Conditional aggregation-based Choquet integral on discrete space

TL;DR

This paper introduces new computational formulas for the generalized Choquet integral using a novel survival function, demonstrating its application to decision-making problems like the Knapsack problem and accommodation options.

Contribution

It develops a new survival function for the Choquet integral and explores conditions under which different survival functions coincide, advancing decision-making theory.

Findings

New formulas for generalized Choquet integral derived

Application demonstrated on Knapsack and accommodation problems

Conditions for survival function equivalence established

Abstract

We derive computational formulas for the generalized Choquet integral based on the novel survival function introduced by M. Boczek et al. [1]. We demonstrate its usefulness on the Knapsack problem and the problem of accommodation options. Moreover, we describe sufficient and necessary conditions under which novel survival functions based on different parameters coincide. This is closely related to the incomparability of input vectors (alternatives) in decision-making processes.