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基于Abel半群上的模糊蕴含
  • ISSN号：1001-7402
  • 期刊名称：《模糊系统与数学》
  • 时间：0
  • 分类：O141[理学—数学;理学—基础数学]
  • 作者机构：[1]江西师范大学数学与信息科学学院,江西南昌330022, [2]石家庄学院数学与信息科学学院,河北石家庄050035
  • 相关基金：国家自然科学基金资助项目（61165014;61563020）;江西省自然科学基金资助项目（20151BAB201019）;石家庄学院2016年科研项目;石家庄学院模糊数学应用研究团队项目
作者： 闵幼梅, 覃锋[1], 李伟才[2]
关键词： 模糊连接词, 模糊蕴含, 阿贝尔半群, 序和蕴含, Fuzzy Connectives, Fuzzy Implications, Abel Semigroups, Ordinal Sum Implications
中文摘要：

本文引入了两种基于阿贝尔半群上的模糊蕴含。一种是由一个严格递减函数f生成的Mf-蕴含,其中函数f的值域属于一个阿钡尔半群。另一种是M-蕴含,它是由Mf-蕴含族所生成。紧接着,我们讨论了这两种模糊蕴含的基本性质,证明了这两种模糊蕴含的确是两类新的模糊蕴含,并表明不同于已知的（S,N）-蕴含,R-蕴含,Yager的f-蕴含和苏勇给出的序和蕴含。

英文摘要：

In this paper, at first, two new families of fuzzy implications are introduced. One is called an Mf-implieation defined by a strictly decreasing function such that its range belongs to an Abel semigroup, the other is said to be an M-implication which is the ordinal sum of a family of Mf-implications. Then the newly proposed properties of Mf-implications and M-implications are studied. Finally, it is shown that Mf-implications and M-implications are really new class, in other words, they are indeed different from the known （S, N）-, R-, Yager ＇s f-implications, and ordinal sum implications given by Y. Su, respectively.

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期刊信息
  • 《模糊系统与数学》
  • 中国科技核心期刊
  • 主管单位:国防科技大学
  • 主办单位:国防科技大学理学院 国防科技大学理学院
  • 主编：刘应明
  • 地址：湖南长沙国防科技大学理学院
  • 邮编：410073
  • 邮箱：fuzzysys@cfsm.cn
  • 电话：0731-84576220
  • 国际标准刊号：ISSN：1001-7402
  • 国内统一刊号：ISSN：43-1179/O1
  • 邮发代号:42-180
  • 获奖情况:
  • 美国《数学评论》（Mathematical Reviews）核心引...,中国科技论文统计源期刊,《中国科学引文数据库》来源期刊
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:8133