# A robust hierarchical nominal classification method based on similarity and dissimilarity using loss function and an improved version of the deck of cards method

## TL;DR

This paper introduces a robust hierarchical nominal classification method combining similarity and dissimilarity measures, an adapted deck of cards elicitation, and stochastic analysis to improve decision-making in complex criteria hierarchies.

## Contribution

It develops a new hierarchical classification approach integrating MCHP, an imprecise parameter elicitation, and a loss function-based final classification procedure, enhancing existing Electre methods.

## Key findings

- The method effectively handles interactions and antagonistic effects between criteria.
- It provides probabilistic classification insights through SMAA.
- The loss function approach ensures decision maker requirements are met.

## Abstract

Cat-SD is a multiple criteria decision aiding method for dealing with nominal classification problems. Actions are assessed according to multiple criteria and assigned to one or more categories. A set of reference actions is used for defining each category. The assignment of an action to a given category depends on the comparison of the action to each reference set according to likeness thresholds. Distinct sets of criteria weights, interaction coefficients, and likeness thresholds can be defined per category. We propose to apply Multiple Criteria Hierarchy Process (MCHP) to Cat-SD. An adapted MCHP is proposed to take into account possible interaction effects between criteria structured in a hierarchical way. On the basis of the known deck of cards method, we also consider an imprecise elicitation of parameters permitting to take into account interactions and antagonistic effects between criteria. The elicitation procedure we are proposing can be applied to any Electre method. With the purpose of exploring the assignments obtained by Cat-SD considering possible sets of parameters, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA). The SMAA methodology allows to draw statistical conclusions on the classification of the actions. The proposed method, SMAA-hCat-SD, helps the decision maker to check the effects of the variation of parameters on the classification at different levels of the hierarchy. We propose also a procedure, based on the concept of loss function, to obtain a final classification fulfilling some requirements given by the decision maker and taking into account the hierarchy of criteria and the probabilistic assignments obtained applying SMAA. Also this procedure can be applied to any classification Electre method.