{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T18:24:21Z","timestamp":1784139861421,"version":"3.55.0"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T00:00:00Z","timestamp":1644537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1623190, HRD-1834620, and HRD-2034030"],"award-info":[{"award-number":["1623190, HRD-1834620, and HRD-2034030"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004347","name":"AT&amp;T (United States)","doi-asserted-by":"publisher","award":["AT&T Fellowship"],"award-info":[{"award-number":["AT&T Fellowship"]}],"id":[{"id":"10.13039\/100004347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation\u2014where he proposed, analyzed, and utilized ordered weighted averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allow several OWA stages, one after another, we obtain a scheme with a universal approximation property\u2014moreover, a scheme which is perfectly equivalent to modern ReLU-based deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of ReLU-based deep learning. We also recall that the existing schemes for decision making under uncertainty are also naturally interpretable in OWA terms.<\/jats:p>","DOI":"10.3390\/info13020082","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T21:08:43Z","timestamp":1644786523000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ordered Weighted Averaging (OWA), Decision Making under Uncertainty, and Deep Learning: How Is This All Related?"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1244-1650","authenticated-orcid":false,"given":"Vladik","family":"Kreinovich","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,11]]},"reference":[{"key":"ref_1","unstructured":"Feynman, R., Leighton, R., and Sands, M. (2005). Feynman Lectures on Physics, Addison Wesley."},{"key":"ref_2","unstructured":"Thorne, K.S., and Blandford, R.D. (2017). Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics, Princeton University Press."},{"key":"ref_3","first-page":"138","article-title":"Derivation of Einstein\u2019s, Brans-Dicke and other equations from group considerations","volume":"Volume 2","author":"Karade","year":"1985","journal-title":"Sir Arthur Eddington Centenary Symposium"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Finkelstein, A., Kreinovich, V., and Zapatrin, R.R. (1986). Fundamental physical equations uniquely determined by their symmetry groups. Global Analysis\u2014Studies and Applications II, Springer.","DOI":"10.1007\/BFb0075964"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1007\/BF01032102","article-title":"Derivation of the Schroedinger equations from scale invariance","volume":"3","author":"Kreinovich","year":"1976","journal-title":"Theor. Math. Phys."},{"key":"ref_6","unstructured":"Huber, P.J. (2004). Robust Statistics, Wiley-Interscience."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1109\/MSMC.2020.3036378","article-title":"Ordered Weighted Averaging Operators: A short review","volume":"7","author":"Csiszar","year":"2021","journal-title":"IEEE Syst. Man, Cybern. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yager, R.R., and Kacprzyk, J. (1997). The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-6123-1"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yager, R.R., Kacprzyk, J., and Belyakov, G. (2011). Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice, Springer.","DOI":"10.1007\/978-3-642-17910-5"},{"key":"ref_10","unstructured":"Ekman, M. (2021). Learning Deep Learning: Theory and Practice of Neural Networks, Computer Vision, Natural Language Processing, and Transformers Using TensorFlow, Addison-Wesley."},{"key":"ref_11","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Leaning, MIT Press."},{"key":"ref_12","unstructured":"Ivakhnenko, A.G., and Lapa, V.G. (1965). Cybernetic Predicting Devices, Naukova Dumka. (In Russian)."},{"key":"ref_13","unstructured":"Ivakhnenko, A.G., and Lapa, V.G. (1967). Cybernetics and Forecasting Techniques, Elsevier."},{"key":"ref_14","unstructured":"Hurwicz, L. (1951). Optimality Criteria for Decision Making Under Ignorance, Cowles Commission for Research in Econoimics. Cowles Commission Discussion Paper, Statistics, No. 370."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Guo, P., and Pedrycz, W. (2014). Decision making under interval uncertainty (and beyond). Human-Centric Decision-Making Models for Social Sciences, Springer.","DOI":"10.1007\/978-3-642-39307-5"},{"key":"ref_16","unstructured":"Luce, R.D., and Raiffa, R. (1989). Games and Decisions: Introduction and Critical Survey, Courier Corporation."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tockel, W. (2019). Social Design: Essays in Memory of Leonid Hurwicz, Springer.","DOI":"10.1007\/978-3-319-93809-7"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/2\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:17:28Z","timestamp":1760134648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/2\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,11]]},"references-count":17,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["info13020082"],"URL":"https:\/\/doi.org\/10.3390\/info13020082","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202201.0028.v1","asserted-by":"object"}]},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,11]]}}}