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A Fuzzy Multicriteria Decision-Making Approach to Crime Linkage

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International Journal of Information Technologies and Systems Approach
Authors:
Soumendra Goala
Soumendra Goala
Soumendra Goala
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Palash Dutta at Dibrugarh University
Palash Dutta
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Abstract

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.
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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.
31


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
32
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
approaches.
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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... Three papers (Santtila et al., 2005;Santtila et al., 2008;Winter et al., 2013) used discriminant function analysis (DFA), which is a method for predicting group membership (Field, 2005). Thus, the aim of DFA is to predict the dependent variable (series membership) from a set of independent variables (e.g., similarity in crime scene behaviours, geographical proximity, temporal proximity). ...
... DFA works by calculating underlying linear dimensions of independent variables. These linear combinations of the independent variables are discriminant function variates that are used to predict which group an entity belongs to Field (2005). In the case of crime linkage, the series to which an offence belongs to is predicted. ...
... MCA and PCA are multivariate techniques for detecting underlining structures in datasets and, like MDS, are used to visualise the relationship between incidents or variables (Yokota et al., 2017). PCA works in a similar way to DFA (Field, 2005). PCA assumes data is continuous and is a dimensionality reduction technique used to identify underlying patterns in big datasets (using probability). ...
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Abstract This paper reviews the crime linkage literature to identify how data were pre-processed for analysis, methods used to predict linkage status/series membership, and methods used to assess the accuracy of linkage predictions. Thirteen databases were searched, with 77 papers meeting the inclusion/exclusion criteria. Methods used to pre-process data were human judgement, similarity metrics (including machine learning approaches), spatial and temporal measures, and Mokken Scaling. Jaccard's coefficient and other measures of similarity (e.g., temporal proximity, inter-crime distance, similarity vectors) are the most common ways of pre-processing data. Methods for predicting linkage status were varied and included human (expert) judgement, logistic regression, multi-dimensional scaling, discriminant function analysis, principal component analysis and multiple correspondence analysis, Bayesian methods, fuzzy logic, and iterative classification trees. A common method used to assess linkage-prediction accuracy was to calculate the hit rate, although position on a ranked list was also used, and receiver operating characteristic (ROC) analysis has emerged as a popular method of assessing accuracy. The article has been published open access and is free to download from https://www.sciencedirect.com/science/article/pii/S1359178924001046
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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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... However, other studies have explored machine learning clustering techniques to evaluate crime linkage decisions [48,75,76]. Additionally, while not strictly classified as machine learning, some authors have utilized fuzzy logic to assess crime linkage scenarios [77,78,79,49]. ...
... For instance, a crime analyst might evaluate the level of violence in a particular case. This approach is common when working with fuzzy logic models, where a degree of membership is required to characterize sets of MOs [49,79,78]. ...
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... 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] . ...
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The development of a filter model for prioritising suspects in burglary offences
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