JOURNAL OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4866, ISSN (o) 2303-4947 www.imvibl.org /JOURNALS / JOURNAL Vol. 9(2019), 1-17 DOI: 10.7251/JIMVI1901001A Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) INTERVAL VALUED BIPOLAR FUZZY IDEALS IN ORDERED Γ-SEMIGROUPS K. Arulmozhi, V. Chinnadurai and A. Swaminathan Abstract. In this paper, we introduce the notion of interval valued (˜ η, ˜ δ) bipolar fuzzy ideal, bi-ideal,interior ideal, (ǫ, ǫ∨q)-bipolar fuzzy ideal of ordered Γ-semigroups and discuss some properties with examples. 1. Introduction Fuzzy set was introduced by Zadeh [19]. Interval valued fuzzy sets were in- troduced independently by Zadeh [20]. Ordered Γ-semigroup was studied by Ke- hayopula [9]. Pavel Pal [13] studied the Regularity of Po-Γ-semigroups in terms of fuzzy subsemigroups and fuzzy bi-ideals. Bipolar fuzzy set was first studied by Lee [11]. Bipolar fuzzy set is an extension of fuzzy set whose membership degree range is enlarged from the interval [0, 1] to [−1, 1]. Faiz Muhammad Khan et al [3] introduced the concepts of (λ, θ)-fuzzy bi-ideal and (λ, θ)-fuzzy subsemigroup. Jun et al [4] provided some results on ordered semigroups characterized by their (ǫ, ǫ ∨ q)-fuzzy bi-ideals. Kazanci and Yamak [5]introduced the concept of a gener- alized fuzzy bi-ideal in semigroup and established some properties of fuzzy bi-ideals in terms of (ǫ, ǫ ∨ q)-fuzzy bi-ideals. Kehayopula and Tsingelies [8] initiated the study of fuzzy ordered semigroups. Bhakat and Das [1] introduced the concepts of (ǫ, ǫ ∨ q)-fuzzy subgroups using the notion “belongingness (∈)” and “quasi- coincidence (y)”. In this paper we define the new notions of interval valued (˜ η, ˜ δ) bipolar fuzzy ideal, bi-ideal, interior ideal, interval valued (˜ ǫ, ˜ ǫ ∨ q)-bipolar fuzzy ideal of ordered Γ-semigroup and discuss some properties with examples. 2010 Mathematics Subject Classification. 08A72; 20M12; 06F05. Key words and phrases. Ordered Γ-semigroups, bipolar fuzzy set, fuzzy bi-ideals, (˜ η, ˜ δ)-fuzzy ideal, (ǫ, ǫ ∨ q)-fuzzy bi-ideal. 1