## 1 Introduction
The models of helicopters currently used in the main Armed Forces of the world can be analyzed in the light of various criteria, whether qualitative or quantitative, such as speed, armaments, autonomy, load capacity, and some more complex, such as maneuverability, systems, and aggregate technologies [11]. In this context, of several alternatives, criteria, and complex scenarios, the Multi-Criteria Decision Analysis (MCDA) can be favorable to support the decision-making process, presenting techniques that allow the decision-maker to structure and evaluate complex problems transparently, introducing quantitative and qualitative criteria [12; 13; 14], defining the importance of variables in an interactive process with other technical-political actors [15]. Contemplating the context of multi-criteria analysis regarding the evaluation of actions in defense scenarios, some previous studies are presented in [16; 17; 18; 19; 20]. In a real decision-making problem, uncertainty is intrinsic. As suggested by [PERSON] et al. [21], MCDA methods should enable an integrated algorithm, providing to perform qualitative and quantitative data, in other words, enabling to evaluate variables based on subjective information, along with data in a quantitative format. In the decision analysis, the presence of uncertainty and subjectivity information is natural [22], considering that obtained information can present a lack of complete data or certainty [23]. In this context, aspects of subjectivity in the MCDA methods play an important role [24], transcribing the preferences of the decision-maker by the modeling, being clear concerning the manipulations and attributions regarding the problem in evaluation [25]. This paper aims to present a case study based on the MCDA methodology through a proposal of a new variant of the family of methods PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) [26]. The hybrid modeling, named PROMETHEE-SAPEVO-M1, represents the integration of two methodological concepts, one intended on cardinal evaluation and the other relative to ordinal evaluation. The algorithm enables the analysis of a set of alternatives considering both quantitative and qualitative criteria, structuring the weights of criteria by ordinal inputs, and exploring the results by three different models of preference analysis along with an intra-criterion analysis by veto threshold. Considering a hypothetical situation of new aircraft acquisitions, the study aims to provide a fundamental procedure to decision-making, to the BN, in search to obtain a ranking of the helicopters and identify the most favorable between them. The article is structured into six sections. After the introduction, Section 2 explores the theoretical foundation related to the concepts of MCDA, the base methods related to the proposal, and introduces the new purpose; Section 3 presents the axiomatic structuring of the PROMETHEE-SAPEVO-M1 followed by the numerical implementation related to the case study in Section 4; Section 5 presents a discussion, exploring the main points related to the new proposal and its correlation to the case study, and in Section 6 the research findings are concluded.