The Fuzzy Perspective on Violence against Women: Challenges and Advancements

Francesca Bettio, Gianni Betti and Elisa Tied


This chapter focuses on the application of the fuzzy-set approach for the measurement of violence against women (VAW). Although the methodology has been developed in detail elsewhere (Bettio, Ticci and Betti, 2020a), here we revisit its founding assumptions, limitations and advantages before exploring selected extensions. To do so, we often rely on concrete applications of this methodology to data from a survey conducted by the Fundamental Rights Agency (FRA) in 2012 in 28 member countries of the European Union (EU) (henceforth, FRA survey)1. The survey administered a detailed face-to-face questionnaire to some 40,000 women in these member states.

Gender-based violence is a complex and multi-faceted phenomenon. It is defined by the United Nations (UN) as

any act of gender-based violence that results in, or is likely to result in, physical, sexual, or psychological harm or suffering to women, including threats of such acts, coercion or arbitrary deprivation of liberty, whether occurring in public or private life.

(UN, 1994, p. 2)

The FRA survey, in line with this definition as well as with the tradition in survey-based research, distinguished three types of violence - physical, sexual and psychological - identifying several types of ‘acts’ with each type (9, 4 and 17, respectively). The survey investigated sexual harassment as a separate form of violence. Sexual harassment has attracted the most media attention in recent years, but it is a late-comer in terms of research and policy on VAW. That is why some uncertainty remains as to where sexual harassment is positioned with respect to the conventional trilogy of VAW types.2 This is one reason that we leave sexual harassment out of our analysis in this chapter; a more general reason is that we primarily address methodological issues, rather than policy targets.

VAW is a universally recognised concern because it results in harm or suffering. Measuring harm is therefore central to measuring violence.

However, physical, psychological, sexual and economic harm caused by violence is bound to differ not only across acts of violence - and, therefore, across types - but also across frequencies and contexts, thus posing a formidable challenge for its measurement. Even when the victims’ testimony comes from responses to a structured survey, translating their complexity into quantitative indicators is far from a trivial exercise. This explains why the most frequent quantitative measure of violence found in the literature avoids this complexity by only accounting for the prevalence of a given act or type of violence in a given population.

In this chapter, we discuss how the fuzzy-set approach advances the measurement of gender-based violence by accounting for the frequency and severity of these different acts in addition to their prevalence. Our proposal answers the call for a comprehensive indicator of violence, which has been repeatedly expressed by UN representatives. Yakin Ertiirk, the special rapporteur on VAW, in her 2008 Report to the Council of Human Rights, recommended that an agreement be reached on an indicator to be used across countries, which could account for severity as well as individual frequency and prevalence in a population (UN, 2008). This reinforced the need previously emphasised by the UN Expert Group Meeting for indicators to measure VAW (2007) that the data used result in meaningful measurement of the severity of abuse. As argued elsewhere (Bettio, Ticci and Betti, 2020a), severity scales that enable going beyond prevalence measurement have long been proposed in the literature but suffer from limitations that, we believe, can be overcome using fuzzy measurement, e.g. the costly gathering of information and various selectivity biases.

Readers who are familiar with the fuzzy measurement of poverty (Cerioli and Zani, 1990; Cheli and Lemmi, 1995) know that the fuzzy approach can be used to translate a binary measure, such as the poverty headcount ratio, into a continuous measure - a fuzzy index - yielding degrees of poverty, rather than a simple binary indication of its occurrence. They are also well acquainted with the fact that fuzzy measurement can account for multiple types of deprivation. In these respects, the analogy between the fuzzy approach to poverty and to violence is straightforward. When applied to violence, the approach yields an index, which can be interpreted as degrees of violence, accounts for the multi-dimensionality of violence (different acts, different types), as well as for the frequency of violence, and allows for aggregation of acts and types of violence across individuals and groups. However, it is less straightforward to see how the fuzzy approach can capture the severity of violence, and that is the main innovation in our proposal. The basic idea is to measure perceived severity in society, rather than individually, and to proxy the former with inverse prevalence. For example, in European countries, being pushed or shoved by one’s partner, an act of physical violence, occurs more frequently than being hit by the partner with a hard object, another act of physical violence, and the latter is usually considered more severe. As another example, 140 of every 100,000 European women reported having been burned at least once by their partner in the year preceding the FRA survey compared with 1,560 women who reported having been slapped. Being burned is generally considered more serious than being slapped, in line with the idea that the lower the prevalence is, the higher the social perception of severity. This is analogous to the way in which the severity of deprivation is evaluated in the fuzzy approach to poverty: the deprivation of a given item is worse when this type of deprivation is less common. In the case of violence, however, further restrictions and qualifications apply to the criterion of inverse prevalence, and we tease them out later in the chapter.

