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A Fuzzy Multicriteria Decision-Making Approach to Crime Linkage



This article describes how serial crimes are very interesting for study in the absence of proper and solid evidence. From a high volume of criminal cases of similar types, it is difficult to detect the crimes that were committed by the same offender or not. The process of linking of crimes which were committed by the same offender or offenders is called Crime Linkage Analysis. In this article, a new hesitant fuzzy distance measure has been introduced and a fuzzy multicriteria decision-making approach has been proposed to help Crime Linkage Analysis, which enables us to find to what extent a pair of crime shares a common offender or offenders.
DOI: 10.4018/IJITSA.2018070103
Volume 11 • Issue 2 • July-December 2018
Copyright © 2018, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
Soumendra Goala, Dibrugarh University, Didrugarh, India
Palash Dutta, Dibrugarh University, Dibrugarh, India
This article describes how serial crimes are very interesting for study in the absence of proper and
solid evidence. From a high volume of criminal cases of similar types, it is difficult to detect the
crimes that were committed by the same offender or not. The process of linking of crimes which
were committed by the same offender or offenders is called Crime Linkage Analysis. In this article,
a new hesitant fuzzy distance measure has been introduced and a fuzzy multicriteria decision-making
approach has been proposed to help Crime Linkage Analysis, which enables us to find to what extent
a pair of crime shares a common offender or offenders.
Crime Linkage, Fuzzy MCDM, Hesitant Fuzzy Distance Measure, Hesitant Fuzzy Set
The objective of crime linkage analysis is to analyze a group of crimes and to find the crimes linked to
each other by a common offender or co-offenders. In the presence of sufficient evidence like forensic
evidence, DNA or fingerprints or proper digital evidence, the task of linking of crimes becomes nearly
certain. But in the absence of such kind of information, the process of linkage analysis becomes a
difficult task.
Every person is different from the other in psychological level. During a crime, an offender
makes decision consistently for target selection, site selection, time selection etc. The actions of the
offender are influenced by his behavior, psychological view, and past experience. For this reason,
each and every action of an offender is a reflection of his or her personality. Whatever is the situation
there should be some similarities between two crimes committed by the same offender due to the
behavior of the offender, called behavioral linkage. An offender may commit two crimes differently
if they are presented similar situation, although some basic similarities will be there. There are three
basic assumptions for crime linkage analysis (Bennell et al. 2005; Goodwill 2006; Grubin et al. 2001;
Woodhams et al. 2007):
1. Although criminal acts differently in different situations, some basic behavioral variables remain
consistent in all crimes.
2. As every person is different from each other by personality, there is some distinctiveness of
behavior of different criminals.
3. The behavior of criminal can be observed, measured, recorded, and coded.
Volume 11 • Issue 2 • July-December 2018
The process for crime linkage analysis has the steps of collection and processing of data which
includes collection of data from the crime scenes and coding of the physical description of the
scene and behavior of the offender (Woodhams, Bull, & Hollin, 2007). For example, location of the
scene, timing, used technique, and victim’s characteristics have to be coded in an appropriate way
to interpret logically. After coding the crimes, they are compared depending on the behavioral or
situational variable.
In practical two crimes were never found to be identical. That is why the terms similarity or
distinctiveness between two crimes are itself uncertain. Sometimes proper information is not found
at the crime scenes. Therefore, the mathematical interpretation of such kind of information is not
certain most of the time and hence fuzzy in nature. In this paper, a fuzzy MCDM approach has been
introduced to help crime linkage analysis by linking crimes pairwise from a collection of crimes.
The crimes have been represented by hesitant fuzzy set in terms of evidence, as it has the efficiency
to cope with the uncertainty that comes into play due to missing information and different pieces of
evidence’s different level of interpretation.
