{"id":10297,"date":"2026-04-06T16:48:21","date_gmt":"2026-04-06T15:48:21","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=10297"},"modified":"2026-06-18T09:14:56","modified_gmt":"2026-06-18T08:14:56","slug":"25-6-11-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/","title":{"rendered":"25.6.11 En"},"content":{"rendered":"\n

Development of an algorithm based on logical operations to detect patterns in data with missing values<\/strong><\/h1>\n\n\n\n

L.A. Lyutikova
<\/strong><\/p>\n\n\n\n

\n

<\/p>\n\n\n\n

\n
\n
PDF<\/a><\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
JATS XML<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n

<\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Abstract<\/strong>.<\/strong> <\/em>This paper presents a method of local interpretation of solutions of a trained neural network by functions of multivalued predicate logic. The local interpretation of a neural network refers to the process of explaining the decisions made by the model on a specific example or in the vicinity of a specific input. The proposed approach is based on a set of functions of multivalued logic, which are generalized operations that meet certain requirements. By combining these functions, it is possible to detect internal patterns in the data and even correct the results obtained with the help of neural networks. The proposed method was investigated in the context of classification problems using multidimensional discrete features. In such cases, each attribute can take one of k possible values and have equal importance for class identification. This approach opens up new possibilities for understanding and explaining the rules underlying the data, which are not always obvious when using conventional neural networks.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Keywords<\/strong>:<\/em><\/strong> interpretation, multivalued logic, neural network, generalized addition, data<\/p>\n\n\n\n

<\/p>\n\n\n\n

For citation<\/strong>.<\/strong> Lyutikova L.A. Development of an algorithm based on logical operations to detect patterns in data with missing values. News of the Kabardino-Balkarian Scientific Center of RAS. 2023. No. 6(116). Pp. 109\u2013115. DOI: 10.35330\/1991-6639-2023-6-116-109-115<\/p>\n\n\n\n

<\/p>\n\n\n\n

R<\/strong>eferences<\/summary>\n
    \n
  1. Zhuravlev Yu.I. On the algebraic approach to solving problems of recognition or classification. Problemy kibernetiki<\/em> [Problems of cybernetics]. 1978. Vol. 33. Pp. 5\u201368. (In Russian)<\/li>\n\n\n\n
  2. Shibzukhov Z.M. Correct algorithms for aggregating operations. Raspoznavaniye obrazov i analiz izobrazheniy <\/em>[Pattern recognition and image analysis]. 2014. No. 3\u201324. Pp. 377\u2013382. (In Russian)<\/li>\n\n\n\n
  3. Naimi A.I., Balzer L.B. Multilevel generalization: an introduction to super learning. European Journal of Epidemiology<\/em>. 2018. Vol. 33. Pp. 459\u2013464.<\/li>\n\n\n\n
  4. Wang H., Smith S. Big data analysis and perturbation using a data mining algorithm. Journal of Soft Computing Paradigm<\/em>. 2021. No. 3\u201301. Pp. 19\u201328.<\/li>\n\n\n\n
  5. Joe MrK Vijesh, Jennifer S. Raj User Recommendation System Dependent on LocationBased Orientation Context. Journal of Trends in Computer Science and Smart Technology<\/em>. 2021. No. 3\u201301. Pp. 14\u201323.<\/li>\n\n\n\n
  6. Grabisch M., Marichal J-L., Pap E. Aggregation functions. Cambridge University Press<\/em>. Vol. 127. P. 16.<\/li>\n\n\n\n
  7. Calvo T., Belyakov G. Aggregating functions based on penalties. Fuzzy sets and systems.<\/em> No. 10\u2013161. Pp. 1420\u20131436.<\/li>\n\n\n\n
  8. Mesiar R., Komornikova M., Kolesarova A., Calvo T. Fuzzy aggregation functions: a revision. Sets and their extensions: representation, aggregation and models. Springer-Verlag. Berlin, 2008.<\/li>\n\n\n\n
  9. Yang F., Yang Zh., Cohen W.W. Differentiable learning of logical rules for reasoning in the knowledge base. Advances in the field of neural information processing systems<\/em>. 2017. Pp. 2320\u20132329.<\/li>\n\n\n\n
  10. Flach P. Mashinnoye obucheniye: nauka i iskusstvo postroyeniya algoritmov, kotoryye izvlekayut znaniya iz dannykh <\/em>[Machine learning: the science and art of building algorithms that extract knowledge from data]. Moscow, DMK Press, 2015. 400 p. (In Russian)<\/li>\n\n\n\n
  11. Lyutikova L.A., Shmatova E.V. Algorithm for constructing logical operations to identify patterns in data. E3S Web of Conferences, Moscow, November 25\u201327, 2020. Vol. 224. P. 01009.<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
    \n

