{"title":"A topology based on nuclei and upsets in residuated lattices","authors":"Supeng Wu, Hui Liu, Jiang Yang","doi":"10.1007/s00500-024-09927-1","DOIUrl":null,"url":null,"abstract":"<p>Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"74 1","pages":""},"PeriodicalIF":3.1000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Soft Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00500-024-09927-1","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Firstly, a topology is constructed by nuclei and upsets in residuated lattices and it is shown that a residuated lattice endowed with this topology becomes a topological space. Furthermore, some properties of the topological space are investigated such as compactness and connectedness. Moreover, we study continuities of all the operations with respect to the topology in a residuated lattice. Finally, the relationships are revealed between the two topologies on quotient residuated lattices.
期刊介绍：
Soft Computing is dedicated to system solutions based on soft computing techniques. It provides rapid dissemination of important results in soft computing technologies, a fusion of research in evolutionary algorithms and genetic programming, neural science and neural net systems, fuzzy set theory and fuzzy systems, and chaos theory and chaotic systems.
Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. By linking the ideas and techniques of soft computing with other disciplines, the journal serves as a unifying platform that fosters comparisons, extensions, and new applications. As a result, the journal is an international forum for all scientists and engineers engaged in research and development in this fast growing field.
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