有界格上最大和最小的(U,N)-蕴涵  

The Largest and the Smallest(U,N)-implications on Bounded Lattices

作　　者：张新 赵彬[1] ZHANG Xin;ZHAO Bin(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《模糊系统与数学》2020年第5期1-7,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11531009)。

摘　　要：本文首先引入了有界格上(U,N)-算子的概念并给出了(U,N)-算子是(U,N)-蕴涵的等价刻画;其次分别给出了以1为余素元的有界格上最大和最小的析取一致模;最后在此基础上分别给出了以1为余素元的有界格上最大和最小的(U,N)-蕴涵。In this paper,we first introduce the concepts of(U,N)-operators on bounded lattices and give a characterization for(U,N)-operators to be(U,N)-implications.Secondly,we give the smallest and the largest disjunctive uninorms on bounded lattices with the co-prime 1,respectively.Finally,on the basis of this result,we obtain the smallest and the largest(U,N)-implications on bounded lattices with the co-prime 1,respectively.

关 键 词：有界格 析取一致模 (U N)-蕴涵 

分 类 号：O159[理学—数学]