One novel dimension of violence measurement that this chapter explores is different aggregation measures. Separate fuzzy indexes for, respectively, physical, sexual and psychological violence can be aggregated into a single index by means of a simple average for the same individual and then for the chosen population sub-groups. Possible alternatives to this basic aggregation are standardising the index (with respect to the reference population group) or considering indexes of fuzzy intersections and fuzzy unions.

The rest of the chapter is structured as follows. The second section provides a step-by-step description of the way in which the basic fuzzy index and the severity scale are constructed. The third section discusses the implications, advantages and qualifying restrictions of using the fuzzy methodology to measure VAW. The forth section explores alternatives to basic aggregation and, together with the fifth section, shows how application of the fuzzy methodology to the FRA survey can resolve topical but controversial problems in the empirical analysis of violence in Europe. The concluding section wraps up the discussion.

The Steps

The procedure for constructing the fuzzy scale and the fuzzy index of VAW has five sequential steps, with steps 1 to 3 leading to the construction of the scale, step 4 developing the fuzzy index of violence for each individual and each type of violence, and step 5 aggregating the type-specific, individual indexes to obtain a single measure of violence. Step 5 is optional and features alternatives that are further examined below.

Let i denote the individual respondent, h the type of violence and / the act of violence, with h = 1, 2j = 1, 2...k. The measure for the frequency of experience in classes is denoted by c and ordered from highest to lowest. The five steps are:

  • 1. Definition of gender ‘violence’ and of the reference population (what and who). One fundamental assumption for the following procedure is that it is applied to a sufficiently homogeneous socio-cultural context (reference population). Within this population, we need to identify types of violence and, for each of them, the different violent acts or incidents to include in the analysis.
  • 2. Victim status. For each woman i and act of violence /', victim status is defined by the membership function pn in the interval [0,1]. The function increases as item j is experienced more frequently by women as follows:

where is the frequency class (i.e. individual frequencies ordered from highest to lowest) of the /th act for the /th individual; F(c ;) is the value of the /th act cumulative function for the /th individual; F(l) is the population value of the cumulative function for the highest frequency class of the /th act. In other words, for each act of violence, all the women are ordered according to whether and how frequently they have experienced that act, and the function identifies the position of each woman in this ranking of victimisation.

3. Assessment of severity weight for each violent act: the fuzzy severity scale. In this step, and with reference to a given type of violence h, each act of violence / is assigned a severity weight using prevalence weights (Guio, 2009). The result is a set of k weights for each type of violence h, calculated as:

This set defines the fuzzy severity scale of violence for type of violence h. Weight wh. is made up of two components:

  • • prevalence component: wah is the coefficient of variation of item / within type h in the reference population. Because it is proportional to the inverse prevalence distribution (Betti and Verma, 2008), this component gives greater importance to items that are less widespread;
  • • correlation component: wt gives less weight to items that are more highly correlated with others (correlation weights). This enables us to correct possible distortions due to redundancy in the definition of overlapping or arbitrary items - for instance, when two similar questions are asked in the same questionnaire.
  • 4. Individual type-specific index scores: For each individual i, membership functions are aggregated over the k items using item-specific weights (wh ) to construct type-specific violence scores (ph (.) or fuzzy indexes.

We refer to phi as ‘type-specific fuzzy index of violence’, or FIV(/?). In addition, weights do not necessarily sum to 1, so they are standardised by dividing them by their sum.

5. Aggregation of individual type-specific index scores. This is an optional step featuring several aggregation options. The basic option is to aggregate the type-specific FIV(A) indexes across types of violence by simply calculating the unweighted mean. For each individual:

is the value of the fuzzy multi-dimensional index of all types of violence at the individual level.

Area-level values - for example, in France, the EU28, or specific sub-populations thereof - are obtained by averaging nh j or pj across the chosen (sub-) population, for instance, French respondents. In the specific application to the FRA survey that we present later, the reference population is women aged 18-74 years in 28 European countries, and it is assumed to be sufficiently homogeneous in terms of legal regulations as well as socio-economic conditions. Types and acts of violence are drawn from the survey, which also asked for the frequency of abuse. To avoid standard problems with recall, we used responses related to episodes in the 12 months prior to the interview. The severity scales for the physical, sexual and psychological abuse are reported in Table A.14.1.

