{"title":"The connection between ordinary and soft $ \\sigma $-algebras with applications to information structures","authors":"T. Al-shami, Z. Ameen, A. Mhemdi","doi":"10.3934/math.2023759","DOIUrl":null,"url":null,"abstract":"The paper presents a novel analysis of interrelations between ordinary (crisp) $ \\sigma $-algebras and soft $ \\sigma $-algebras. It is known that each soft $ \\sigma $-algebra produces a system of crisp (parameterized) $ \\sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \\sigma $-algebra from a system of crisp $ \\sigma $-algebras. Different methods of producing soft $ \\sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \\sigma $-algebras. Lastly, we show that elements of a soft $ \\sigma $-algebra contain information about a specific event.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/math.2023759","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $ \sigma $-algebras. It is known that each soft $ \sigma $-algebra produces a system of crisp (parameterized) $ \sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \sigma $-algebra from a system of crisp $ \sigma $-algebras. Different methods of producing soft $ \sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \sigma $-algebras. Lastly, we show that elements of a soft $ \sigma $-algebra contain information about a specific event.
期刊介绍:
AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.