**1. Introduction**

Pollution levels in recent years have been reaching dangerous limits. Important contributors to global pollution are diesel engines, which are e fficient machines but emit important levels of particulate matter (PM), NOx, CO2, CO, HC, SOx, etc. [1–5]. Between these, NOx and SOx are characteristic of marine diesel engines [6–10]. According to the International Maritime Organization (IMO), NOx and SOx from ships represent 5% and 13% of global NOx and SOx emissions, respectively [11]. IMO regulates NOx and SOx in the shipping sector. Regarding SOx, since the sulfur content of the fuel is the reason for SOx emission, IMO limits the sulfur content of fuels or requires the use of exhaust gas cleaning systems to reduce sulfur emissions [12]. Regarding NOx, IMO imposes even increasing limitations. According to this, several NOx reduction procedures have been developed in recent years. Some of them, called primary measurements, operate on the engine performance, such as EGR, water injection, modification of the injection parameters, etc. On the other hand, other NOx reduction procedures, called secondary measurements, remove this pollutant from exhaust gases by downstream cleaning techniques, such as selective catalytic reduction (SCR). The present work focuses on pre-injection systems. It is well known that pilot injections reduce NOx noticeably [13–17], but sometimes pilot injections can increase consumption and other pollutants such as smoke or hydrocarbons (HC) [18–22], mainly depending on parameters such as injection time, duration, number of pre-injections, dwelling time, etc. Since these parameters provide conflicting results, a formal tool to establish the most appropriate injection pattern is

necessary. According to this, multiple-criteria decision-making (MCDM) approaches constitute a formal tool for handling complex decision-making problems. MCDM methods are complex decision-making tools for choosing the optimal option in cases where there are conflicting criteria. Since the start of the MCDM methods in the 1960s, they were employed in many fields such as sustainability, supply chain management, materials, quality management, GIS, construction and project management, safety and risk management, manufacturing systems, technology, information management, soft computing, tourism management, etc. [23]. One of the handicaps of MCDM methods is the determination of the criteria weights, i.e., the degree of importance for each criterion. It is important to focus on the criteria weights due to their influence on the overall result. According to this, several approaches to define the criteria weights can be found in the literature. Briefly, these approaches can be divided into subjective, i.e., based on the estimations of experts, and objective, i.e., calculated through mathematical expressions. In practice, subjective weights are most commonly used [24]. Contrary to subjective methods, the objective weights are based on mathematical methods and decision-makers have no role in determining the relative importance of criteria. Common objective methods are entropy [25], CRITIC [26], standard deviation [27], variance, mean weight, etc.

The present paper proposes a MCDM approach to select the most appropriate injection pattern using a pilot injection in the marine diesel engine Wärtsilä 6L 46. The pre-injection rate, duration, and starting instants were analyzed and the criteria were specific fuel consumption (SFC) and NOx, CO, and HC emissions. These emissions and consumption were characterized through CFD (Computational Fluid Dynamics) analyses. Due to the importance of the criteria weights on the overall result, a comparison of several weighting methods was realized. A subjective criteria weighting method was compared to four objective criteria weighting methods: entropy, CRITIC, variance, and standard deviation.