Strengths and Weaknesses of the Fuzzy Measurement of Violence

What are the specific advantages and limitations of employing a fuzzy measurement of VAW? We noted in the introduction that fuzzy indexes improve on the prevalence indicator by using a graduated measurement along a continuum, while, at the same time, accurately accounting for multi-dimensionality. Here, accuracy refers to the fact that different kinds of abuse (in the same type of violence) are not simply ‘added on’, as occurs with prevalence but, rather, are ‘weighted’ to account for possible redundancy (see step 3) and, crucially, for severity. The way in which severity is gauged by the proposed fuzzy indexes has some clear advantages over the existing alternatives. However, in absence of clear qualifications, fuzzy severity can be rather controversial. The following section discusses conditions and strengths.

224 F. Bettio, G. Betti and E. Tied Conditions

As mentioned earlier, the inverse prevalence criterion underpinning our severity scale (step 3) is meant to gauge socially perceived severity, namely, how a given social and economic context ranks different acts of violence in terms of their perceived severity. This is radically different from asserting that certain acts of violence should be considered or are intrinsically less serious simply because they occur more frequently. In addition, and equally important, our severity scale gauges relative severity strictly for a given type of violence while remaining intentionally silent about the comparative severity of acts of different types of violence. For instance, being hit with a hard object (physical abuse) cannot be directly compared to being prevented from seeing one’s family (psychological abuse) in terms of severity. This strict separation of the scale by the type of violence is mitigated only in part when type-specific fuzzy indexes are aggregated into a single index (step 5). To repeat, however, aggregation across types is an optional step, with the strong proviso of giving the same weight to each type of violence, e.g. by simple averaging.

This relative (and compartmentalised) notion of perceived severity of harm might be considered inferior to an absolute, actual measure of harm that other violence severity scales have tried to quantify (see below). One serious counterargument, however, is that severity cannot be entirely decoupled from perception of harm, and the latter is influenced by cultural beliefs and the social context (Beck, 1976; Iacoviello et ah, 2009). For instance, it has been argued that The negative effects of [one’s partner] abuse may vary as a function of the extent to which wives believe that husbands’ abusive behavior must inherently be justified’ (Do et ah, 2013, p. 2). This is especially likely to apply to the emotional, psychological, mental or social consequences of violence, such as shame, embarrassment, guilt, stigmatisation, social isolation and marginalisation. And it also implies that the evaluation of the harm from the same act of violence can vary across individuals with different norms and beliefs. Although we accept this possibility, the notion of harm that we support is a kind of ‘average social perception’ that need not vary across individuals and enables us to carry out unbiased comparisons among groups, countries and so on, as long as the groups being compared are sufficiently homogeneous in socio-economic terms.

This brings us to the next major condition, namely that both the fuzzy scale and the fuzzy indexes refer to a fairly homogeneous socio-economic population. The importance of accounting for significant cultural differences is acknowledged in the recent kNOwVAW data initiative promoted by the United Nations Population Fund (UNFPA) and the Australian Department of Foreign Affairs and Trade to strengthen the measurement of violence against women in Asia and the Pacific. Although most of the countries in this macro region investigated violence using the survey design in the World Health Organisation (WHO) study on women’s health and domestic violence as their reference point (UNFPA, 2019), in some cases the list of acts was tailored to the local context.

Lastly, the fuzzy measurement of violence that we propose is intended for interpersonal, adult violence, not armed conflict or other organised or collective forms of violence. We also suggest excluding harmful cultural practices.5 On the one hand, harmful cultural practices are socially constructed as interpersonal violence is. On the other hand, the distinction between the two is still subject to debate (Longman and Bradley, 2015). Given that resolving these kinds of debates is beyond the scope of our proposal, we use a conservative approach, which excludes these practices from the field of application of our methodology. Unlike other forms of interpersonal VAW, the latter ‘take on an aura of morality in the eyes of those practicing them’ (UN, 1995, pp. 1-2).


Adopting the fuzzy approach to measuring violence has some advantages. In our view, it has two main advantages: less risk of arbitrariness and simplicity and economy of calculation. It is easier to understand these advantages if we compare the fuzzy severity scale we propose with existing alternatives.