Basically there are two approaches in multi-criteria decision making problems (a) multiple
attribute decision making (MADM), in which decision has to be taken in discrete space and focused
on how to select different alternatives from existing alternatives and (b) multiple objective decision
making (MODM) in which decision has to be taken in continuous apace and several objective
functions are to be achieved simultaneously. The concept of the fuzzy set theory was first introduced
by Zadeh (1965). Then Bellman and Zadeh (1970) and Zimmerman (1978) gave an approach to
multi-criteria decision making using fuzzy sets. Yager (1978) illustrated that in fuzzy multi-criteria
decision making (FMCDM), the best alternatives have the highest membership grades. Saaty (1980)
developed Analytical Hierarchy Process (AHP). Later Saaty (1996) developed Analytical Network
Process (ANP). Fan et al. (2002) proposed a new approach to solve the MADM problems. Hawang
and Yoon (1981) developed TOPSIS, the technique where similarity is measured to ideal solutions.
Liang (1992) presented FMCDM on the basis of an ideal solution and anti-ideal solution. Then Yoong
and Hawang (1995) proposed the advance fuzzy TOPSIS procedure. Later due to the flexibility and
reliability of the TOPSIS procedure it is developed and used gradually. These are some MADM
approaches used for decision making under fuzzy environment most of the time. Similarly, Fuzzy
Linear programming, Goal Programming, mixed integer programming are some example of MODM
Many Researchers discussed crime prevention, prediction in serial crime and linkage analysis
from the background of Fuzzy Mathematics. Queck et al. (2001) introduced a pseudo outer product
based fuzzy neural network (POPFNN), which detects similarity between two fingerprints and decide
whether they belong to the same person or not. Grubestic (2006) used fuzzy clustering to detect
crime hot-spot in a city. Sheng et al. (2010) gave an intelligent decision support system to uncover
the crime pattern and relationship between the pattern with police duty deployment using fuzzy
time series analysis and fuzzy self-arranging map network. Nurul et al. (2012) gave an analysis to
detect most crime potential area using AHP approach, combining with the geographical information
system. Stofel et al. (2012) introduced a fuzzy clustering based approach to detect a pattern of crime
data from original forensic data. Shrivastav et al. (2012) used fuzzy time series to make a prediction
of crime. Albertetti et al. (2013) used Multi-attribute utility theory (MADM) approach to crime
linkage analysis in high volume crimes. Adeyiga et al. (2016) proposed a fuzzy clustering technique
for criminal profiling to provide investigator an intelligent system to detect and prevent crime. The
fuzzy system is used to identify the trait of an individual. Gupta et al. (2015) took five different
characteristics like economic status, family background, educational level, alcoholic or drug addict
and criminal history for mapping of crime potential areas with the help of fuzzification and after
defuzzification, the value helps in detecting crimes.
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... For example, Xu and Xia (2011) investigated distance measure and similarity measure on hesitant fuzzy sets. Recently, a new distance measure on hesitant fuzzy sets has been developed by Goala and Dutta (2018) and applied in fuzzy multi-criteria decision-making to help crime linkage analysis. ...
... In Xu and Xia's (2011) approach, one needs to add extra elements in hesitant fuzzy elements (HFEs) using the method for finding distance between HFEs if they have a different number of elements, which may lead to wrong results. Although Goala and Dutta (2018) tried to overcome this limitation, in their approach, they were unable to show that the distance between full HFE and empty HFE is 1. These limitations directed us to reflect on the following main objectives: ...
... In this section, we cite some numerical examples for displaying the advantages of our proposed distance measure over the existing distance measures. Major drawbacks are encountered in the existing approaches presented by Xu and Xia (2011) and Goala and Dutta (2018). In Xu and Xia (2011) approach, extra elements are added in HFEs with a view to balance the order of HFEs. ...
