Pythagorean Fuzzy Q-Filters of Q-Algebras

Abstract

In this paper, we introduce the notion of a level Pythagorean fuzzy Q-filter (LPFQ-filter) in a bounded Q-algebra. The proposed structure combines the theory of Q-filters with Pythagorean fuzzy sets by requiring the nonempty (α, β)-level sets of a Pythagorean fuzzy set to be Q-filters. We first establish the basic framework of LPFQ-filters and provide a non-constant example to demonstrate that the proposed notion is nontrivial. We then investigate the structural properties of their level sets. In particular, we prove a nestedness property and characterize the intersection of two (α, β)-level sets in terms of the maximum membership threshold and the minimum non-membership threshold. As a consequence, we show that the intersection of two nonempty level sets of an LPFQ-filter is again a Q-filter. These results establish a direct connection between Pythagorean fuzzy structures and ordinary Q-filters and provide a framework for further investigations of fuzzy filter structures in bounded Q-algebras.
Keywords: Q-algebra; Q-filter; Pythagorean fuzzy set; Pythagorean fuzzy Q-filter; level sets; fuzzy algebra.