Generalized valuations on MTL-algebras

作     者：Juntao WANG Pengfei HE Juntao WANG;Pengfei HE

作者机构：School of ScienceXi’an Shiyou UniversityXi’an710065China School of Mathematics and StatisticsShaanxi Normal UniversityXi’an710119China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2022年第17卷第4期

页      面：521-543页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12001423,12171294,61976244,11961016) Natural Science Foundation of Shaanxi Province(Grant Nos.2020JQ-762,2021JQ-580,2021JQ-579) Natural Science Foundation of Education Committee of Shannxi Province(Grant No.19JK0626) Fundamental Research Funds for the Central Universities(Grant Nos.GK202003003,GK200101009) 

主　　题：Fuzzy logic MTL-algebra generalized valuation filter 

摘      要：In this paper,we study some kinds of generalized valuations on MTL-algebras,discuss the relationship between the cokernel of generalized valuations and types of filters on ***,we give some equivalent characterizations of positive implicative generalized valuations on ***,we characterize the structure theory of quotient MTL algebras based on the congruence relation,which is constructed by generalized *** results of this paper not only generalize related theories of generalized valuations,but also enrich the algebraic conclusion of probability measure,on algebras of triangular norm based fuzzy logic.