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

• Main Authors: Khan, Hidayat Ullah, Sarmin, Nor Haniza, Khan, Asghar, Khan, Faiz Muhammad
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2016
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/73937/1/HidayatUllahKhan2016_BIIdealsOfOrderedSemigroupsBased.pdf; http://eprints.utm.my/id/eprint/73937/; https://www.scopus.com/inward/record.uri?eid=2-s2.0-84957876493&doi=10.11113%2fjt.v78.3841&partnerID=40&md5=8094f3a3392cb52af42e766a82e00d8f
• Institution: Universiti Teknologi Malaysia

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.