Making decisions is an action that permeates human life. Some decisions are simple, like choosing which tie to wear. Others are complex and impact the lives of people, organizations, economies, and countries, like selecting a policing strategy to reduce the crime rate. Deciding implies making choices that are not always easy to make. The decision maker is not immune to macro-environment variables and can be influenced by organizational and personal objectives. Over the last four decades, researchers have developed and applied decision support methods that allow large volumes of information to be systematized, presenting the decision maker with the alternatives that, when compared pair-by-pair and criterion-by-criterion under the influence of weights, are best classified.

Basilio et al. [1] affirm that MCDA methods solve decision-making problems in various areas, including information and communication technology, business intelligence, environmental risk analysis, water resources management, remote sensing, flood risk management, health technology assessment, climate change, energy, international law, human resources policy, financial management, supplier selection, e-commerce and mobile commerce, agriculture and horticulture, chemical and biochemical engineering, software evaluation, flood risk management, health, transportation research, nanotechnology research, climate change, energy, human resources, financial management, performance and benchmarking, supplier selection, chemical and biochemical engineering, education and social policy, and public safety.

In their research, Basilio et al. [1] report that AHP, TOPSIS, VIKOR, PROMETHEE, and ANP are the methods most frequently used by authors in their respective studies. An essential issue in the decision-making process that profoundly impacts the evaluation of alternatives is the weights to be assigned to the criteria. Experts classify weighting methods as objective, subjective, and hybrid [2]. The AHP [1,3] is the method most researchers use when integrating methods for measuring weights with methods for ordering alternatives. This is followed by DEMATEL [4], SWARA [5,6,7], ANP [4], ENTROPY [8], CRITIC [9], BWM [10], CILOS [11], IDOCRIW [11], FUCOM [12,13], LBWA [14], SAPEVO-M [15], and MEREC [16,17]. From the taxonomy described by Ayan [2], we can infer that hybrid weight measurement methods are used to find a resulting position between the techniques used. However, generating a weight for each criterion reduces a certain degree of uncertainty, which, when inserted into the ordering method, will produce a ranking of the alternatives.

This study aims to combine objective and subjective methods, not to produce a single weight per criterion. Instead, this study aims to build a weight range for each criterion, preserving the characteristics of each technique. Each weight range comprises lower and upper limits, which can be combined to generate random numbers, producing “t” sets of weights per criterion, and making it possible to obtain “t” final rankings. The alternatives are given a value corresponding to their position in each ranking generated. At the end of the process, they will be ranked in descending order, thus obtaining the final definitive ranking. In this way, managers can analyze the behavior of each alternative throughout the process, and the final ranking will be more consistent due to the incorporation of the variations observed due to the influence of the weight of the criteria on the alternatives. In this study, we chose the ENTROPY-CRITIC methods and the weights generated by the decision makers to deal with the problem of selecting a policing strategy to reduce crime rates.

The CRITIC method aims to define weights by using the contract intensity and the conflicting character of the evaluation criteria. The CRITIC method is proposed by Diakoulaki et al. [18]. CRITIC is one of the most frequently used objective methods for criterion weight determination [9]. Since its first introduction, research has focused mainly on two topics. The first area aims to improve the CRITIC model, and the improvements focus on the normalization procedure. The studies focus on using vague information by employing fuzzy logic and alternative similarity and distance measures. By utilizing different approaches, new studies are performed. Normalization procedures are performed using various methods; to name a few, employing fuzzy logic [19], logarithmic normalization [20], and alternative rankings [21] are used. Another point for improvement is the weighting technique. The model is limited to deficiency in capturing the correlation between criteria [22]. A recent study employed a new D-CRITIC approach to overcome this limitation [9]. The proposed research aims to integrate different strategies to overcome such constraints using a hybrid system.

Another approach used for weight determination is the entropy approach. Entropy is based on a different discipline. The technique has its origins in the field of Thermodynamics [23]. The entropy approach was proposed first by Clausius [24]. Shannon and Weaver [25] proposed the entropy concept. The method employs a measure of uncertainty in information formulated regarding probability theory. The entropy method evaluates the relative contrast intensities of the criteria [23]. The approach does not consider the decision makers but the value of each alternative per criterion.

Since its introduction, the entropy model has been applied in different areas. To name a few, cryptocurrency evaluation [26], supplier selection [23], study of poverty alleviation [27], and industrial arc robot selection [28]. Other studies have focused on improving the entropy method. Szmidt and Kacprzyk [29] proposed an entropy measure for intuitionistic fuzzy sets (IFS) that was extended. The difference between normalized Euclidean distance and normalized Hamming distance is investigated. A new entropy method was proposed by Liu and Ren [30], which considered both the uncertainty and hesitancy degree. Thakur et al. [31] proposed a new approach using the COPRAS Model under IFS. As the literature shows, entropy is used in calculating weights [32].

The second stage of the proposed model uses the PROMETHEE approach to classify the alternatives. This model was proposed by Brans et al. [33]. A few years later, several versions of the PROMETHEE methods were developed such as PROMETHEE III, PROMETHEE IV, PROMETHEE V [34], PROMETHEE VI [35], PROMETHEE GDSS [36], and the GAIA interactive visual module for graphical representation [37]. These versions were developed to help with more complicated decision-making situations [38]. Like other methods, applications in new areas are carried out simultaneously, including cryptocurrency portfolio allocation [39], a barrier assessment framework for carbon sink project implementation [40], and an application of hybrid composites [41].

The motivation for developing the proposed model is based on the need to reduce uncertainty in the decision-making process without dehumanizing the process. The proposed method combines objective and subjective methods to strengthen the results presented to the decision maker. The methods chosen are widely disseminated among the scientific community and are easy to understand and implement. The concept used allows for expansion and integration with other methods. By using hybrid approaches, the results are supposed to be more efficient and balance the subjectivity of the decision makers. EC-PROMETHEE does not use combined weights between the three methods. However, it will operate with a range of weights based on the upper and lower limits of the values obtained in the three methods. The final ranking will not be accepted by applying a single set of weights, but with “m” iterations using a set of random weights produced within the respective weight ranges, criterion by criterion.

In this article, we will revisit the research developed by Basilio et al. [42,43,44,45], which dealt with identifying and choosing policing strategies customized to local criminal demands. The research was conducted in Rio de Janeiro, Brazil, and analyzed the criminal demand from 2016 to 2019. The authors used the PROMETHEE method, Electre IV, and Electre I to identify the most appropriate policing strategies for the observed criminal demands. At the time, the researchers used equal weights for each criterion. In the present research, we seek to answer the question: how can using objective weighting methods influence the ranking of policing strategies in the case studied? In response, the authors developed the EC-PROMETHEE method, which combines objective and subjective methods of weighting criteria, implementing a range of weights for criteria, and defining the final ranking from a certain number of iterations.

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