Less risk of arbitrariness. Two types of scales are found in the literature, which we call ‘subjective’ and ‘objective’ for convenience. Objective scales attempt to classify different acts of VAW on the basis of observed, objective harm. In doing so, they face the challenge that aggregating different types of harm - physical, emotional, economic and so on - poses serious problems of commensurability. A popular way to overcome this problem is to focus on one component of harm - often physical harm - under the implicit or explicit assumption that the measured and unmeasured components are strictly correlated. The Conflict Tactic Scale (CTS; Straus, 1979) and its revised version, the CTS-2 (Straus et al., 1996), inspired several categorisations (WHO, 2013) and questionnaires in surveys on VAW (see e.g. Black et al., 2011). This scale expresses the severity of an assault as ‘the potential for producing an injury that requires medical treatment’ (Straus, 1990, p. 77) and is inspired by the US legal system as shown by the fact that its distinction between severe and minor violence ‘is roughly parallel to the legal distinction in the United States between “simple assault” and “aggravated assault’”, with ‘aggravated assault’ meaning an ‘attack that is likely to cause grave bodily harm’ (Straus, 2007, p. 191). In other words, the claim to objective measurement is justified by anchoring the assessment of harm to an actual, existing legal system. In a similar vein, and despite being critical of CTS,

Walby and Towers (2017, p. 28) proposed a definition of violence which ‘is anchored in law, which includes both action and harm’ because ‘[T]he framework that most consistently uses this concept of “action + harm” is that of criminal law’. Therefore, these endeavours to be objective do not appear to avoid a double source of arbitrariness. First, the correlation between measured and unmeasured harm need not be strong, as Marshall (1992) argued with regard to physical and psychological harm.4 Second, these measures of harm may be unduly influenced by specific historical and geographical legal contexts.

In our case, in contrast, the risk that the scale developed at a given time and for a given area will be applied years later on a different continent, as occurred with the CTS, is largely avoided by the qualification that the scale applies to population sub-groups that are sufficiently homogeneous in socioeconomic terms. Our scale also avoids arbitrariness due to the choice of one type of harm to proxy all others. This is because inverse frequency proxies overall comparative severity, hence providing a comprehensive notion of harm. The subjective severity scales found in the literature also attempt to capture an overall perception of harm when they ask respondents to rank different acts of violence based on their comparative assessment of severity (Hudson and McIntosh, 1981; Marshall, 1992; Rodenburg and Fantuzzo, 1993). However, subjective assessment has well-known shortcomings (Uher, 2018), whereas we proxy social assessment and use objective statistical evidence (inverse prevalence) for this purpose.

Economy and simplicity of construction. Last but not least, the construction of objective or subjective scales is usually data and research-time intensive, for example, because they are based on separate questionnaires or surveys: the CTS-2, the Index of Spouse Abuse (ISA; Hudson and McIntosh, 1981), the Severity of Wife Abuse Scale (SWAS; Marshall, 1992) and the revised version of the Sexual Experiences Survey (SES; Koss et al., 2007) are all cases in point. In contrast, the fuzzy scale only exploits prevalence records from one existing survey and relies on a well-defined algorithm for its construction.

Economy, simplicity and less arbitrariness are actual advantages in favour of the fuzzy scale, provided the latter yields ‘credible’ results. To assess credibility, we validated our scale using both internal and external procedures, and the results are reassuring (Bettio, Ticci and Betti, 2020a). For internal validation, we used the subjective evaluation section of the FRA questionnaire and compared the ranking of the various acts of intimate partner violence that emerged from the fuzzy scale with those inferred from a ‘subjective’ assessment. The comparison revealed a good degree of congruence. For external validation, we compared the ranking of the fuzzy scale with that of three of the most common alternatives in the domestic violence literature: the CTS-2, the SWAS and the ISA. Again, the results showed a low incidence of misalignment between our scale and the other three.

The ultimate advantage of a novel methodology is its ability to throw new light on old problems or to open new avenues of research. The fuzzy approach to poverty has significantly advanced understanding of poverty dynamics, for instance, by reducing over-estimation of transient poverty in longitudinal studies - i.e. the spurious fluctuations of at-risk people moving in and out of poverty in successive years (Cheli and Betti, 1999). Also, the fuzzy at-persistent-risk-of-poverty indicator proposed by Verma et al. (2017) - i.e. the fuzzy counterpart of the corresponding Laeken indicator used at the EU level - has brought considerable refinement to a widely used indicator.