    Lyutikova Larisa Adolfovna<\/strong>, Candidate of Physical and Mathematics Sciences, Head of the Department of Neuroinformatics and Machine Learning, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    360000, Russia, Nalchik, 89 A Shortanov street;
    lylarisa@yandex, ORCID: https:\/\/orcid.org\/0000-0003-4941-7854<\/p>\n\n\n\n

    <\/p>\n\n\n\n


    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n<\/div>\n<\/details>\n","protected":false},"excerpt":{"rendered":"

    Development of an algorithm based on logical operations to detect patterns in data with missing values L.A. Lyutikova Abstract. This paper presents a method of local interpretation of solutions of a trained neural network by functions of multivalued predicate logic. The local interpretation of a neural network refers to the process of explaining the decisions […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-10297","page","type-page","status-publish","hentry"],"yoast_head":"\n25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Development of an algorithm based on logical operations to detect patterns in data with missing values L.A. Lyutikova Abstract. This paper presents a method of local interpretation of solutions of a trained neural network by functions of multivalued predicate logic. The local interpretation of a neural network refers to the process of explaining the decisions […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-18T08:14:56+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-11-en\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-11-en\\\/\",\"name\":\"25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\"},\"datePublished\":\"2026-04-06T15:48:21+00:00\",\"dateModified\":\"2026-06-18T08:14:56+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-11-en\\\/#breadcrumb\"},\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-11-en\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-11-en\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430\",\"item\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"25.6.11 En\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"description\":\"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b\",\"publisher\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ru-RU\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"contentUrl\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"width\":1828,\"height\":2560,\"caption\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\"},\"image\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/","og_locale":"ru_RU","og_type":"article","og_title":"25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","og_description":"Development of an algorithm based on logical operations to detect patterns in data with missing values L.A. Lyutikova Abstract. This paper presents a method of local interpretation of solutions of a trained neural network by functions of multivalued predicate logic. The local interpretation of a neural network refers to the process of explaining the decisions […]","og_url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/","og_site_name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","article_modified_time":"2026-06-18T08:14:56+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/","url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/","name":"25.6.11 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","isPartOf":{"@id":"https:\/\/izvestiyakbncran.ru\/#website"},"datePublished":"2026-04-06T15:48:21+00:00","dateModified":"2026-06-18T08:14:56+00:00","breadcrumb":{"@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-11-en\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430","item":"https:\/\/izvestiyakbncran.ru\/"},{"@type":"ListItem","position":2,"name":"25.6.11 En"}]},{"@type":"WebSite","@id":"https:\/\/izvestiyakbncran.ru\/#website","url":"https:\/\/izvestiyakbncran.ru\/","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","description":"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b","publisher":{"@id":"https:\/\/izvestiyakbncran.ru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/izvestiyakbncran.ru\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/izvestiyakbncran.ru\/#organization","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","url":"https:\/\/izvestiyakbncran.ru\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/","url":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","contentUrl":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","width":1828,"height":2560,"caption":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb"},"image":{"@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/comments?post=10297"}],"version-history":[{"count":15,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10297\/revisions"}],"predecessor-version":[{"id":15093,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10297\/revisions\/15093"}],"wp:attachment":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/media?parent=10297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}