{"title":"封闭区间正集上的模糊蕴涵与共蕴涵","authors":"Juan Dai, Yexing Dan, Xiaodong Pan","doi":"10.1007/s40314-024-02906-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper, under the inclusion order, we focus on the investigations of fuzzy implications and coimplications on the poset of closed intervals of a given bounded poset. We first propose a method for constructing a fuzzy implication on the poset of closed intervals of a given bounded poset through the use of a fuzzy implication and a fuzzy coimplication on that given bounded poset. This process of constructing fuzzy implications is an extension of the fuzzy implication on that given bounded poset. We then explore some properties of this extended fuzzy implication and discuss about which properties of fuzzy implications are preserved in this extension. Moreover, we would like to apply the method of extending fuzzy implications for fuzzy coimplications. Although we present two methods for constructing fuzzy coimplications on the poset of closed intervals of a given bounded poset, these two methods are not the extension of the fuzzy coimplication on that given bounded poset. We also provide some illustrative examples.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"152 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fuzzy implications and coimplications on the poset of closed intervals\",\"authors\":\"Juan Dai, Yexing Dan, Xiaodong Pan\",\"doi\":\"10.1007/s40314-024-02906-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, under the inclusion order, we focus on the investigations of fuzzy implications and coimplications on the poset of closed intervals of a given bounded poset. We first propose a method for constructing a fuzzy implication on the poset of closed intervals of a given bounded poset through the use of a fuzzy implication and a fuzzy coimplication on that given bounded poset. This process of constructing fuzzy implications is an extension of the fuzzy implication on that given bounded poset. We then explore some properties of this extended fuzzy implication and discuss about which properties of fuzzy implications are preserved in this extension. Moreover, we would like to apply the method of extending fuzzy implications for fuzzy coimplications. Although we present two methods for constructing fuzzy coimplications on the poset of closed intervals of a given bounded poset, these two methods are not the extension of the fuzzy coimplication on that given bounded poset. We also provide some illustrative examples.</p>\",\"PeriodicalId\":51278,\"journal\":{\"name\":\"Computational and Applied Mathematics\",\"volume\":\"152 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40314-024-02906-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40314-024-02906-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fuzzy implications and coimplications on the poset of closed intervals
In this paper, under the inclusion order, we focus on the investigations of fuzzy implications and coimplications on the poset of closed intervals of a given bounded poset. We first propose a method for constructing a fuzzy implication on the poset of closed intervals of a given bounded poset through the use of a fuzzy implication and a fuzzy coimplication on that given bounded poset. This process of constructing fuzzy implications is an extension of the fuzzy implication on that given bounded poset. We then explore some properties of this extended fuzzy implication and discuss about which properties of fuzzy implications are preserved in this extension. Moreover, we would like to apply the method of extending fuzzy implications for fuzzy coimplications. Although we present two methods for constructing fuzzy coimplications on the poset of closed intervals of a given bounded poset, these two methods are not the extension of the fuzzy coimplication on that given bounded poset. We also provide some illustrative examples.
期刊介绍：
Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics).
The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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