Confidence Levels-Based p, q-Quasirung Orthopair Fuzzy Operators and Its Applications to Criteria Group Decision Making Problems

The
$p,q$
-quasirung orthopair fuzzy (
$p,q$
-QOF) set, an extension of the
$q$
-rung orthopair fuzzy set (
$q$
-ROF) set, offers a more comprehensive approach to information representation, adept at managing data uncertainties. Unlike the restrictive conditions of
$q$
-ROF set, which require that the sum of
$q^{th}$
power of membership (
$\eta$
) and non-membership function (
$\vartheta$
) must not exceed one (
$\eta ^{q}+\vartheta ^{q}\preccurlyeq 1$
),
$p,q$
-QOFS relaxes these limitations. Here, the combined value of the
$p^{th}$
power of membership and
$q^{th}$
power of non-membership is confined within one i.e.,
$\eta ^{p}+\vartheta ^{q} \preccurlyeq 1$
, under the conditions
$p,q \succcurlyeq 1$
and various relationships between
$p$
and
$q$
(
$p=q$
,
$p\succ q$
or
$p\prec q$
). This study explores leveraging confidence levels tied to each
$p,q$
-quasirung orthopair fuzzy number (
$p,q$
–QOFN) to devise a set of averaging and geometric aggregation operators (AOs). These operators effectively combine rating values from distinct criteria, as presented by decision-makers. By harnessing these operators, a novel approach for multi-criteria group decision-making (MCGDM) is formulated, well-suited to resolving real-life decision-making (DM) challenges. An illustrative example underscores the method’s efficacy and validity. Finally, a comparative assessment against existing methods highlights the superior performance of the proposed approach.