Various (ζ1, ζ2) neutrosophic ideals of an ordered ternary semigroups

Abstract

In this paper, we introduce the notion of ζ1, ζ2-ternary neutrosophic subsemigroup (TNSS), ternary neutrosophic left ideal(TNLI), ternary neutrosophic right ideal(TNRI), ternary neu-trosophic lateral ideal (TNLATI), ternary neutrosophic ideal (TNI), ternary neutrosophic
bi-ideal(TNBI) of an ordered ternary semigroups and discuss some of their properties. The concept of ζ1, ζ2-TNI is a new extension of TNI over ternary semigroups T . A non-empty subset εζ1 is a (ζ1, ζ2)-TNSS (TNLI, TNRI, TNLATI, TNBI) of T . Then the lower level set Λζ1 is an TSS (T LI, T RI, T LAT I, T BI) of T , where Λζ1 = {℘ ∈ T |Λ(℘) ζ1}, Ξζ1 = {℘ ∈ T |Λ(℘) ζ1} and Υζ1 = {℘ ∈ T |Λ(℘) ≺ ζ1}. A subset ε = [Λ, Ξ, Υ] is
a (ζ1, ζ2) − T N SS[T N LI, T N RI, T N LAT I, T N BI] of T if and only if each non-empty level subset εt is a TSS [T LI, T RI, T LAT I, T BI] of T for all t ∈ (ζ1, ζ2]. Some examples are provided to illustrate our results.