摘要
本文研究了MTL-代数上的几类广义赋值,讨论了MTL-代数上广义赋值、态以及滤子之间的关系,获得了MTL-代数上广义赋值成为(正)关联广义赋值的等价刻画,并基于广义赋值构造的同余关系研究了MTL-代数的商结构.所得结果推广了基于三角模的模糊逻辑代数上广义赋值的相关理论,进一步丰富了基于三角模的模糊逻辑代数上概率测度的代数结论.
In this paper,we study the kinds of generalized valuations on MTL-algebras,discuss the relationship among generalized valuations,states and types of filters onMTL-algebras.Then,we give some equivalent characterizations of the generalized valuations to be the positive implicative generalized valuations on MTL-algebras.Finally,we study the structure theory of quotient MTL-algebras based on the congruence relation induced by generalized valuations.The results of this paper not only generalize the related theories of generalized valuations,but also enrich the algebraic conclusion of probability measure,on the algebras of triangular norm based on fuzzy logics.
作者
王军涛
贺鹏飞
WANG Juntao;HE Pengfei(School of Science,Xi'an Shiyou University,Xi'an,Shaanxi,710065,P.R.China;School of Mathematics and Statistics,Shaanxi Normal University,Xi'an,Shaanxi,710119,P.R.China)
出处
《数学进展》
CSCD
北大核心
2022年第3期426-446,共21页
Advances in Mathematics（China）
基金
国家自然科学基金(Nos.12001423,12171294,61976244,11961016)
陕西省自然科学基础研究计划资助项目(Nos.2020JQ-762,2021JQ-580,2021JQ-579)
陕西省教育厅自然科学研究专项计划项目(No.20JK0626)
中央高校基本科研业务费项目(Nos.GK202003003,GK200101009)。
