On new algebraic structures approach towards (ς1,ς2) intuitionistic Q fuzzy ideals of an ordered ternary semigroups

Abstract

Introducing the concept of ς1,ς2-intuitionistic Q fuzzy ternary subsemigroup (IQFTSS), we
explore some of the properties of these ordered ternary semigroups, including intuitionistic Q fuzzy left ideal (IQFLI), intuitionistic Q fuzzy right ideal (IQFRI), intuitionistic
Q fuzzy lateral ideal (IQFLATI), intuitionistic Q fuzzy ideal (IQFI), and intuitionistic Q
fuzzy bi-ideal (IQFBI). We provide a novel extension of IQFI over ternary semigroups M:
ς1,ς2-IQFI. A non-empty subset ℵς1
is a (ς1,ς2)-IQFTSS (IQFLI, IQFRI, IQFLATI, IQFBI)
of M. Then the lower level set aς1
is an TSS (TLI, TRI, TLATI, TBI) of M, where
aς1 = {` ∈ M|a(`, q) > ς1} and ✵ς1 = {` ∈ M|a(`, q) < ς1}. A subset ℵ = [a, ✵]
is a (ς1,ς2) − IQF TSS[IQFLI, IQFRI, IQF LATI, IQFBI] of M if and only if each
non-empty level subset ℵt
is a TSS [TLI, TRI, TLATI, TBI] of M for all t ∈ (ς1,ς2]. We
present a few instances to demonstrate our findings.