The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships betw...The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.展开更多
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 cha...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.展开更多
This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice....This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.60875034)the Key Science Foundation of Education Committee of Hubei Province (Grant Nos.D20092901+1 种基金 D20092907)the Natural Science Foundation of Hubei Province (Grant No.2009CDB340)
文摘The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.
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)+1 种基金Natural Science Foundation of Education Committee of Shannxi Province(Grant No.19JK0626)Fundamental Research Funds for the Central Universities(Grant Nos.GK202003003,GK200101009).
文摘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.
文摘This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.
