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Top1. Introduction
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.
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.