In VAW research, the fuzzy approach was introduced very recently but has nevertheless generated some notable results. A topical question in the VAW literature is whether women’s empowerment reduces or prompts domestic violence. The empirical literature has given different answers depending on the country and empowerment indicator. In Europe, in particular, attention has been focused on the ‘Nordic paradox’ in which countries with the highest scores on the European Index of Gender Equality (EIGE), a comprehensive gender equality indicator, tend to report a higher prevalence of domestic violence across all types of violence (Gracia et al., 2019). Although several explanations have been offered for this finding (Davoine and Jarret, 2018; Nevala, 2017), Bettio, Tied and Betti (2020a, 2020b) show that the paradox vanishes when fuzzy indexes of domestic violence are used, instead of simple prevalence indicators. Specifically, the correlation between the EIGE and the fuzzy index of intimate partner violence (IPV) across the 28 EU countries turns negative and significant, with more gender-equal countries showing tendentially lower levels of fuzzy IPV. In other words, the paradox is resolved by using a more accurate measurement of violence afforded by fuzzy indexes. This raises expectations that additional methodological improvements to this approach may be analytically fruitful. The next section refines the final step of our fuzzy index construction, namely, aggregation across types of violence.

Refinements: Aggregating and Intersecting Different Forms of Violence

In step 5, the three different types of violence - physical, psychological and sexual - are aggregated into the overall fuzzy index of violence (FIV) using a simple arithmetic average, giving equal weight to each type. This option has some advantages but also an important drawback: it implicitly gives more importance to dimensions with a higher prevalence, e.g. psychological violence in the European context.

The first extension to the basic methodology (steps 1-5) that we propose in this section is the rescaling or standardisation of FIVs. This is obtained by dividing each (individual) index by the corresponding mean for the reference population. For example, the standardised FIV for France is the average ratio across French women of their respective FIV and the EU28 value.

The second and third extensions that we propose are, respectively, the ‘fuzzy intersection index’ and the ‘fuzzy union index’, both of which are also standardised. The reason for introducing these new indexes is that aggregation through averaging - for the FIV or its standardised version - does not shed light on where each type of violence stands in relation to the other types. In particular, it does not indicate the degree and the ways in which the different types of violence overlap. To illustrate this point, we briefly explore the FRA source, focusing, for simplicity, only on abused women with partners. Two salient findings emerge from Table A.14.1:

  • 1. Overlapping between types of violence is not the rule. In all the European countries, a small percentage of abused women with partners - i.e. women who relate at least one act of violence by an intimate partner (IPV) - report having experienced physical, sexual and psychological violence: their share ranges from 0.5% in the UK to 12.1% in Italy, with an average across Europe of less than 4%. A slightly higher frequency of women report having experienced two types of violence, with an average 10.3% of the abused women with partners in the EU28. However, the overwhelming majority of women abused by their partners report only one type of IPV: from 85% in Latvia to as much as 92.2% in Poland, with an EU average of 86%.
  • 2. Poly-victimisation exponentially increases violence.5 When overlapping occurs between types of violence, the fuzzy level of violence - encompassing frequency and severity - rises exponentially with respect to the number of types experienced, suggesting cumulative and interactive effects among the different types. This is shown in Table A.14.1 by the exponential rise in the standardised FIV between women who experienced only one type of violence and those who experienced two types, up to those who experienced all types.6

The implications of poly-victimisation for the measurement of violence can be explored using the (standardised) fuzzy intersection index. This index is especially useful for jointly assessing the prevalence of poly-victimisation and the level of violence suffered by women who are affected by it. The fuzzv union index might be used, instead, to infer the level of violence from the worst experiences, technically from the highest type-specific level assigned to each individual woman.

In more formal terms, and because all three types of violence have a common, ‘negative’ dimension, [1]

where цх цг;, fi3j are, respectively, the individual fuzzy measures of sexual, physical and psychological violence. In other words, gauges the overlapping of type-specific ‘violence’, i.e. the minimum level recorded across all the types of violence experienced by individual i. The standardised fuzzy intersection index takes a value of 0 for all women who did not experience all three types of violence.

