{"title":"半重叠函数及其残差的模糊逻辑","authors":"Lei Du, Songsong Dai, Lvqing Bi","doi":"10.3390/axioms13080498","DOIUrl":null,"url":null,"abstract":"Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"41 7","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Fuzzy Logic for Semi-Overlap Functions and Their Residua\",\"authors\":\"Lei Du, Songsong Dai, Lvqing Bi\",\"doi\":\"10.3390/axioms13080498\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved.\",\"PeriodicalId\":502355,\"journal\":{\"name\":\"Axioms\",\"volume\":\"41 7\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Axioms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/axioms13080498\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Axioms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/axioms13080498","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
半重叠函数作为左连续 t-norm 的一般化，也有残差。本文基于半重叠函数及其残差，发展了一种新的残差逻辑 SOL-逻辑。本文定义了相应的代数结构 SOL-代数，并证明了 SOL 关于 SOL-代数的完备性。
A Fuzzy Logic for Semi-Overlap Functions and Their Residua
Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved.
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