Bi-ideals of ordered semigroups based on the interval-valued fuzzy point

Interval-valued fuzzy set theory (advanced generalization of zadeh’s fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. in this paper,we introduce the notion of generalized quasi-coincident with (q(formula presented)) relation of an interval-valued fuzzy point with an interval-valued fuzzy set. in fact,this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. applying this newly defined idea,the notion of an interval-valued (∈,∈vq(formula presented)) -fuzzy bi-ideal is introduced. moreover,some characterizations of interval-valued (∈,∈vq(formula presented)) -fuzzy bi-ideals are described. it is shown that an interval-valued (∈,∈vq(formula presented)) -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. finally,the concept of implication-based interval-valued fuzzy bi-ideals,characterizations of an interval-valued fuzzy bi-ideal and an interval-valued (∈,∈vq(formula presented)) - fuzzy bi-ideal are considered. © 2016 penerbit utm press. all rights reserved.