• the most appropriate operator for the standardised fuzzy union index и . is the maximum value among the standardised indexes for the dif- ferent types of violence experienced (Betti and Verma, 2008):

Practical Applications

How do these alternative aggregation measures - the standardised fuzzy index, the standardised fuzzy intersection index and the standardised fuzzy union index - advance analyses of violence? Again, we use country comparisons based on the FRA data source for illustration, and again we focus on IPV during the 12 months preceding the survey for convenience. In our first exercise, we gauge the extent to which the new indexes produce significantly different IPV values and rankings for European countries.

Because it picks the maximum type-specific value, the fuzzy union IPV rescales levels of violence upwards compared to the average, fuzzy IPV. In contrast, the fuzzy intersection IPV rescales downwards because it picks the minimum type-specific value (Figure 14.1). However, the fuzzy union index alters the country ranking less than the intersection alternative compared to the average index.

This is shown by the Spearman and Pearson coefficients of correlation reported in Figure 14.1. The three indexes tend to be highly correlated across countries. However, the Pearson coefficient between the average and the intersection indexes is nine percentage points lower than that between the average and the union indexes. And the decline is even more noticeable for the Spearman coefficient (about 15 points), indicating a more pronounced change in the ranking when the intersection measure is used. This is because, unlike average IPV, intersectional IPV rises exponentially, moving from low- to high-value countries. For example, Italy’s IPV average score is 11 times higher than the UK’s score, but its IPV intersection score is 329 times higher. Put differently, the comparison between the ‘worst’ and the ‘best’ countries is much less favourable to the former if we use the intersection than if we use the average or the union alternatives, because overall levels of violence appear to rise exponentially along with the incidence of poly-victimisation.

Three fuzzy indexes for IPV compared across European countries. Source

Figure 14.1 Three fuzzy indexes for IPV compared across European countries. Source: FRA survey, 2012.

This latter finding, combined with the evidence in Table 14.1 documenting a limited (and variable) incidence of poly-victimisation across countries, questions a widespread tenet in the literature on violence: that either different types of violence (in particular IPV) generally occur simultaneously or that one leads to another in a self-reinforcing process. This narrative is often justified by the fact that all forms of interpersonal VAW appear to share the same risk factors, such as ‘growing up in a violent or broken home, substance abuse, social isolation, rigid gender roles, poverty and income inequality’ (WHO, 2002, p. 19). The emphasis on co-occurrence of different types of violence probably originates in the strong selectivity of existing studies, many of which are small scale and focus on the most seriously affected female victims. For example, Rodenburg and Fantuzzo (1993) found that sexual abuse was related to severe non-sexual physical abuse in marital relationships using data on a sample of women who were receiving services from a clinic or a battered women’s shelter. More recently, Basile and Hall (2011) found that, in a sample of 340 perpetrators arrested for physical assault of their female partner and court ordered to enrol in batterer intervention programmes, almost 97% of male participants reported

Table 14.1 Population share and rescaled fuzzy index of overall violence from current partner by level of poly-victimisation and by country, IPV in the previous 12 months



Women who experienced one type oflPV

Women who experienced two types of IPV

Women who experienced all three types of IPV

Share of abused women with a partner

Standardised, average fuzzy index for IPV

Share of abused women with a partner

Standardised, average fuzzy index for IPV

Share о/ abused women with a partner

: Standardised average fuzzy index for IPV





































































































































































































having perpetrated at least one act of physical, sexual and psychological violence. The sub-group of victims under investigation in these kinds of study often represents a strong case of intersectionality (UNWomen, 2019), i.e. women affected by multiple inequalities/oppressions (sexuality, gender identity, ethnicity, indigeneity, immigration status, disability). Guruge et al.

(2012), among others, found that it is common for immigrant and refugee women in Canada to experience various types of violence. Groups other than immigrants and refugees that are also often found to be at risk of cruel, repeated and multiple types of violence include displaced women, those with mental health problems or disabilities, some ethnic groups, and sex workers (Araujo et ah, 2019; Curry et ah, 2009; Deering et ah, 2014).

Aggregation by means of the fuzzy union operator considerably amplifies the levels of violence measured because it selects the worst types of violence reported. In terms of country ranking, however, the union index broadly confirms the ranking yielded by a standardised arithmetic average, with few exceptions at the opposite end of the spectrum, such as Italy and Slovenia. However, whereas the (standardised) average and union fuzzy indexes appear to be largely fungible when applied to FRA data and intercountry comparisons, these results need not be replicated in analyses other than inter-country comparisons.

