{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:18Z","timestamp":1760242518440,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T00:00:00Z","timestamp":1507766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Russian Fund for Basic Research","award":["16-07-00854 a"],"award-info":[{"award-number":["16-07-00854 a"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>In this paper we define a non-deterministic dynamic neighborhood model. As a special case, a linear neighborhood model is considered. When a non-deterministic neighborhood model functions, it is possible to introduce a restriction on the number of active layers, which will allow the variation of the non-determinism of the model at each moment of time. We give the notion of the non-determinacy measure and prove that it has the properties of a probability measure. We formulate the problem of reachability with partially specified parameters, layer priorities, and the non-determinacy measure. An algorithm for solving the attainability problem for a neighborhood model with variable indeterminacy and layer priorities is presented. An example of its solution is shown, which shows that when the priorities are compared and the measure of non-determinism is used, the solution of the problem can be obtained more quickly than by a method that does not use priorities.<\/jats:p>","DOI":"10.3390\/systems5040049","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T13:06:19Z","timestamp":1507813579000},"page":"49","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Measure of the Non-Determinacy of a Dynamic Neighborhood Model"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8454-6032","authenticated-orcid":false,"given":"Anatoliy","family":"Shmyrin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lipetsk State Technical University, 398600 Lipetsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0012-8103","authenticated-orcid":false,"given":"Irina","family":"Sedykh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lipetsk State Technical University, 398600 Lipetsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"ref_1","unstructured":"Blumin, S.L., and Shmyrin, A.M. (2005). Neighborhood Systems, LEGI."},{"key":"ref_2","unstructured":"Blumin, S.L., Shmyrin, A.M., and Shmyrina, O.A. (2006). Bilinear Neighborhood Systems, LEGI."},{"key":"ref_3","first-page":"91","article-title":"Use of neighborhood-time modeling in the tasks of forming organizational structures","volume":"18","author":"Tomilin","year":"2007","journal-title":"Large Syst. Control."},{"key":"ref_4","first-page":"228","article-title":"Petri nets with variable non-determinism as neighborhood systems","volume":"3.2","author":"Blumin","year":"2008","journal-title":"Control Syst. Inf. Technol."},{"key":"ref_5","unstructured":"Blumin, S.L., Shmyrin, A.M., Sedykh, I.A., and Filonenko, V.Y. (2010). Neighboring Modeling of Petri Nets, LEGI."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1134\/S0005117910060275","article-title":"Identification and control algorithms of functioning for neighborhood systems based on Petri nets","volume":"71","author":"Shmyrin","year":"2010","journal-title":"Autom. Remote Control"},{"key":"ref_7","unstructured":"Sedykh, I.A. (2016, January 1). Parametric identification of a linear dynamic neighborhood model. Proceedings of the International Scientific and Practical Conference \u201cInnovative Science: Past, Present, Future\u201d, Ufa, Russia."},{"key":"ref_8","first-page":"867","article-title":"Discrete models in the class of neighborhood systems","volume":"17","author":"Shmyrin","year":"2012","journal-title":"Bull. Tambov Univ."},{"key":"ref_9","first-page":"5039","article-title":"Neural Networks Neighborhood Models","volume":"12","author":"Shmyrin","year":"2016","journal-title":"Glob. J. Pure Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"070201","DOI":"10.1088\/1674-1056\/19\/7\/070201","article-title":"Multi-agent coordination in directed moving neighborhood random networks","volume":"19","author":"Shang","year":"2010","journal-title":"Chin. Phys. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"023116","DOI":"10.1063\/1.4976959","article-title":"Consensus in averager-copier-voter networks of moving dynamical agents","volume":"27","author":"Shang","year":"2017","journal-title":"Chaos"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/4\/49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:47:07Z","timestamp":1760208427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/5\/4\/49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,12]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["systems5040049"],"URL":"https:\/\/doi.org\/10.3390\/systems5040049","relation":{},"ISSN":["2079-8954"],"issn-type":[{"type":"electronic","value":"2079-8954"}],"subject":[],"published":{"date-parts":[[2017,10,12]]}}}