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Executive Summary In the contemporary time, the reliability of any product has become a big issue from the customer’s perspective due to exponentially mushrooming markets of electronics and digital gadgets. Since the use of digital equipment is tremendously increasing, as a consequence, the production and availability of products are also increasing rampantly. Due to the flooding of digital products, customers often end up in a dilemma regarding the abundant choice and subsequently, become very much dependent upon the reviews of experts and fellow customers as well. In many cases, unfortunately, it is encountered that the products are not reliable enough as suggested by the reviewers. Besides, it is often seen that the manufacturing companies provide almost similar types of features and facilities for products and customers usually end up in a dilemma The confusion gets triggered when varieties of commodities are manufactured and supplied by different manufacturers bearing almost the same features nearly at the same price. In such situations, the reviews of experts and customers already using the product become essential. The reliability of a product relies upon the reviews of the previous customers of the same product. In this article, fuzzy multi-criteria decision-making methodology has been employed to find the reliability of a product considering different features of the product based on the reviews of customers and experts. This paper presents a neo distance measure on hesitant fuzzy set which is found on the notion of score function and mean deviation. Explanatory instances are provided to reveal the distinctiveness and merit of our proposed idea on distance measure over existing distance measures. After that, the proposed distance measure is applied in the decision-making approach for taking up the best electronic products. It is evidenced that the proposed distance measure is beneficial to measure distance degree between two unequal Hesitant Fuzzy Elements (HFEs) without putting extra elements in the shorter HFE. The proposed distance measures can be utilized in the decision-making field in the near future under diverse conditions to display undetermined particulars in a much-clarified manner.
... The third assumption is the measurability of criminal behavior, it means the criminal behavior can be observed, recorded, and measured. The three assumptions make the behavioral linking of crime be widely studied [26][27][28][29] . ...
... Brown and Hagen [31,32] measured the similarity between crimes by the weighted average of the similarity of all attributes. The multicriteria decision-making [27,33] has also been used, values of criminal behaviors are described by linguistic variables, and the similarity between crimes is calculated according to their linguistic variables. Machine learning classification algorithms are more popular in crime linkage and have achieved excellent effect, including neural networks [34] , logistic regression [35][36][37][38] , decision trees [39] , Bayesian classification [40] , and random forest [5,41] , etc. ...
Crime linkage is a difficult task and is of great significance to maintaining social security. It can be treated as a binary classification problem. Some crimes are difficult to determine whether they are serial crimes under the existing evidence, so the two-way decisions are easy to make mistakes for some case pairs. Here, the three-way decisions based on the decision-theoretic rough set are applied and its key issue is to determine thresholds by setting appropriate loss functions. However, sometimes the loss functions are difficult to obtain. In this paper, a method to automatically learn thresholds of the three-way decisions without the need to preset explicit loss functions is proposed. We simplify the loss function matrix according to the characteristic of crime linkage, re-express thresholds by loss functions, and investigate the relationship between overall decision cost and the size of the boundary region. The trade-off between the uncertainty of the boundary region and the decision cost is taken as the optimization objective. We apply multiple traditional classification algorithms as base classifiers, and employ real-world cases and some public datasets to evaluate the effect of our proposed method. The results show that the proposed method can reduce classification errors.
... Gupta et al., [7] considered different types of geo-physical and demographic characteristics to map down to help in crime detection. Goala and Dutta [3] used distance measure on the hesitant fuzzy set to find the distinction between two crimes and gave the pair wise comparisons in fuzzy MCDM for crime linkage. Goala and Dutta [4] introduced a novel resemblance function for IFSs and used the resemblance function for detecting serial crimes. ...
... Most obviously, the higher resemblance reflects the higher the possibility of relationship among the corresponding subset of crimes. Now, a threshold value (Goala and Dutta [3]; Goala and Dutta [4]) for the resemblance measure has been fixed a real number between [0, 1] above or equal to which the decision maker may consider that the corresponding subset of crimes are related by common offender or offenders. By checking resemblance measures of each collection of crimes, whether they exceed the threshold value or not one can get the set of related crimes easily. ...