The second exercise we performed verifies the extent to which the negative association, which we found elsewhere between a country’s gender equality and its fuzzy level of violence, continues to hold after the basic FIV above (unstandardised average across types) is replaced by the three new indicators. Tables 14.2a and 14.2b report the values and significance levels of the Pearson and the Spearman correlation coefficients between each European country gender equality score, on the one hand, and alternative fuzzy indexes of violence, on the other hand. Calculations are repeated using the gender stereotype index (GEI), instead of the EIGE. The latter is a composite indicator ranging from 1 (total inequality) to 100 (full equality) and measuring gender gaps and disparities in six core domains: work, money, knowledge, time, power and health. The GEI is based on the Special Eurobarometer 465 survey (TNS Opinion & Social Network, 2017), which conducted interviews across 28 EU countries on citizens’ opinions about gender equality and stereotypes. It is computed by averaging the scores assigned to the respondents’ evaluation of four statements investigating stereotypes. The EIGE and GEI are expected to move in opposite directions: the higher the EIGE indicator, the greater the degree of actual equality, whereas the perception of gender stereotypes is expected to be stronger in correspondence with higher levels of the GEI.

As shown in Table 14.2, the standardised fuzzy index of IPV confirms the negative association between the EIGE measure of gender equality and intimate partner violence found using the unstandardised version. The union index slightly strengthens the correlation, while the intersection index weakens it. The same applies, with opposite signs, to the GEI indicator of perceived stereotypes. In this exercise, therefore, alternative methods of aggregation across types of violence add little to what can be obtained with simple, unstandardised aggregation. This is unsurprising, given that we are

Table 14.2a Pearson correlation between fuzzy indexes of IPV and gender inequality/ stereotype perception

Simple average fuzzy index for 1PV

Standardised average fuzzy index for IPV

Standardised fuzzy IPV intersection

Standardised fuzzy IP V union



















Notes: p-values in italics.

Table 14.2b Spearman correlation between fuzzy indexes of IPV and gender inequality or stereotype indexes

Simple average fuzzy index for IPV

Standardised average fuzzy index for IPV

Standardised fuzzy IPV intersection

Standardised fuzzy IPV union



















Notes: p-values in italics.

using correlation analysis, and correlation is strong across all the alternative indexes examined.


In this chapter, we briefly illustrated, assessed and extended the fuzzy approach to VAW measurement that we recently introduced elsewhere. The parallel to a fuzzy analysis of poverty is useful for understanding the challenges and advantages of applying this approach to VAW, but only up to a point. The specific difficulty that a fuzzy measurement of violence faces is defining severity in terms of the overall harm caused by acts of violence and constructing a severity scale which overcomes problems of commensurability in the aggregation of different types of harm - mental, physical, economic and so on. We argued that understanding severity as relative and socially perceived harm caused by a given act of violence and proxying it with the inverse prevalence of this act in the reference population meets the challenge, but only with important qualifications. From a methodological perspective, the key qualifications are that the analysis must be confined to a fairly homogeneous population in socio-economic terms, and comparisons of severity across different types of abuse must be ruled out, i.e. the severity of a given physical abuse cannot be compared to that of a psychological abuse. We also argued that meeting this challenge has some notable advantages in addition to those normally offered by the fuzzy approach, such as multi-dimensionality and the objectivity of measurement. We specifically highlighted the economy of information and simplicity of computation involved in the construction of our severity fuzzy scale, together with lower risk of arbitrariness and cultural bias, compared to existing alternatives.

The ultimate advantage of a novel methodology is its ability to reveal new findings or shed new light on existing controversies, and the fuzzy approach to VAW has already revealed its potential by disproving the Nordic paradox and showing that the most gender-equal countries report a lower, not higher, level of IPV after the severity and frequency of violence are accounted for (see Bettio, Ticci and Betti, 2020a, 2020b compared to Gracia et al., 2019). This begs the question of whether refining the basic fuzzy methodology we introduced elsewhere can further advance analysis of VAW. The refinement considered here offers three ways of aggregating type-specific indexes of violence as an alternative to the arithmetic mean: the standardised mean, aggregation by intersection and aggregation by union (as in Betti and Verma, 2008). Standardisation simply ensures that aggregation is not unduly influenced by the more widespread type of violence, whereas aggregation by intersectionality looks at the overlap between different types of VAW and identifies it with the least harmful type of violence being experienced. Finally, aggregation by union looks at and counts only the worst type of VAW being experienced. We calculated the three alternative indexes for 28 European countries and confirmed that only aggregation by intersection alters the ranking of countries to a noticeable extent compared with aggregation by arithmetic mean. The intersection index therefore is suitable when the analysis targets sub-groups of women at risk of the worst combination of different types of violence. We also checked whether using the three newly defined indexes alters our previous finding of a negative and significant association between fuzzy measures of IPV and indicators of gender equality across European countries. We found that all the indexes are broadly fungible in the latter respect, resulting in limited differences in the strength of the correlation with gender equality indicators. However, fungibility need not be confirmed by analyses focusing on, say, interpersonal or group comparisons instead of country-level comparisons. Hence, this latter result warrants further investigation.


