{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:07:51Z","timestamp":1767704871922,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T00:00:00Z","timestamp":1716768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["2024"],"award-info":[{"award-number":["2024"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This investigation explores the effects of applying fuzzy time series (FTSs) based on neural network models for estimating a variety of spectral functions in integer time series models. The focus is particularly on the skew integer autoregressive of order one (NSINAR(1)) model. To support this estimation, a dataset consisting of NSINAR(1) realizations with a sample size of n = 1000 is created. These input values are then subjected to fuzzification via fuzzy logic. The prowess of artificial neural networks in pinpointing fuzzy relationships is harnessed to improve prediction accuracy by generating output values. The study meticulously analyzes the enhancement in smoothing of spectral function estimators for NSINAR(1) by utilizing both input and output values. The effectiveness of the output value estimates is evaluated by comparing them to input value estimates using a mean-squared error (MSE) analysis, which shows how much better the output value estimates perform.<\/jats:p>","DOI":"10.3390\/sym16060660","type":"journal-article","created":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T03:48:49Z","timestamp":1716868129000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhancing Integer Time Series Model Estimations through Neural Network-Based Fuzzy Time Series Analysis"],"prefix":"10.3390","volume":"16","author":[{"given":"Mohammed H.","family":"El-Menshawy","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Naser City, Cairo 11884, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laila A.","family":"Al-Essa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-3536","authenticated-orcid":false,"given":"Rashad M.","family":"EL-Sagheer","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Naser City, Cairo 11884, Egypt"},{"name":"High Institute of Computer and Management Information System, First Statement, Cairo 11865, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0165-0114(93)90372-O","article-title":"Fuzzy time series and its models","volume":"54","author":"Song","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/S0165-0114(00)00057-9","article-title":"Effective lengths of intervals to improve forecasting in fuzzy time series","volume":"123","author":"Huarng","year":"2001","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.physa.2004.07.024","article-title":"A refined fuzzy time-series model for forecasting","volume":"346","author":"Yu","year":"2005","journal-title":"Phys. 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