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Serial Crimes is a major problem in our society and long term psychological impacts on the people of the society. Moreover, the investigation process for serial crimes are very troublesome sometime due to absence of evidences and sometimes the investigator finds difficult to solve the crimes due to a large number of similar criminal cases. In this paper, crime linkage, which is the process of studying and detecting serial crimes by an investigator is discussed to utilize a novel Resemblance measure of Intuitionistic fuzzy set along with an approach in Intuitionistic fuzzy multi criteria decision making. Further, a case study has been carried out on an existing data set to validate the proposed Resemblance measure.
... Gupta et al. [38] took five different characteristics like economic status, family background, educational level, alcoholic and drug addict and criminal history and mapped with the help of fuzzification and after defuzzification the value helps in detecting crimes. Goala and Dutta [39] used hesitant fuzzy distance measure to find the distinctiveness between two crimes and gave pair wise comparisons and used fuzzy MCDM approach for crime linkage. ...
... But, not much study found solely on crime linkage using behavioral patterns. One study is done on behavioral similarities of offenders based on fuzzy MCDM, but it can check similarities among crimes in a pair wise way only [39]. To overcome these problems, this study is done in crime linkage analysis based upon behavioral patterns only. ...
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... Most obviously, a higher similarity degree will imply a higher relationship between two crimes and can be considered committed by the same offender. Now, a threshold value (Goala and Dutta [52]) for the similarity value has been set by the decision-maker, above or equal to which the decision-maker may consider that the same offender or offenders relate to the corresponding pair crimes. ...
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... Reich and Porter designed a semisupervised Bayesian model-based clustering algorithm to group similar crimes [27]. Some researchers have applied fuzzy multicriteria decision making(MCDM) to combine several attributes to aggregate a single value denoting the overall similarity between crimes [28,29]. Qazi and William extracted reasonable correlations by combining human interaction with the machine learning method to identify crime series [30]. ...
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... Researchers use unsupervised methods to identify all serial crimes rather than serial crime pairs, various clustering algorithms [33], outlier detection [34] and Restricted Boltzmann Machine (RBM) [35], etc. In addition, some scholars applied semi-supervised algorithms [13] and fuzzy multi-criteria decision making [36,37] to associate crimes. ...
Crime linkage is a challenging task in crime analysis, which is to find serial crimes committed by the same offenders. It can be regarded as a binary classification task detecting serial case pairs. However, most case pairs in the real world are nonserial, so there is a serious class imbalance in the crime linkage. In this paper, we propose a novel random forest based on the information granule. The approach doesn’t resample the minority class or the majority class but concentrates on indistinguishable case pairs at the classification boundary. The information granule is used to identify case pairs that are difficult to distinguish in the dataset and constructs a nearly balanced dataset in the uncertainty region to deal with the imbalanced problem. In the proposed approach, random trees come from the original dataset and the above mentioned nearly balanced dataset. A real-world robbery dataset and some public imbalanced datasets are employed to measure the performance of the approach. The results show that the proposed approach is effective in dealing with class imbalances, and it can be extended to combine with other methods solving class imbalances.
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Crime is a significant issue in society, with the causes of crime needing more attention and action from social, governmental, and judicial entities. Investigating crimes can be challenging due to uncertainties and unreliable evidence. Crime linkage helps investigators identify and solve crimes committed by the same individuals or groups. Fuzzy sets and intuitionistic fuzzy sets have been helpful in decision-making problems related to crime linkage due to the uncertainty involved. Similarity measures are essential in decision-making problems, but the existing measures must be revised when dealing with three or more intuitionistic fuzzy sets. The proposed resemblance measure based on intuitionistic fuzzy sets can find similarities between more than two sets and be used in the crime linkage. The proposed measure’s superiority is demonstrated through examples and applied to crime linkage through case studies. A methodology for the psychological profiling of offenders is also presented through case studies. These proposed methods can help law enforcement solve decision-making problems related to crime linkage and psychological profiling.
