullnorms on bounded lattices is defined and properties of introduced nullnorms are deeply investigated. Thus by defining such algebraic properties and direct product of nullnorms, triangular norms and triangular conorms are extended to a more general form. Finally, we study some properties concerning orders induced by nullnorms acting on lattices.\n                  <\/jats:p>","DOI":"10.3233\/jifs-181602","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:44:41Z","timestamp":1558093481000},"page":"5745-5756","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Direct product of nullnorms on bounded lattices"],"prefix":"10.1177","volume":"36","author":[{"given":"Emel","family":"A\u015f\u0131c\u0131","sequence":"first","affiliation":[{"name":"Department of Software Engineering, Karadeniz Technical University, Faculty of Technology, Trabzon, Turkey"}]},{"given":"Radko","family":"Mesiar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering,  Slovak University of Technology, Radlinsk\u00e9ho, Bratislava, Slovakia"},{"name":"Centre of Excellence IT4Innovations, Division University of Ostrava, IRAFM, dubna 22, 70103 Ostrava, Czech Republic"}]}],"member":"179","published-online":{"date-parts":[[2019,5,12]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Social Choice and Individual Values","author":"Arrow K.","year":"1963","unstructured":"K.Arrow, Social Choice and Individual Values, Wiley, 2 nd edition, 1963.","edition":"2"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.12.004"},{"key":"e_1_3_2_4_2","first-page":"78","volume-title":"Advances in Fuzzy Logic and Technology 2017 IWIFSGN 2017, EUSFLAT 2017 Advances in Intelligent Systems and Computing","author":"A\u015f\u0131c\u0131 E.","year":"2018","unstructured":"E.A\u015f\u0131c\u0131, Some notes on the F-partial order, In: J.Kacprzyk, E.Szmidt, S.Zadro\u017any, K.Atanassov and M.Krawczak, (eds), Advances in Fuzzy Logic and Technology 2017 IWIFSGN 2017, EUSFLAT 2017 Advances in Intelligent Systems and Computing, vol 641, Springer, Cham, 2018, pp. 78\u201384."},{"key":"e_1_3_2_5_2","first-page":"69","volume-title":"Advances in Fuzzy Logic and Technology 2017 IWIFSGN 2017, EUSFLAT 2017 Advances in Intelligent Systems and Computing","author":"A\u015f\u0131c\u0131 E.","year":"2018","unstructured":"E.A\u015f\u0131c\u0131, Some remarks on an order induced by uninorms, In: J.Kacprzyk, E.Szmidt, S.Zadro\u017any, K.Atanassov and M.Krawczak, (eds), Advances in Fuzzy Logic and Technology 2017 IWIFSGN 2017, EUSFLAT 2017 Advances in Intelligent Systems and Computing, vol 641, Springer, Cham, 2018, pp. 69\u201377."},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.11.008"},{"key":"e_1_3_2_7_2","first-page":"319","volume-title":"Information Processing and Management of Uncertainty in Knowledge-Based Systems. 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