Structural Insights into (m,n)-Type Intuitionistic Fuzzy Ideals in Ordered Semigroups

In this paper, we explore new classes of intuitionistic fuzzy ideals in ordered semigroups by introducing the notions of intuitionistic fuzzy ([Formula: see text]) [Formula: see text]-ideals, [Formula: see text]-deals and [Formula: see text]-ideals. We begin by establishing that [Formula: see text] bi-ideals, right ideals and left ideals naturally fall under the categories of [Formula: see text]deals, [Formula: see text]-deals and [Formula: see text]-deals, respectively. Through illustrative examples, we demonstrate that the converse does not necessarily hold. To bridge this gap, we identify specific conditions under which these generalized ideals coincide with classical [Formula: see text] bi-, left and right ideals. We further investigate their structural properties and provide various characterizations, enriching the understanding of intuitionistic fuzzy ideals in the framework of ordered semigroups.