Generalized valuations on MTL-algebras  

作　　者：Juntao WANG Pengfei HE 

机构地区：[1]School of Science,Xi’an Shiyou University,Xi’an,710065,China [2]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an,710119,China

出　　处：《Frontiers of Mathematics in China》2022年第4期521-543,共23页中国高等学校学术文摘·数学（英文）

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).

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 MTL-algebras.Then,we give some equivalent characterizations of positive implicative generalized valuations on MTL-algebras.Finally,we characterize the structure theory of quotient MTL algebras based on the congruence relation,which is constructed by generalized valuations.The 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.

关 键 词：Fuzzy logic MTL-algebra generalized valuation filter 

分 类 号：O15[理学—数学]