Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making

The consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with enhanced capabilities in depicting ambiguous information. The Bonferroni operator proficiently mitigates the influences of interrelations between attributes in decision-making dilemmas. To address the Multi-Attribute Decision Making (MADM) conundrum wherein attribute values are associative Triangular Pythagorean Fuzzy Numbers (TPFNs), a novel methodology leveraging the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Mean (GTPFWBM) operator and the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Geometric Mean (GTPFWBGM) operator is advanced. Initiating with the foundational Triangular Pythagorean Fuzzy Set and the Generalized Bonferroni Mean (GBM) operator, both the GTPFWBM and GTPFWBGM operators are delineated. Subsequent exploration dives into the intrinsic properties of these pioneering operators, encompassing facets like reducibility, permutation invariance, idempotency, monotonicity and boundedness. Building upon this foundation, a MADM methodology predicated on the GTPFWBM and GTPFWBGM operators is conceptualized. The culmination of this research underscores the method's rationality and practicality, illustrated through a venture capital investment exemplar.