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Date of Publication:2014-01-01

Journal:模糊系统与数学

Affiliation of Author(s):数学科学学院

Volume:28

Issue:1

Page Number:1-8

ISSN No.: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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