Exploring Multipolar Fuzzy Hyperfilters in Ordered Semihypergroups

The notion of multipolar fuzzy sets ([Formula: see text]-p[Formula: see text]s) extends the idea of bipolar fuzzy sets and offers a powerful framework for dealing with multiattribute data under uncertainty. While several research papers have been published on fuzzy hyperfilters and bipolar fuzzy hyperfilters in ordered semihypergroups, the study of hyperfilters within the multipolar fuzzy setting has remained unexplored. In this work, we advance the theoretical foundation of hyperfilters in ordered semihypergroups by applying [Formula: see text]-p[Formula: see text]s. Specifically, we introduce the concepts of [Formula: see text]-[Formula: see text] left and right hyperfilters, and examine their essential properties through multipolar level sets and multipolar characteristic fuzzy sets. We show that arbitrary intersection of [Formula: see text]-[Formula: see text] left/right hyperfilters is an [Formula: see text]-[Formula: see text] left/right hyperfilter, whereas arbitrary union of [Formula: see text]-[Formula: see text] left/right hyperfilters is not necessarily an [Formula: see text]-[Formula: see text] left/right hyperfilter which is shown by an illustrative example. We provide a sufficient condition under which union of [Formula: see text]-[Formula: see text] left/right hyperfilters is an [Formula: see text]-[Formula: see text] left/right hyperfilter. Furthermore, we define and investigate [Formula: see text]-[Formula: see text] bi-hyperfilters, and explore their relationships with [Formula: see text]-p completely prime fuzzy hyperideals and [Formula: see text]-p completely prime fuzzy bi-hyperideals.