Table A.14.1 Fuzzy violence scale: Severity weights by act and type of violence based on FRA survey data

Violence type Acts (items of violence)





How often has your current partner...

Belittled or humiliated you in private?


Got angry if you speak with another man/woman?


Insisted on knowing where you are in a way that goes beyond general concern?


Belittled or humiliated you in front of other people?


Become suspicious that you are unfaithful?


Done things to scare or intimidate you on purpose, for example, by yelling and smashing things?


Tried to keep you from seeing your friends?


Prevented you from making decisions about family finances and from shopping independently?


Tried to restrict your contact with your family of birth or relatives?


Threatened to hurt you physically?


Forbidden you to work outside the home?


Threatened to take the children away from you?


Forbidden you to leave the house, taken away your car keys, or locked you up?


Threatened to hurt or kill someone else/someone you care about?


Hurt your children?


Threatened to hurt your children?




How often has something like this happened to you? Your current partner/Someone has ...

Pushed you or shoved you?


Slapped you?


Grabbed you or pulled your hair?


Thrown a hard object at you?


Beaten you with a fist or a hard object or kicked you?


Beaten your head against something?


Tried to suffocate you or strangle you?


Burned you?


Cut or stabbed you or shot at you?




Have you consented to sexual activity because you were afraid of what your current partner might do if you refused?/of what might happen if you refused?


Has your current partner/someone: Made you take part in any form of sexual activity when you did not want to or you were unable to refuse?


Attempted to force you into sexual intercourse by holding you down or hurting you in some way?


Forced you into sexual intercourse by holding you down or hurting you in some way?


Source: Authors’ computation using FRA survey microdata (entire sample for 28 European countries).

Notes: Psychological violence refers to abuse by current partner. Sexual and physical violence refer to episodes in the prior 12 months by the current partner or non-partners. Answer options for psychological violence are: never, sometimes, often, all the time, I don’t know, No answer, Refused. Answers options for sexual and physical violence.- never, once, 2-5 times, six or more times, I don’t know, No answer, Refused.

  • 236 F. Bettio, G. Betti and E. Tied Notes
  • 1 Individual, anonymised records from the FRA survey are currently handled by the UK DATA SERVICE and are available upon request.
  • 2 The International Labour Organisation (ILO), in the Violence and Harassment Convention No. 190, issued in June 2019 at its 108th session of the International Labour Conference, took a pragmatic approach in defining violence and harassment at work worldwide: ‘Definitions vary and lines are often blurred. For example, sexual “harassment” is often classified as a form of gender-based “violence”’. The Conference defined violence and harassment as ‘a range of unacceptable behaviours and practices’ that ‘aim at, result in, or are likely to result in physical, psychological, sexual or economic harm’ (answer to FAQ: -en/index.htm; accessed July 2020).
  • 3 Examples include female genital mutilation, early marriage and pregnancy, practices which prevent women from controlling their own fertility, traditional birth practices, and female infanticide.
  • 4 To cite a more recent example, in a case study on the Philippines, Antai et al. (2014) find that psychological abuse was a stronger predictor of suicide attempts than physical abuse.
  • 5 We borrow and adapt to our context the term ‘poly-victimization’ introduced by Finkelhor et al. (2007) to describe children’s exposure to multiple types of victimization.
  • 6 Violence by non-partners takes a similar pattern in Europe (evidence not reported here) though, in this case, poly-victimization is reduced to experiencing two types of violence, sexual and physical, because the FRA survey did not gather information on psychological abuse by non-partners.


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15 System Safety Analysis of

  • [1] the most appropriate operator for the standardised fuzzy intersectionindex ipimj) is the minimum value among the standardised indexes forthe different type of violence experienced (Betti and Verma, 2008):
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