Decision making via generalized Bajraktarevi\'c means

TL;DR

This paper introduces a new class of decision-making functions based on multidimensional generalized Bajraktarević means, providing a nonlinear framework with properties like delegativity, causativity, and convexity, and explores their equality, synergy, and null-synergy characteristics.

Contribution

It defines and analyzes a novel class of decision functions derived from generalized Bajraktarević means, extending decision-making theory with new properties and characterizations.

Findings

Established key properties like delegativity, causativity, and convexity.

Solved the equality problem for these decision functions.

Characterized null-synergy decision-making functions.

Abstract

We define decision-making functions which arise from studying the multidimensional generalization of the weighted Bajraktarevi\'c means. It allows a nonlinear approach to optimization problems. These functions admit several interesting (from the point of view of decision-making) properties, for example, delegativity (which states that each subgroup of decision-makers can aggregate their decisions and efforts), casuativity (each decision affects the final outcome except two trivial cases) and convexity-type properties. Beyond establishing the most important properties of such means, we solve their equality problem, we introduce a notion of synergy and characterize the null-synergy decision-making functions of this type.