计算机工程与应用 ›› 2016, Vol. 52 ›› Issue (13): 64-68.

• 理论与研发 • 上一篇    下一篇

MV-代数上的不确定性测度

谢茂森1,张家录2   

  1. 1.四川文理学院 数学与财经学院,四川 达州 635000
    2.湘南学院 数学与金融学院,湖南 郴州 423000
  • 出版日期:2016-07-01 发布日期:2016-07-15

Uncertainty measures on MV-algebras

XIE Maosen1, ZHANG Jialu2   

  1. 1.School of Mathematics and Finance, Sichuan University of Arts and Science, Dazhou, Sichuan 635000, China
    2.School of Mathematics and Finance, Xiangnan University, Chenzhou, Hunan 423000, China
  • Online:2016-07-01 Published:2016-07-15

摘要: 定义MV-代数上关于Boole划分的下近似和上近似运算,给出关于Boole划分的下近似和上近似运算的性质。利用MV-代数的全体Boole元素集合上的mass函数定义MV-代数上的信任函数和似然函数,讨论MV-代数的上、下近似与信任函数和似然函数的关系。

关键词: MV-代数, 下近似, 上近似, 信任函数, 似然函数, 不确定性测度

Abstract: A lower approximate operation and an upper approximate operation with respect to a Boole partition on MV-algebras are defined, and then their properties are given. By using a mass function on the set of all Boole elements of MV-algebras, a belief measure and a plausibility measure on MV-algebras are defined. The relation between lower approximate operation, upper approximate operation and belief measure, plausibility measure are discussed.

Key words: MV-algebra, lower approximate, upper approximate, belief measure, plausibility measure, uncertainty measure