Release Time:2022-09-22  Hits:

Date of Publication: 2014-01-01

Journal: 模糊系统与数学

Institution: 数学科学学院

Volume: 28

Issue: 1

Page Number: 1-8

ISSN: 1001-7402

Abstract: By use of the concept of interval-valued level cut set on
   interval-valued fuzzy set,the neighborhood relations between the
   interval-valued fuzzy point and the interval-valued fuzzy set are
   presented. By applying these neighborhood
   relations,the(alpha,beta)-interval-valued fuzzy subgroups are defined.
   It is pointed that the significant ones in 16 kinds
   of(alpha,beta)-interval-valued fuzzy subgroups are the(,),(,_q)and(
   q,)-interval-valued fuzzy subgroups. It is proved that an
   interval-valued fuzzy subgroup A over a group G is a(,)-interval-valued
   fuzzy subgroup((,_q)-interval-valued fuzzy subgroup,or(q,)-
   interval-valued fuzzy subgroup)if and only if the interval-valued level
   cut set Alambda is a three-valued fuzzy subgroup for any lambda
   =[a_1,a_2]≤[0. 5,0. 5]and lambda =[a_1,a_2]>[0. 5,0. 5](or for any
   lambda =[a_1,a_2]≤[0. 5,0.5]or lambda = [a_1,a_2]> [0. 5,0.
   5],respectively). Therefore,we established a kind of new interval-valued
   fuzzy subgroup theory based on the neighborhood relation between
   interval-valued fuzzy point and interval-valued fuzzy set.

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