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The purpose of this study is to determine if readily available information about commercial and residential serial burglaries, in the form of the offender's modus operandi, provides a statistically significant basis for accurately linking crimes committed by the same offender. Logistic regression analysis is applied to examine the degree to which various linking features can be used to discriminate between linked and unlinked burglaries. Receiver operating characteristic (ROC) analysis is then performed to calibrate the validity of these features and to identify optimal decision thresholds for linking purposes. Contrary to crime scene behaviours traditionally examined to link serial burglaries, the distance between crime site locations demonstrated significantly greater effectiveness as a linking feature for both commercial and residential burglaries. Specifically, shorter distances between crimes signalled an increased likelihood that burglaries were linked. Thus, these results indicate that, if one examines suitable behavioural domains, high levels of stability and distinctiveness exist in the actions of serial burglars, and these actions can be used to accurately link crimes committed by the same offender. Copyright © 2005 John Wiley & Sons, Ltd.
In this paper, we introduce the Bonferroni geometric mean, which is a generalization of the Bonferroni mean and geometric mean and can reflect the correlations of the aggregated arguments. To describe the uncertainty and fuzziness more objectively, intutionistic fuzzy set could be used for considering the membership, non-membership and uncertainty information. To aggregate the Atanassov's intuitionistic fuzzy information, we further develop the Atanassov's intuitionistic fuzzy geometric Bonferroni mean describing the interrelationship between arguments, and some properties and special cases of them are also discussed. Moreover, considering the importance of each argument, the weighted Atanassov's intuitionistic fuzzy geometric Bonferroni mean is proposed and applied to multi-criteria decision making. An example is given to compare the proposed method with the existing ones.
Conference Paper
Grouping events having similarities has always been interesting for analysts. Actually, when a label is put on top of a set of events to denote they share common properties, the automation and the capability to conduct reasoning with this set drastically increase. This is particularly true when considering criminal events for crime analysts, conjunction, interpretation and explanation can be key success factors to apprehend criminals. In this paper, we present the CriLiM methodology for investigating both serious and high-volume crime. Our artifact consists in implementing a tailored computerized crime linkage system, based on a fuzzy MCDM approach in order to combine spatio-temporal, behavioral, and forensic information. As a proof of concept, series in burglaries are examined from real data and compared to expert results.
Hesitant fuzzy sets (HFSs), which allow the membership degree of an element to a set represented by several possible values, can be considered as a powerful tool to express uncertain information in the process of group decision making. We derive some correlation coefficient formulas for HFSs and apply them to clustering analysis under hesitant fuzzy environments. Two real world examples, i.e. software evaluation and classification as well as the assessment of business failure risk, are employed to illustrate the actual need of the clustering algorithm based on HFSs, which can incorporate the difference of evaluation information provided by different experts in clustering processes. In order to extend the application domain of the clustering algorithm in the framework of HFSs, we develop the interval-valued HFSs and the corresponding correlation coefficient formulas, and then demonstrate their application in clustering with interval-valued hesitant fuzzy information through a specific numerical example.
This paper discusses the development of a filter model for prioritizing possible links in dwelling burglary. The filters utilize the central aspects of crime scene information that is available and accessible to investigators in burglary, namely geo-spatial, temporal, behavioural, and dwelling information. The proposed filters were analysed using a sample of 215 dwelling burglaries committed by 43 serial burglars (i.e. 5 offences each) in order to determine the sequence in which the filters should be considered in prioritizing possible linked offences. The results indicated that the following order (i.e. better performance to worse performance) was most effective at linking offences, utilizing: (1) geo-spatial information, (2) temporal aspects, (3) behavioural information and, lastly, (4) dwelling characteristics. Specifically, the results indicated that offences in close proximity to one another should be given priority. Further, any offence occurring within a 28-day span before or after the index offence should be given priority. The paper argues that behavioural and dwelling characteristics are less effective for linking than geo-spatial and temporal information because the former two aspects are influenced significantly by situational and contextual cues on offender decision-making.