The generalizations of fuzzy monoids and vague monoids

The generalizations of fuzzy monoids and vague monoids | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The generalizations of fuzzy monoids and vague monoids Wei Li, Haohao Wang, Yuanhao Liu, Bin Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1697865/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Apr, 2023 Read the published version in Soft Computing → Version 1 posted 5 You are reading this latest preprint version Abstract In this paper, we present the fuzzy monoids and vague monoids by using aggregation operators. The unit interval with a t-norm or a t-conorm is a special monoid, so we mainly talk about fuzzy subsets of monoids. Firstly, the classification of fuzzy sets based on some special aggregation operators is discussed. At the same time, we give two basic propositions about submonoids of t-norm and t-conorm. The fuzzification by uninorm and nullnorm are denoted and some properties can be drawn. Next, we briefly present fuzzy subsets on lattice. Finally, the vague monoids on aggregation operators are redefined and further consider the special cases of uninorms and nullnorms. Uninorms Nullnorms t-norms t-conorms Aggregation functions Fuzzy monoids Vague monoids Full Text Supplementary Files DECLARATION.pdf Cite Share Download PDF Status: Published Journal Publication published 11 Apr, 2023 Read the published version in Soft Computing → Version 1 posted Editorial decision: Major Revision 03 Jan, 2023 Reviewers agreed at journal 31 Aug, 2022 Reviewers invited by journal 26 Aug, 2022 Editor assigned by journal 01 Jun, 2022 First submitted to journal 30 May, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1697865","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":132018599,"identity":"89f29e69-4f18-4d37-8332-9a80eecae069","order_by":0,"name":"Wei Li","email":"","orcid":"","institution":"Northwest A\u0026F University: Northwest Agriculture and Forestry University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Li","suffix":""},{"id":132018600,"identity":"787e0893-6851-4fd6-80cf-e62eec2cbd6c","order_by":1,"name":"Haohao 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